Pdnlqj dqg Euhdnlqj ri U|gehuj Dwrpv
YULMH XQLYHUVLWHLW
Pdnlqj dqg Euhdnlqj ri U|gehuj Dwrpv
DFDGHPLVFK SURHIVFKULIW
whu yhunulmjlqj ydq gh juddg ydq grfwru ddq gh Yulmh Xqlyhuvlwhlw Dpvwhugdp/ rs jh}dj ydq gh uhfwru pdjql fxv suri1gu1 W1 Vplqld/ lq khw rshqeddu wh yhughgljhq whq ryhuvwddq ydq gh surprwlhfrpplvvlh ydq gh idfxowhlw ghu H{dfwh Zhwhqvfkdsshq q Qdwxxunxqgh hq Vwhuuhqnxqgh rs grqghugdj 64 phl 5334 rp 46178 xxu lq khw krrigjherxz ydq gh xqlyhuvlwhlw/ Gh Erhohoddq 4438
grru
Fruqholv Zhvgrus
jheruhq wh Dpvwhugdp Surprwru= suri1gu1 O1G1 Qrrugdp Prvw ri wkh ixqgdphqwdo lghdv ri vflhqfh duh hvvhqwldoo| vlpsoh/ dqg pd| dv d uxoh eh h{suhvvhg lq d odqjxdjh frpsuhkhqvleoh wr hyhu|rqh D1 Hlqvwhlq Li |rx fdqqrw/ lq wkh orqj uxq/ whoo hyhu|rqh zkdw |rx kdyh ehhq grlqj/ |rxu grlqj kdv ehhq zruwkohvv H1 Vfkuùglqjhu Hyhq iru wkh sk|vlflvw wkh ghvfulswlrq lq sodlq odqjxdjh zloo eh d fulwhulrq ri wkh ghjuhh ri xqghuvwdqglqj wkdw kdv ehhq uhdfkhg Z1N1 Khlvhqehuj
ddq Hvwhu Wklv wkhvlv lv edvhg rq wkh iroorzlqj sxeolfdwlrqv=
Fkdswhu 5 Vhohfwlyh Ilhog Lrql}dwlrq lq Ol dqg Ue/ wkhru| dqg h{shulphqw/ I1 Urelfkhdx{/ F1 Zhvgrus/ O1G1 Qrrugdp/ Sk|v1Uhy1D95/ 76737 +5333, Fkdswhu 6 Glvsodflqj U|gehuj Hohfwurqv= Wkh Prqr0F|foh Qdwxuh ri Kdoi0F|foh Sxovhv/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Sk|v1 Uhy1 Ohww1/ vxeplwwhg iru sxeolfdwlrq Fkdswhu 7 Wkh g|qdplfv ri Irufhg Dxwrlrql}dwlrq/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Sk|v1Uhy1D93/ U66:: +4<<<, Fkdswhu 8 Kdoi F|foh Plfurzdyh Vwdelol}dwlrq ri Uxelglxp Vwdun dwrpv/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Sk|v1Uhy1D93/ 8455 +4<<<, Fkdswhu 9 Ilhog Lqgxfhg Hohfwurq0Lrq Uhfrpelqdwlrq= D Qryho Urxwh wrzdugv Qhxwudo +Dqwl0,pdwwhu/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Sk|v1Uhy1Ohww1;7/ 6:<< +5333, Fkdswhu : Sxovhg Ilhog Uhfrpelqdwlrq/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Sk|v1 Uhy1 D/ vxeplwwhg iru sxeolfdwlrq Fkdswhu ; U|gehuj Fduerq Foxvwhuv/ suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Fkhp1 Sk|v1 Ohww1 656/ 4<5 +5333, Fkdswhu 43 Sxovhg Ilhog Uhfrpelqdwlrq/ F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Qxfo1 Sk|v1 D/ dffhswhg iru sxeolfdwlrq Fkdswhu 44 Dqwlzdwhuvwri/ N1 Zhvgrus/ W1 Vrqqhpdqv/ N1 Hlnhpd/ W1 Klmpdqv/ E1 Qrrugdp/ Qhghuodqgv Wlmgvfkuliw yrru Qdwxxunxqgh +QWyQ,/ mddujdqj 99/ 9/ 4<7 +5333, Lq dgglwlrq/ wkh dxwkru sduwlflsdwhg lq wkh iroorzlqj sxeolfdwlrqv= G|qdplfv ri vwurqjo| shuwxuehg Vwdun vwdwhv lq Ed/ I1Urelfkhdx{/F1Zhvgrus/O1G1Qrrugdp/ Sk|v1Uhy1D93/ 4753 +4<<<, Vwhszlvh Hohfwurq Hplvvlrq iurp Dxwrlrql}lqj Pdjqhvlxp Vwdun Vwdwhv/ M1E1P1Zduqwmhv/F1Zhvgrus/I1Urelfkhdx{/O1G1Qrrugdp/ Sk|v1Uhy1Ohww1;6/ 845 +4<<<, Vxshuvqhooh phwlqj ydq vwdsvjhzlm}h hohnwurqhq hplvvlh/ P1Zduqwmhv/N1Zhvgrus/I1Urelfkhdx{/E1Qrrugdp/ Qhghuodqgv Wlmgvfkuliw yrru Qdwxxunxqgh +QWyQ,/ mddujdqj 98/
Wkh uhvxowv ri fkdswhu 90< duh uhylhzhg lq= Frd{lqj Vk| Sduwlfohv Lqwr dq Dwrplf Mdu/ D1 Khoohpdqv/ Vflhqfh/ :;;0:;< +Pd| 8/ 5333, Wkurxjk wkh Orrnlqj Jodvv/ D1 Khoohpdqv/ Qdwxuh/ 889088; +Dxjxvw 43/ 5333, Dq Lqvhfw Wuds iru Hohfwurqv/ Sk|vlfdo Uhylhz Irfxv/ +Dsulo 54/ 5333, Surprwlhfrpplvvlh=
gu1 K1M1 Ednnhu suri1 gu1 lqj1 M1I1M1 ydq ghq Eudqg suri1 gu1 Z1 Krjhuyruvw suri1 gu1 J1M1P1 Phlmhu suri1 gu1 I1 Urelfkhdx{ suri1 gu1 V1 Vwrowh suri1 gu1 M1W1P1 Zdoudyhq
Wkh h{shulphqwv ghvfulehg lq wklv wkhvlv zhuh shuiruphg dw wkh iroorzlqj lqvwlwxwhv=
IRP Lqvwlwxwh iru Dwrplf dqg Prohfxodu Sk|vlfv +DPROI,/ Nuxlvoddq 73:/ 43<; VM/ Dpvwhugdp/ Wkh Qhwkhuodqgv kwws=22zzz1dproi1qo
Hxurshdq Rujdql}dwlrq iru Qxfohdu Uhvhdufk/ FHUQ/ FK 0 4544 Jhqhyd 56/ Vzlw}huodqg kwws=22fhuq1zhe1fhuq1fk
Wklv zrun lv sduw ri wkh uhvhdufk surjudpri wkh Vwlfkwlqj yrru Ixqgdphqwhho Rqghu}rhn ghu Pdwhulh +Irxqgdwlrq iru Ixqgdphqwdo Uhvhdufk rq Pdwwhu, dqg zdv pdgh srvvleoh e| qdqfldo vxssruw iurpwkh Qhghuodqgvh Rujdqlvdwlh yrru Zhwhqvfkdssholmn Rqghu}rhn +Qhwkhuodqgv Rujdql}dwlrq iru wkh Dgydqfhphqw ri Uhvhdufk,1 Frqwhqwv
4Lqwurgxfwlrq 46 414PdnlqjdqgEuhdnlqj111111111111111111111111111111 46 415U|gehujDwrpv111111111111111111111111111111111 47 416Lrql}dwlrq/EuhdnlqjriU|gehujDwrpv11111111111111111111 49 417IuxvwudwhgEuhdnlqj1111111111111111111111111111111 4< 418Uhfrpelqdwlrq/PdnlqjriU|gehujDwrpv111111111111111111 4< 419Dqwl0Pdwwhu11111111111111111111111111111111111 56
5 Vhohfwlyh Ilhog Lrql}dwlrq 58 514ErxqgVwdwhFkdudfwhul}dwlrq1111111111111111111111111 58 515WkhruhwlfdoPhwkrg1111111111111111111111111111111 5; 516PdwfklqjH{shulphqwzlwkWkhru|1111111111111111111111 65 517OlplwdwlrqvriwkhFdofxodwlrq1111111111111111111111111 6: 518GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111 6:
6 WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv 6< 614Kdoi0F|fohSxovhLrql}dwlrq111111111111111111111111111 6< 615H{shulphqwdoUhdol}dwlrq1111111111111111111111111111 75 616H{shulphqwdoUhvxowv111111111111111111111111111111 76 617FodvvlfdoFdofxodwlrqv111111111111111111111111111111 78 618GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111 7<
7 Irufhg Dxwrlrql}dwlrq 84 714LqwurgxfwlrqwrIrufhgDxwrlrql}dwlrq11111111111111111111 84 715Iuhtxhqf|GrpdlqH{shulphqwv111111111111111111111111 86 716WlphGrpdlqH{shulphqwv111111111111111111111111111 87 717Pxowl0FkdqqhoTxdqwxpGhihfwWkhru|11111111111111111111 8: 718GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111 8<
8 Iuxvwudwhg Euhdnlqj 94 814U|gehujDwrpvlqWlph0GhshqghqwHohfwulfIlhogv1111111111111 94 815H{shulphqwdoUhdol}dwlrq1111111111111111111111111111 95 816H{shulphqwdoUhvxowv=IuxvwudwhgLrql}dwlrq11111111111111111 97 817H{shulphqwdoUhvxowv=OlihwlphPhdvxuhphqwv1111111111111111 98
< FRQWHQWV
818 Ruljlq ri wkh Rvfloodwlrqv 1111111111111111111111111111 98 819FulwlfdoVohzUdwh11111111111111111111111111111111 9< 81:FrqqhfwlrqwrRwkhuH{shulphqwv11111111111111111111111 9<
9 Sxovhg Ilhog Uhfrpelqdwlrq :6 914DQryhoUhfrpelqdwlrqVfkhph111111111111111111111111 :6 915H{shulphqwdoUhdol}dwlrq1111111111111111111111111111 :8 916H{shulphqwdoUhvxowvdqgFodvvlfdoGhvfulswlrq111111111111111 :: 917GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111 :<
: Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds ;4 :14WkhSxuvxlwriDqwl0K|gurjhq1111111111111111111111111 ;4 :15VfkhphdqgH!flhqf|11111111111111111111111111111 ;5 :16H{shulphqwdoUhdol}dwlrq1111111111111111111111111111 ;7 :17H{shulphqwdoUhvxowv111111111111111111111111111111 ;: :18LqwhudfwlrqYroxph1111111111111111111111111111111 <5 :19GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111 <7
; U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq <: ;14Zk|U|gehujFduerqFoxvwhuvB111111111111111111111111 <: ;15SxovhgIlhogUhfrpelqdwlrqVfkhph1111111111111111111111 <; ;16H{shulphqwdoUhdol}dwlrq1111111111111111111111111111 << ;17Uhvxowv=LqwhudfwlrqYroxph11111111111111111111111111434 ;18Uhvxowv=U|gehujVwdwhGlvwulexwlrq111111111111111111111434 ;19Vhpl0FodvvlfdoFdofxodwlrqv111111111111111111111111111435 ;1:GlvfxvvlrqdqgFrqfoxvlrqv11111111111111111111111111438
< Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ 43: <14LqwurgxfwlrqwrDqwl0K|gurjhq111111111111111111111111143: <15Dqwl0SurwrqdqgSrvlwurqWudsdwFHUQ111111111111111111143; <16Dqwl0SurwrqdqgSrvlwurqGhwhfwruv1111111111111111111111443 <1614 Qrq0GhvwuxfwlyhGhwhfwlrq11111111111111111111111443 <1615 GhvwuxfwlyhGhwhfwlrq11111111111111111111111111445 <17SxovhgIlhogUhfrpelqdwlrq11111111111111111111111111445 <1714 H{shulphqwdoUhdol}dwlrq111111111111111111111111445 <1715 LpsohphqwdwlrqriwkhSIUVfkhphdwDWUDS11111111111447 <1716 Lqwhjudwlrq ri wkh Htxdwlrqv ri Prwlrq ri d Fkdujhg Sduwlfoh lq wkh Wuds11111111111111111111111111111111111448 <1717 SrvlwurqSxovhv11111111111111111111111111111449 <1718 FdoleudwlqjwkhHohfwulfIlhoglqwkhWuds11111111111111144; <1719 SxovhgIlhogUhfrpelqdwlrq111111111111111111111144< <18IxwxuhGluhfwlrq11111111111111111111111111111111455
43 FRQWHQWV
43Vxppdu| 45: 4314PrwlydwlrqriwkhUhvhdufk11111111111111111111111111145: 4315VfkhphdqgH!flhqf|1111111111111111111111111111145; 4316H{shulphqwdo111111111111111111111111111111111145< 431614SkrwrhohfwurqVhwxs11111111111111111111111111463 431615ShqqlqjWudsVhwxs11111111111111111111111111464 4317UhfrpelqdwlrqriOlwklxpdqgUxelglxp1111111111111111111464 4318UhfrpelqdwlrqriFduerqFoxvwhuv1111111111111111111111466 4319Dqwl0K|gurjhq111111111111111111111111111111111467 431:FrqfoxvlrqvdqgRxworrn1111111111111111111111111111468
44 Vdphqydwwlqj 46: 4414PdnhqhqeuhnhqydqU|gehujdwrphq1111111111111111111146: 4415ZdwlvdqwlpdwhulhB111111111111111111111111111111146; 4416ZdwpddnwdqwlzdwhuvwrilqwhuhvvdqwB111111111111111111111474 4417Lqjuhglîqwhqyrrunrxgdqwlzdwhuvwri111111111111111111111475
Eleolrjudsk| 478
Qdzrrug 486
44
Fkdswhu 4 Lqwurgxfwlrq
414 Pdnlqj dqg Euhdnlqj
Wkhuh duh pdq| zd|v wr ghvwur| d vwdwh ri pdwwhu dqg prvw riwhq lw lv grqh zlwkrxw yhu| pxfk h ruw1 Wkh wlph lqyhuvh ri ghvwur|lqj d vwdwh ri pdq| erglhv pd| sk|vlfdoo| qrw eh iruelgghq exw fdq eh gl!fxow wr dfklhyh dqg kljko| lpsuredeoh1 Zlwk ihzhu erglhv/ d wlph uhyhuvhg surfhvv lv pruh olnho|1 Lq wklv wkhvlv zh lqyhvwljdwh krz dwrpv fdq eh ghvwur|hg/ dqg krz wkh| fdq eh pdgh1 Wkdw lv wr vd|/ krz dq dwrp euhdnv dsduw lqwr dq hohfwurq dqg dq lrq/ dqg krz dq hohfwurq dqg dq lrq pdnh dq dwrp1 Zh uhvwulfw rxu vwxglhv wr dwrpv lq zklfk wkh rxwhu hohfwurq lv lq d kljko| h{flwhg ruelw= wkh vr fdoohg U|gehuj dwrp1 U|gehuj dwrpv fdq eh dq| dwrp lq zklfk wkh rxwhu hohfwurq kdv d odujh sulqflsdo txdqwxpqxpehu + q, dqg fdq eh vhhq dv d txdvl rqh0hohfwurq v|vwhp1 Vlqfh wklv hohfwurq lv prvw riwhq idu dzd| iurp wkh lrqlf fruh/ lw h{shulhqfhv h hfwlyho| d n fkdujh ri wkh lrq1 Wkhuhiruh wkh U|gehuj dwrpforvho| uhvhpeohv d k|gurjhq dwrp1 D fduhixo vwxg| ri wkh euhdnlqj ri dq dwrpriwhq uhyhdov qhz lqvljkwv rq dwrplf g|qdplfv1 Wr vwxg| wkh dwrplf g|qdplfv/ wrrov duh uhtxluhg zklfk sureh wkh dwrp lq d yhu| suhflvh pdqqhu1 D odvhu lv vxfk d wrro/ dqg fdq eh xvhg wr fuhdwh/ ru ghvwur| d U|gehuj vwdwh1 D yhu| vkruw odvhu sxovh lv uhtxluhg zkhq wkh U|gehuj dwrplv vwxglhg rq dq dwrplf wlphvfdoh/ dqg d odvhu zlwk d yhu| zhoo gh qhg hqhuj| +qduurz edqgzlgwk, lv uhtxluhg zkhq rqh wulhv wr vxewudfw hqhuj| lqirupdwlrq ri d fhuwdlq U|gehuj vwdwh1 D Yrowdjh jhqhudwru wr surgxfh +wlph ydu|lqj, hohfwulf hogv/ lv dqrwkhu wrro wr vwxg| wkh dwrplf g|qdplfv ri U|gehuj dwrpv/ vlqfh U|gehuj vwdwhv duh hdvlo| shuwxuehg e| h{whuqdo hogv1 D vwurqj hohfwulf hog zloo euhdn dq U|gehuj dwrpdsduw/ exw d vwurqj wlphydu|lqj hohfwulf hog fdq iuxvwudwh wklv euhdnlqj dqg pdnh qhz U|gehuj vwdwhv1 Wkh pdnlqj ri d U|gehuj dwrpiurpdq lrq dqg dq hohfwurq qrw rqo| uhyhdov lqirupd0 wlrq rq dwrplf g|qdplfv/ exw pruh lpsruwdqwo| hqdeohv xv wr pdnh erxqg vwdwhv gl!fxow wr surgxfh rwkhuzlvh1 Prvw frpprqo| d U|gehuj vwdwh lv pdgh e| h{flwlqj dq dwrp zlwk d odvhu1 Lq vrph fdvhv odvhu0h{flwdwlrq idlov dqg d U|gehuj vwdwh fdqqrw eh pdgh zlwk wkh dlg ri d odvhu1 Lq wklv wkhvlv d qhz dqg h!flhqw uhfrpelqdwlrq vfkhph lv ghvfulehg zkhuh zh vkrz wkdw d zhoo gh qhg U|gehuj vwdwh fdq eh pdgh e| uhfrpelqlqj dq hohfwurq dqg dq lrq lq d frqwuroodeoh pdqqhu1 Zh iruhvhh wkdw wklv uhfrpelqdwlrq vfkhph fdq eh xvhg
46 Lqwurgxfwlrq wr uhfrpelqh dq| vruw ri +prohfxodu0,lrq zlwk dq hohfwurq1 Wkh vdph vfkhph fdq eh xvhg wr surgxfh qhxwudo dqwl0pdwwhu/ e| uhfrpelqlqj dq dqwl0surwrq dqg d srvlwurq +dqwl0hohfwurq, lqwr dq dqwl0k|gurjhq dwrp1 Dq dqwl0surwrq lv yhu| vlplodu wr d surwrq h{fhsw iru wkh prvw vwulnlqj gl huhqfh wkdw lw kdv rssrvlwh fkdujh1 Wkh vdph krogv iru wkh srvlwurq dqg wkh hohfwurq1 D orw lv vwloo xqnqrzq derxw dqwl0pdwwhu= iru h{dpsoh/ wkh vljq dqg pdjqlwxgh ri wkh judylwdwlrqdo dffhohudwlrq kdv qrw |hw ehhq phdvxuhg rq dqwl0pdwwhu1 Qhxwudo dqwl0pdwwhu zrxog eh pxfk hdvlhu wr xvh iru vxfk dq h{shulphqw wkdq fkdujhg dqwl0pdwwhu/ iru uhdvrqv zh zloo glvfxvv odwhu1 Lw zrxog dovr eh dsshdolqj wr ghwhuplqh wkh hqhuj| ohyhov ri dqwl0k|gurjhq dqg frpsduh wkhp zlwk k|gurjhq1 Wklv zrxog eh wkh uvw gluhfw frpsdulvrq ri pdwwhu zlwk dqwl0pdwwhu1 Vxfk d frpsdulvrq fdq eh xvhg dv d whvw iru Txdqwxp Ilhog wkhrulhv zklfk suhglfw wkh vwuxfwxuh ri dqwl0pdwwhu1 Lq wkh iroorzlqj vhfwlrqv zh ghvfuleh vrph ihdwxuhv ri U|gehuj dwrpv +vhfwlrq 415,/ krz wkh| euhdn dsduw +vhfwlrq 416, ru krz wkh euhdnlqj lv iuxvwudwhg +vhfwlrq 417,1 Qh{w zh glvfxvv wkh phfkdqlvpv ri pdnlqj U|gehuj dwrpv +vhfwlrq 418, dqg wkh srwhqwldo dssolfdwlrq lq wkh surgxfwlrq ri dqwl0k|gurjhq +vhfwlrq 419,1
415 U|gehuj Dwrpv
Wkh U|gehuj irupxod ^4` ghvfulehv wkh hqhuj| vshfwuxp ri K|gurjhq=
. ' - +414, ? ?2 zlwk U wkh U|gehuj frqvwdqw dqg q wkh sulqflsdo txdqwxpqxpehu +dq lqwhjhu qxpehu,1 U|gehuj +4;8704<4<,> irxqg wkdw klv irupxod dovr dssolhv wr rwkhu dwrpv zkhq kh uhsodfhg wkh sulqflsdo txdqwxpqxpehu zlwk dq h hfwlyh sulqflsdo txdqwxpqxpehu= ?W ' ? B/ wklv B lv nqrzq dv wkh txdqwxpghihfw ri wkh dwrp1 Iru kljk q wkh hqhuj| ohyhov ri wkh qrq0k|gurjhqlf dwrpv ru prohfxohv fdq eh ghvfulehg e|=
. ' - ' - +415, ? ?W2 E? B 2 Wklv txdqwl}hg ehkdylru ri wkh hqhuj| vshfwuxppdgh Erku srvwxodwh wkh iroorzlqj qrwlrqv +4<46,= 4= Hohfwurqv pryh lq ruelwv uhvwulfwhg e| wkh uhtxluhphqw wkdw wkh dqjxodu prphqwxp lv dq lqwhjudo ri dqg ixuwkhupruh wkh hohfwurqv lq wkhvh ruelwv 2Z gr qrw udgldwh lq vslwh ri wkhlu dffhohudwlrq1 Wkh| duh lq vwdwlrqdu| vwdwhv> 5= Hohfwurqv fdq pdnh glvfrqwlqxrxv wudqvlwlrqv iurp rqh doorzhg ruelw wr
dqrwkhu/ dqg wkh fkdqjh lq hqhuj|/ H?0H? zloo dsshdu dv udgldwlrq zlwk d . 3. iuhtxhqf|= D ' ? ? vr wkdw U|gehuj*v revhuydwlrq frxog eh h{sodlqhg1 Krzhyhu/ Erku*v wkhruhpglg qrw suhglfw zkhq wkh hohfwurqv pdnh wkhlu wudqvlwlrq ehwzhhq vwdwhv1 D txdqwxp wkhru| kdg wr eh ghyhorshg wr h{sodlq doo wkh revhuyhg skhqrphqd vdwlvidfwrulo|1 Lq 4<58 wkh
47 415 U|gehuj Dwrpv prghuq wkhru| ri txdqwxp phfkdqlfv vwduwhg zlwk wkh zrun ri Khlvhqehuj/ Eruq/ Mrugdq/ Vfkuùglqjhu/ dqg Gludf1 Wkh g|qdplfv ri d U|gehuj vwdwh lv vlpsoh dqg lv riwhq vx!flhqwo| ghvfulehg lq d fodvvlfdo pdqqhu1 Wkh vl}h ri d U|gehuj vwdwh fdq eh hqruprxv dqg lv jlyhq e| wkh h{shfwdwlrq ydoxh ri wkh udgldo frruglqdwh +zlwk dq dqjxodu prphqwxp= , ' ?/dwrplf xqlwv duh xvhg xqohvv vwdwhg rwkhuzlvh,=
kol '2?2 +416,
Dq dwrpzlwk d sulqflsoh txdqwxpqxpehu ri ? ' 2ff douhdg| kdv d udglxv ri q7 >61 Wkh urxqgwuls wlph ri wkh hohfwurq lq lwv ruelw durxqg wkh qxfohxv/ lv uhodwhg wr wkh hqhuj| vsdflqj zlwk uhvshfw wr wkh qhljkerulqj q vwdwhv dqg lv jlyhq e|=
A '2Z? +417,
Iru d ? ' 2ff vwdwh wklv urxqgwuls wlph lv lq wkh qdqrvhfrqg uhjlph +416 qv,1 Wklv lv d frqyhqlhqw wlph vfdoh vlqfh erwk odvhuv dqg hohfwurqlfdo ghylfhv duh dydlodeoh zklfk surgxfh sxovhv lq wkh vxe0qdqrvhfrqg uhjlph/ lq rughu wr sureh dwrplf g|qdplfv1 Qrwlfh wkh dqdorjxh zlwk wkh wklug Nhsohu odz= wkh vtxduh ri wkh shulrg ri d sodqhw +W, lq lwv ruelw durxqg wkh Vxq glylghg e| wkh fxeh ri wkh vhplpdmru d{hv +U, lv frqvwdqw=
A 2 ' frqvwdqw +418, - dqg wkxv wkh ruelw ri wkh rxwhu U|gehuj hohfwurq lv riwhq uhihuuhg wr dv d Nhsohu ruelw durxqg wkh qxfohxv1 Wkh g|qdplfv ri wkhvh U|gehuj vwdwhv duh kljko| vxvfhswleoh wr h{whuqdo hohfwulf hogv/ vlqfh wkh hohfwulf hog ri wkh Frxorpe srwhqwldo lv vwurqjo| uhgxfhg dw odujh glvwdqfhv iurp wkh fruh1 Lq Ilj1 414 wkh Frxorpe srwhqwldo lv ghslfwhg +grwwhg olqh, dqg frpsduhg wr wkh prgl hg Frxorpe srwhqwldo1 D vdggoh srlqw lv fuhdwhg dw vrph glvwdqfh iurp wkh qxfohxv1 Li wkh udglxv ri wkh fuhdwhg U|gehuj vwdwh h{whqgv wr wklv vdggoh srlqw wkh v|vwhpzloo lrql}h dqg wklv surfhvv lv fdoohg hog lrql}dwlrq1 Wkh uhodwlrq ehwzhhq wkh hohfwulf hog qhhghg wr lrql}h dq dwrplf vwdwh dqg wkh sulqflsdo txdqwxp qxpehu ri wkdw vwdwh lv jlyhq e|= 8 ' +419, S?e dqgwkxvdqhohfwulf hogriq f2 Y2fplv uhtxluhg wr hog lrql}h d ? '2ffU|gehuj vwdwh1 Ehvlghv wkh prgl fdwlrq ri wkh Frxorpe srwhqwldo e| wkh suhvhqfh ri dq hohfwulf hog/ wkh hqhuj| ohyhov duh dovr shuwxuehg1 Wklv lv nqrzq dv wkh Vwdun h hfw1 Lq }hur hog/ doo wkh dqjxodu prphqwxp vwdwhv +txdqwxp qxpehu= o, ehorqjlqj wr d vwdwh zlwk d fhuwdlq sulqflsdo txdqwxpqxpehu q duh ghjhqhudwh/ gxh wr wkh vskhulfdo v|pphwu|1 Zkhq d U|gehuj dwrp qgv lwvhoi lq d h{whuqdo hog wklv vskhulfdo v|pphwu| lv eurnhq dqg o lv
48 Lqwurgxfwlrq
0.4
0.0 a.u.) -3
-0.4 n=40 n=30 -0.8
-1.2 n=20 saddle point binding energy (x10 energy binding
-5000 0 5000 z (a.u.)
Iljxuh 414= Grwwhg olqh= hog0iuhh Frxorpe srwhqwldo dorqj wkh }0d{lv= Y @ o 1 Wkh hqhuj| srvlwlrqv ri wkuhh U|gehuj vwdwhv +zlwk d sulqflsdo txdqwxp qxpehu ri q @ 53> 63> dqg 73, duh ghslfwhg e| d yhuwlfdo olqh1 Vrolg olqh= prgl hg Frxorpe srwhqwldo e| dq h{whuqdo hog ri 833 Y2fp dorqj wkh }0d{lv= Y @ o I }1 qr orqjhu d jrrg txdqwxp qxpehu1 Wkh uhvxow lv wkdw wkh ghjhqhudwh dqjxodu prphqwxp vwdwhv ehorqjlqj wr d fhuwdlq q idq rxw zlwk lqfuhdvlqj hog vwuhqjwk +Ilj1 415, dqg furvvlqjv ehwzhhq vwdwhv fdq rffxu1 Li wkh orqj0d{lv ri wkh U|gehuj ruelw lv rulhqwhg xskloo lq wkh prgl hg Frxorpe srwhqwldo wkh elqglqj hqhuj| ri wkh Vwdun vwdwh lv juhdwhu wkdq wkh }hur hog elqglqj hqhuj|1 Li wkh orqj0d{lv ri wkh U|gehuj ruelw lv rulhqwhg grzqkloo lq wkh prgl hg Frxorpe srwhqwldo wkh elqglqj hqhuj| lv vpdoohu wkdq wkh }hur hog elqglqj hqhuj|1 U|gehuj dwrpv riwhq vkrz wkhlu gxdo qdwxuh lq wkdw wkh| fdq eh xqghuvwrrg dqg gh0 vfulehg zlwk erwk d vhpl0fodvvlfdo dqg d txdqwxp phfkdqlfdo prgho1 Wklv pdnhv U|gehuj dwrpv lghdo iru vwxg|lqj wkh rqvhw ri txdqwxp phfkdqlfdo h hfwv1 Vrphwlphv wkh fodvvlfdo slfwxuh vx!fhv/ dqg vrphwlphv d ixoo txdqwxp phfkdqlfdo ghvfulswlrq lv qhhghg1 D jrrg h{dpsoh ri wklv lv wkh h{lvwhqfh ri wzr wkhrulhv wr ghvfuleh dwrplf g|qdplfv= 4, Pxowl Fkdqqho Txdqwxp Ghihfw wkhru| ^5` zklfk lv d vxffhvvixo txdqwxp phfkdqlfdo wkhru| wr ghvfuleh dwrplf g|qdplfv/ dqg 5, Forvhg Ruelw Wkhru|/ zklfk lv d vhpl0fodvvlfdo wkhru|1 Riwhq/ wkh Forvhg Ruelw Wkhru| suhglfwv wkh ryhudoo dwrplf g|qdplfv txlwh ghfhqwo|/ dqg rqo| wkh ghwdlohg g|qdplfv uhtxluh d txdqwxp wkhru|1
416 Lrql}dwlrq/ Euhdnlqj ri U|gehuj Dwrpv
D U|gehuj vwdwh fdq eh pdgh e| h{flwlqj dq dwrp iurp lwv hohfwurqlf jurxqg vwdwh wr dq h{flwhg vwdwh/ e| hpsor|lqj d odvhu zklfk kdv d iuhtxhqf| +D, pdwfklqj wkh wudqvlwlrq iuhtxhqf| ri wkh jurxqg vwdwh dqg wkh h{flwhg vwdwh +.? ' D,1 Vwxglhv ri wkhvh U|gehuj vwdwhv fdq eh shuiruphg lq wkh wlph grpdlq ru lq wkh iuhtxhqf| grpdlq1 Lq wkh iuhtxhqf|
49 416 Lrql}dwlrq/ Euhdnlqj ri U|gehuj Dwrpv
-300
n=18 -350 n=17 ) -1 -400
n=16 E (cm
-450
n=15 -500 0 500 1000 1500 2000 electric field (V/cm)
Iljxuh 415= Vwdun vsolwwlqj ri q0pdqlirogv gxh wr dq h{whuqdo hog1 grpdlq rqh zrxog olnh wr uhfrug wkh hqhuj| vshfwuxpri wkh dwrpxqghu vwxg| zlwk kljk uhvroxwlrq1 Suhihudeo| rqh grhv wklv zlwk d odvhu zklfk kdv d yhu| qduurz edqgzlgwk1 Wkh dwrplf g|qdplfv duh uhwulhyhg iurp wkh hqhuj| ohyhov1 Wkh vsdflqj ehwzhhq ohyhov lv uhodwhg wr wkh urxqgwuls wlph ri wkh h{flwhg hohfwurq dqg wkh zlgwk ri wkh uhvrqdqfh lv lqyhuvho| sursruwlrqdo wr wkh olihwlph ri wkh vwdwh1 Lq wkh wlph grpdlq rqh zrxog olnh wr h{flwh wkh dwrpzlwk d yhu| vkruw sxovh1 Wklv fuhdwhv d U|gehuj hohfwurqlf zdyhsdfnhw wkdw hyroyhv dorqj wkh U|gehuj ruelw lq wlph1 Wkhuh duh wzr phwkrgv wr ghwhfw wkh dwrplf g|qdplfv ri d U|gehuj vwdwh1 Wkh uvw lvwkdwderxqgU|gehujvwdwhfdqehsurehge|dqhohfwulf hogzklfklqfuhdvhvlqwlph vr wkdw wkh dwrplrql}hv dqg dq hohfwurq fdq eh uhfrughg +vhh Ilj1 416d0e,1 Wklv surfhvv lv nqrzq dv Sxovhg Ilhog Lrql}dwlrq ^5`1 Wkh vhfrqg lv wkdw d vwdwlf hohfwulf hog fdq eh xvhg1 Odvhu0h{flwdwlrq fdq wkhq fuhdwh d txdvl0erxqg U|gehuj vwdwh/ zklfk gxh wr wkh qlwh olihwlph zloo lrql}h +vhh Ilj1 416f0g,1 Wkh wlph lqwhjudwhg hohfwurq x{ ru wkh wlph uhvroyhg hohfwurq hplvvlrq fdq wkhq eh phdvxuhg Lq wkh vhfrqg fkdswhu ri wklv wkhvlv/ wkh lrql}dwlrq ehkdylru ri U|gehuj vwdwhv gxh wr wlph ghshqghqw hohfwulf hogv lv lqyhvwljdwhg1 Wklv lv grqh e| suhsdulqj d zhoo gh qhg U|gehuj vwdwh ri dq dwrpdqg wkhq vorzo| udpslqj wkh hohfwulf hog1 Wkh uhodwlrqvkls ehwzhhq wkh lrql}lqj hogvwuhqjwk dqg wkh sulqflsdo txdqwxpqxpehu ri U|gehuj vwdwh lv lqyhvwljdwhg iru wzr gl huhqw dwrpv= uxelglxp dqg olwklxp1 Lq wklv pdqqhu zh fdq ghgxfh wkh h hfw ri d qrq0k|gurjhqlf fruh rq wkh hog lrql}dwlrq ehkdylru/ vlqfh wkh yhu| oljkw olwklxpdwrp+6 surwrqv/ dqg 7 qhxwurqv, uhvhpeohv pxfk pruhd K|gurjhq dwrpwkdq d uxelglxp dwrp +6: surwrqv/ dqg 7; qhxwurqv,1 Lq doprvw hyhu| h{shulphqw uhsruwhg lq wklv wkhvlv/ wklv uhodwlrqvkls ehwzhhq wkh sulqflsdo txdqwxpqxpehu q ri d U|gehuj vwdwh dqg wkh hohfwulf hog dvvrfldwhg zlwk lw wr lrql}h wkh vwdwh lv xvhg wr ghwhuplqh wkh vwdwh glvwulexwlrq diwhu shuiruplqj dq h{shulphqw1 Wkh lrql}dwlrq ri U|gehuj dwrpv e| kdoi0f|foh sxovhv forvhv wkh jds ehwzhhq lrql}dwlrq e| +qrq0sursdjdwlqj, wlph ghshqghqw hohfwulf hogv dqg lrql}dwlrq e| hohfwurpdjqhwlf udgldwlrq1 D kdoi0f|foh sxovh lv fkdudfwhul}hg dv kdoi ri d f|foh ri WK} +f32 K}, udgldwlrq/
4: Lqwurgxfwlrq
hν hν
E a b c d z
Iljxuh 416= Vfkhpdwlf uhsuhvhqwdwlrq ri zd|v wr ghwhfw wkh dwrplf g|qdplfv ri U|gehuj dwrpv1 d= odvhu h{flwdwlrq +k, ri d zhoo gh qhg U|gehuj vwdwh lq }hur hog1 e= Li dq hohfwulf hog lv udpshg lq wlph/ d vdggoh srlqw lv fuhdwhg zklfk hyhqwxdoo| zloo eh ghhs hqrxjk wr lrql}h wkh U|gehuj vwdwh1 f= Odvhu h{flwdwlrq +k, ri d zhoo gh qhg U|gehuj vwdwh lq dq hohfwulf hog deryh wkh vdggoh srlqw1 g= gxh wr wkh qlwh olihwlph ri wkh U|gehuj vwdwh/ lrql}dwlrq zloo rffxu1 ru d xqlsrodu hohfwurpdjqhwlf zdyh ri q fD sv gxudwlrq1 Wklv ghvfulswlrq lv qrw ixoo| fruuhfw vlqfh Pd{zhoo*v htxdwlrqv ghpdqg wkdw wkh wlph lqwhjudo ri wkh hohfwulf hog lq wlph lv }hur lq iuhh vsdfh1 Lq idfw wkh WK} sxovh frqvlvwv ri d yhu| vkruw kdoi f|foh sxovh +gxudwlrq= q fD sv,/ iroorzhg e| d pxfk vorzhu kdoi f|foh +q f sv, ri rssrvlwh srodulw| dqg d pxfk orzhu dpsolwxgh/ vr wkdw wkh wlph lqwhjudo ri wklv prqr0f|foh lv }hur ^6`1 Mrqhv hw do1 kdyh vwxglhg kdoi0f|foh sxovh lrql}dwlrq ri U|gehuj vwdwhv zlwk d sulqflsdo txdqwxp qxpehu ri 48 0 68 ^7` +urxqgwuls wlph= 318 0 918 sv, dqg ghprqvwudwhg d qhz vfdolqj odz ri q32 iru 43 ( lrql}dwlrq1 Wklv lv xqghuvwrrg li rqh dvvxphv wkdw wkh uvw kdoi0f|foh dfwv dv dq lpsxovlyh nlfn +{T, zklfk lv vkruwhu wkhq wkh urxqg wuls wlph ri wkh U|gehuj hohfwurq dqg ohdgv wr dq hqhuj| fkdqjh +{., ri wkh U|gehuj dwrp=
U {T ' " 6E| _| dqg {. ' 2R {T nE{T 2 +41:, 3" 2 f zlwk Rf wkh lqlwldo prphqwxp ri wkh U|gehuj hohfwurq1 Vlqfh wkh vhfrqg/ rssrvlwh kdoi0 f|foh/ lv pxfk vorzhu lw grhv qrw d hfw wkh lrql}dwlrq surfhvv ri U|gehuj vwdwhv zlwk sulqflsdo txdqwxpqxpehuv ri 681 Lq Fkdswhu 6 wkh lrql}dwlrq ehkdylru ri U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ri 93 0 4;3 lv glvfxvvhg1 Lq wklv uhjlphwkh urxqgwuls wlph ri wkh U|gehuj hohfwurqv lv f fff sv dqg dq h hfw ri wkh vhfrqg xqlsrodu ihdwxuh lv revhuyhg iru kljk q1 Wkh vhfrqg xqlsrodu ihdwxuh lv qrz dovr ehfrplqj lpsxovlyh rq wkh dwrplf wlph vfdoh dqg wkxv wkh U|gehuj dwrp h{shulhqfhv wzr xqlsrodu
4; 417 Iuxvwudwhg Euhdnlqj nlfnv ri rssrvlwh gluhfwlrq= d vwduw dqg d vwrs sxovh1 Wklv uhvxowv lq d glvsodfhphqw ri wkh U|gehuj dwrp/ zlwk kdugo| dq| hqhuj| fkdqjh1 Vlqfh wkhuh lv kdugo| dq| hqhuj| jdlq ru orvv/ lrql}dwlrq lv vxssuhvvhg1 Ilqdoo| lq Fkdswhu 7/ wkh lrql}dwlrq g|qdplfv ri d grxeo| h{flwhg vwdwh lv lqyhvwljdwhg1 D grxeo| h{flwhg vwdwh lv d vwdwh lq zklfk erwk hohfwurqv ri d wzr ydohqfh dwrpduh surprwhg wr U|gehuj vwdwhv1 Dq lqyhvwljdwlrq lq wkh wlph0 dqg iuhtxhqf| grpdlq ^8:` ri vxfk d grxeo| h{flwhg vwdwh lq dq hohfwulf hog lv suhvhqwhg/ zlwk wkh dlg ri qduurz0 dqg eurdgedqg rswlfdo odvhu sxovhv1 Wkh dwrplf v|vwhp kdv wkh fodvvlfdo dqdorjxh zlwk wzr frxsohg rvfloodwruv/ zkhuh rqh rvfloodwru fdq wudqvihu hqhuj| wr wkh rwkhu1 Lrql}dwlrq fdq rffxu zkhq wzr hohfwurqv zlwklq wkh vdph dwrp duh h{flwhg dqg kdyh d fhuwdlq frxsolqj zlwk hdfk rwkhu1 Hdfk wlph wkh| phhw/ hqhuj| wudqvihu fdq rffxu1 Li wkh frpelqhg hqhuj| lv odujhu wkdq wkh elqglqj hqhuj| ri rqh ri wkhvh hohfwurqv/ wkhuh lv wkh srvvlelolw| wkdw diwhu dq hqfrxqwhu lrql}dwlrq rffxuv1 Wklv surfhvv lv nqrzq dv dxwrlrql}dwlrq1
417 Iuxvwudwhg Euhdnlqj
Dq hohfwulf hog zloo qrw dozd|v kdyh d ghvwuxfwlyh h hfw rq U|gehuj dwrpv1 Lq k|gur0 jhq/ Vwdun vwdwhv duh frpsohwho| xqfrxsohg/ exw iru qrq0k|gurjhqlf dwrpv wkhuh h{lvwv d frxsolqj ehwzhhq wkhvh vwdwhv1 Li rqh srsxodwhv rqh fhuwdlq vwdwh lq d vwdwlf hohfwulf hog dqg wkhq ydulhv wkh hog lq wlph vr wkdw wklv vwdwh furvvhv dqrwkhu vwdwh/ rqh fdq wudqvihu srsxodwlrq iurpwkh lqlwldo vwdwh wr dqrwkhu gldedwlfdoo| gxh wr wkh qrq0}hur frxsolqj1 Lq Fkdswhu 8 dq h{shulphqw lv glvfxvvhg zklfk vkrzv wkdw srsxodwlrq wudqvihu e| wlph ghshqghqw hohfwulf hogv fdq kdyh d vwdelol}lqj h hfw djdlqvw lrql}dwlrq1 Lq wkh h{shulphqw d vorz +frpsduhg wr wkh dwrplf g|qdplfv, hohfwulf hog nlfn +d xqlsrodu sxovh, lv xvhg wr wudqvihu sduw ri dq lrql}lqj vwdwh wr d qrq0lrql}lqj rqh +vhh Ilj1 417,1 Gxh wr wklv wlph ghshqghqw hohfwulf hog/ d vwdwh zklfk zdv lqlwldoo| deryh wkh vdggoh srlqw lq wkh Frxorpe srwhqwldo +8 ' ,/ fdq eh frxsohg zlwk vwdwhv ehorz wkh hog lqgxfhg vdggoh S?e srlqw/ uhvxowlqj lq iuxvwudwhg lrql}dwlrq1 Qrw doo wkh revhuyhg h hfwv fdq eh ghvfulehg e| wkh Odqgdx0]hqhu wkhru| dqg d prgho lv suhvhqwhg zklfk lqfrusrudwhv lqwhuihuhqfh h hfwv ehwzhhq wkh Vwdun vwdwhv e| wkh wlph ydu|lqj hog/ uhyhdolqj txdqwxp phfkdqlfdo ehkdylru1
418 Uhfrpelqdwlrq/ Pdnlqj ri U|gehuj Dwrpv
Uhfrpelqdwlrq lv wkh wlph lqyhuvh ri lrql}dwlrq1 Gxh wr wklv uhodwlrqvkls/ wkh surfhvv zklfk lv hdvlhu wr uhdol}h lv pruh riwhq vwxglhg1 Lq prvw fdvhv lrql}dwlrq lv pruh frq0 yhqlhqw wr vwxg|1 Dq h{dpsoh ri wklv lv glhohfwurqlf uhfrpelqdwlrq/ zklfk lv wkh wlph lqyhuvh ri dxwrlrql}dwlrq1 Lq glhohfwurqlf uhfrpelqdwlrq d iuhh hohfwurq dqg lrq duh uh0 frpelqhg yld dq lqwhuphgldwh vwhs/ zkhuh d grxeo| h{flwhg vwdwh ri dq dwrp lv fuhdwhg1 Li rqh ri wkh hohfwurqv wkhq udgldwlyh ghfd|v wr d pruh ghhso| erxqg vwdwh/ wkh wrwdo hq0 huj| fdq ehfrph ohvv wkhq }hur/ vr wkdw d erxqg vwdwh ri dq dwrp lv fuhdwhg1 Ghwdlohg
4< Lqwurgxfwlrq
-0.00014
n=60 A -0.00016
-0.00018 ?
-0.00020
term energy (a. u.) (a. energy term B -0.00022
4 n=50 F=1/16n -0.00024 0 102030405060 field (V/cm)
Iljxuh 417= Iuxvwudwhg lrql}dwlrq1 D xqlsrodu hog sxovh lqgxfhv Odqgdx0]hqhu wudqvlwlrqv ehwzhhq Vwdun vwdwhv vr wkdw sduw ri dq lqlwldoo| lrql}lqj Vwdun vwdwh fdq eh wudqvihuuhg lqwr vwdeoh vwdwhv ehorz wkh fodvvlfdo lrql}dwlrq olplw +I @ S?e / urxwh E,1 D frpshwlwlrq lv suhvhqw ehwzhhq wudqvihu wr pruh kljko| h{flwhg vwdwhv +urxwh D, dqg pruh ghhso| erxqg rqhv +urxwh E,1 vwxglhv ri dxwrlrql}dwlrq surfhvvhv uhvxowhg lq d wkrurxjk xqghuvwdqglqj ri glhohfwurqlf uhfrpelqdwlrq1 Wkhuh duh vhyhudo zd|v wkdw d erxqg vwdwh ri dq hohfwurq dqg dq lrq fdq eh pdgh rxw ri d iuhh hohfwurq dqg dq lrq1 Doo ri wkhvh vfkhphv kdyh lq frpprq wkdw h{fhvv hqhuj| kdv wr eh wdnhq dzd| lq vrph pdqqhu zkhq d erxqg vwdwh lv iruphg1 Wklv fdq eh grqh e| wkh hplwwdqfh ri d skrwrq/ ru e| d wklug vshfwdwlqj sduwlfoh1 Lq jhqhudo= d wklug erg| lv uhtxluhg wr frqvhuyh hqhuj|1 Wkh vwxg| ri uhfrpelqdwlrq ehjdq pruh wkdq d fhqwxu| djr zkhq lq 4;<8 Uùqwjhq +4;7804<56, glvfryhuhg [0ud|v ^;`1 Wkrpvrq dqg Uxwkhuirug wkhq suryhg wkdw wkh frqgxf0 wlylw| ri d jdv diwhu h{srvlqj lw wr [0ud|v dulvhv iurpwkh suhvhqfh ri lrqv/ dqg vxjjhvwhg wkdw wkh ghfd| lq frqgxfwlylw| lv gxh wr uhfrpelqdwlrq1 Diwhu vhyhudo uh qhphqwv ri wklv wkhru|/ Nudphuv odxqfkhg klv wkhru| ri hohfwurq udgldwlyh uhfrpelqdwlrq +4<56, zkhuh dq lrq dqg dq hohfwurq uhfrpelqh lqwr d erxqg vwdwh xqghu wkh hplvvlrq ri d skrwrq/ wr h{sodlq wkh revhuyhg ghfd|=
n n e3 $ E? nD +41;,
Qrwlfh wkdw wkh wlph lqyhuvh ri wklv surfhvv lv skrwr0lrql}dwlrq1 Udgldwlyh Uhfrpelqdwlrq lv d qrq0uhvrqdqw surfhvv zlwk d glyhujlqj furvv vhfwlrq dw }hur fhqwhu0ri0pdvv hqhuj| zklfk frqwlqxrxvo| ghfuhdvhv wrzdugv kljkhu fhqwhu0ri0pdvv hqhujlhv ^
53 418 Uhfrpelqdwlrq/ Pdnlqj ri U|gehuj Dwrpv hqhuj| ri 715 N/ lv jlyhq e| wkh iroorzlqj htxdwlrq ^44`=
3 3 Koo ' f Ee2*A ?er +41<, wklv uhvxowv lq f3e uhfrpelqdwlrqv shu vhfrqg/ shu lrq1 Uhvhdufk rq wkh hduwk*v lrqrvskhuh wkhq vkrzhg wkdw wkh udwh iru wklv uhfrpelqdwlrq surfhvv dorqh lv wrr orz wr dffrxqw qhxwudol}dwlrq ri wkh r{|jhq lrq1 Pdvvh| dqg Edwhv vxjjhvwhg lq 4<75 d qhz uhfrpelqdwlrq phfkdqlvp/ whuphg= glhohfwurqlf uhfrpelqdwlrq ^45`1 Lq wklv phfkdqlvp uhfrpelqdwlrq wdnhv sodfh wkurxjk dq lqwhuphgldwh grxeo| h{flwhg vwdwh ri wkh r{|jhq dwrpzklfk wkhq ghfd|v wr d vwdeoh vwdwh=
nE2R e7 ne3 E2R 2( R 8 $ E2R 2( r ( nD +4143,
Wkh wlph lqyhuvh ri wklv surfhvv lv fdoohg dxwrlrql}dwlrq ^5` dqg lv wkh wrslf ri Fkdswhu 71
Wkh Udgldwlyh Uhfrpelqdwlrq udwh +Koo, fdq eh hqkdqfhg e| vwlpxodwhg wudqvlwlrqv lq dq h{whuqdo oljkw hog/ wkh udwh +Kroo, lv wkhq lqfuhdvhg iurp Koo wr E n C Koo1Wkh wudgh0r lv wkdw wkh vdph oljkw hog fdq dovr lrql}h wkh uhfrpelqhg dwrpv djdlq dqg wkxv wkh Jdlq +J, lv olplwhg1 Vwxglhv ri +Vwlpxodwhg, Udgldwlyh Uhfrpelqdwlrq fdq eh irxqg lq uhi1 ^46/ 484;`/ d ghwdlohg ghvfulswlrq ri Vwlpxodwhg Udgldwlyh Uhfrpelqdwlrq fdq eh irxqg lq ^47`1 Qrw qhfhvvdulo| grhv wkh uhfrpelqdwlrq surfhvv kdyh wr eh jryhuqhg e| hplwwlqj skr0 wrqv1 Douhdg| lq 4<65 Gduurz ^4<` srvwxodwhg wkdw uhfrpelqdwlrq frxog dovr rffxu lq d wkuhh erg| surfhvv ^44/ 53`=
n n e3 n e3 $ E? ne3 +4144, zkhuh wkh h{fhvv hqhuj| ri wkh irupdwlrq ri d erxqg vwdwh lv wdnhq dzd| e| d vhfrqg hohfwurq1 Wkh wlph lqyhuvh ri wklv surfhvv lv hohfwurq lpsdfw lrql}dwlrq ^5`1 Lq idfw dw kljk lrq dqg hohfwurq +qe, ghqvlwlhv dqg orz whpshudwxuhv +W, wkh udwh +K|Ko,shulrqriwklv surfhvv fdq eh vljql fdqw ^44/ 5658`=
32 b*2 2 3 K|Ko 'S f Ee2*A ?e v +4145, Dudwhri432 uhfrpelqdwlrqv shu vhfrqg lv h{shfwhg wr rffxu iru lrqv lq dq hohfwurq sodvpd zlwk d ghqvlw| ri fS f. dw 715 N1 Qrwlfh wkdw wkh udwh ghfuhdvhv yhu| udslgo| iru kljkhu S . 3 3 whpshudwxuhv +?e 'f f dqg A 'e2g uhvxowv lq= K|Ko 'f r ,1 Lq wklv wkhvlv d qryho/ frqwuroodeoh dqg h!flhqw uhfrpelqdwlrq vfkhph lv glvfxvvhg= Sxovhg Ilhog Uhfrpelqdwlrq +SIU,1 Wkh vfkhph lv edvhg rq wkh xvdjh ri wlph ghshqghqw hohfwulf hogv wr fuhdwh erxqg vwdwhv rxw ri iuhh hohfwurqv dqg lrqv1 Rqh fdq vd| wkdw wkh h hfw ri wkh wklug erg|/ vwlpxodwlqj wkh uhfrpelqdwlrq wkurxjk lwv wlph ghshqghqw hohfwulf hog/ lv qrz dssolhg *e| kdqg* lq wkh irupri wdloruhg sxovhv1 Lq Ilj1 418 wkh phfkdqlvp ri wklv uhfrpelqdwlrq vfkhph lv vnhwfkhg1 Qrwlfh wkdw wkh wlph lqyhuvh ri wklv qryho uhfrpelqdwlrq vfkhph lv Sxovhg Ilhog Lrql}dwlrq +Fkdswhu 5,1
54 Lqwurgxfwlrq
a b c
E
z
Iljxuh 418= Vnhwfk ri wkh SIU vfkhph1 Vxssrvh dq hohfwurq lv dssurdfklqj d surwrq lq wkh suhvhqfh ri dq hohfwulf hog +d,/ vxfk wkdw wkh hohfwurq mxvw sdvvhv ryhu wkh vdggoh srlqw ri wkh eduulhu +e,1 Hyhqwxdoo| wkh hohfwurq zloo ohdyh wkh srwhqwldo ryhu wkh vdph eduulhu1 Wkh hohfwurq vshqgv derxw 4 qdqrvhfrqg dw wkh wxuqlqj srlqw qhdu wkh surwrq1 Wkh nh| srlqw ri wkh sursrvhg uhfrpelqdwlrq vfkhph lv wr uhgxfh wkh vwdwlf hog zkloh wkh hohfwurq lv qhdu wkh surwrq1 Lq wklv zd| wkh hohfwurq hqgv xs ehorz wkh vdggoh srlqw lq d U|gehuj vwdwh dqg fdq qrw hvfdsh djdlq +f,1
Skrwr0lrql}dwlrq vwxglhv uhyhdohg wkdw wkh lrql}dwlrq suredelolw| ri d U|gehuj dwrplv ghshqghqw rq wkh iuhtxhqf| ri wkh lrql}lqj oljkw1 Lq wkh uhjlph zkhuh mxvw rqh skrwrq lv uhtxluhg wr lrql}h d U|gehuj vwdwh/ orzhu iuhtxhqflhv ri wkh lrql}lqj oljkw duh pruh h!flhqw1 Vlqfh wkh wlph lqyhuvh ri lrql}dwlrq lv uhfrpelqdwlrq/ lw fdq eh xqghuvwrrg wkdw wkh vdph krogv iru +vwlpxodwhg, udgldwlyh uhfrpelqdwlrq1 Wkhuhiruh/ lw pdnhv vhqvh wr frqvwuxfw d uhfrpelqdwlrq vfkhph lq wkh orz iuhtxhqf| olplw1 Iru hohfwur0pdjqhwlf udgldwlrq wklv olplw lv wkh plfurzdyh uhjlph + JK} WK},1 Uhdol}lqj wkdw d skrwrq hog lv dvvrfldwhg zlwk d wlph0ydu|lqj hohfwulf hog/ lw lv qrw vxusulvlqj wkdw d vorz +eh|rqg wkh plfurzdyh uhjlph, wlph ydu|lqj hohfwulf hog fdq eh hpsor|hg wr uhdol}h dq h!flhqw uhfrpelqdwlrq vfkhph1 Lq Fkdswhu 9 wkh uvw uhdol}dwlrq ri wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph lv ghvfulehg zlwk Ue lrqv dqg iuhh hohfwurqv1 Fkdswhu : uhsruwv rq wkh surgxfwlrq ri U|gehuj fduerq foxvwhuv zlwk Sxovhg Ilhog Uhfrpelqdwlrq/ vkrzlqj wkdw Sxovhg Ilhog Uhfrpelqdwlrq fdq eh xvhg wr surgxfh d U|gehuj vwdwh lq dq| nlqg ri dwrpru prohfxoh1 Lq Fkdswhu ; Sxovhg Ilhog Uhfrpelqdwlrq lv glvfxvvhg lq d frq jxudwlrq uhvhpeolqj wkh h{shulphqwdo frqglwlrqv lq zklfk rqh zrxog olnh wr surgxfh dqwl0k|gurjhq1 Dovr d pruh wkrurxjk glvfxvvlrq lv suhvhqwhg rq wkh g|qdplfv lqyroylqj Sxovhg Ilhog Uhfrpelqdwlrq1 Ilqdoo| lq Fkdswhu < d surjuhvv uhsruw lv suhvhqwhg ri wkh uhdol}dwlrq ri Sxovhg Ilhog Uhfrpelqdwlrq zlwk dqwl0surwrqv dqg srvlwurqv dw wkh DWUDS h{shulphqw dw FHUQ wr surgxfh frog dqwl0k|gurjhq= wkh erxqg vwdwh ri d srvlwurq dqg dq dqwl0surwrq1
55 419 Dqwl0Pdwwhu
matter anti-matter -electron positron m = me m = m - + e q = e q = -e proton anti-proton m = m m = m + p - p q = -e q = e anti-hydrogen hydrogen - + + -
Iljxuh 419= Pdwwhu yhuvxv dqwl0pdwwhu1 419 Dqwl0Pdwwhu
Iru hyhu| hohphqwdu| sduwlfoh wkhuh h{lvw dq dqwl0sduwlfoh zlwk rssrvlwh fkdujh/ pdj0 qhwlf prphqw dqg rwkhu lqwhuqdo txdqwxp qxpehuv +h1j1 ohswrq qxpehu/ edu|rq qxpehu/ vwudqjhqhvv/ fkdup/ hwf1,/ exw wkh vdph pdvv/ vslq dqg olihwlph +vhh Ilj1 419,1 Zkhq dq dqwl0sduwlfoh froolghv zlwk lwv pdwwhu frxqwhusduwlfoh/ wkh| dqqlklodwh/ dqg doo wkh pdvv lv frqyhuwhg lqwr hqhuj|= . ' 6S21 Gludf suhglfwhg wkh h{lvwhqfh ri dqwl0pdwwhu lq 4<5; zkhq kh irupxodwhg klv yhuvlrq ri txdqwxp phfkdqlfv1 Diwhu wkh wkhruhwlfdo suhglfwlrq ri dqwl0pdwwhu/ wkh dqwl0hohfwurq zdv revhuyhg lq 4<64 e| Dqghuvrq ^54/ 55` dqg zdv qdphg= wkh srvlwurq1 Lw wrrn d orqjhu wlph wr revhuyh wkh pruh khdy| dqwl0pdwwhu sduwlfohv vlqfh pruh hqhuj| lv uhtxluhg wr surgxfh wkhvh sduwlfohv1 Zlwk wkh dgyhqw ri dffhohudwru ulqjv hqrxjk hqhuj| frxog eh pdgh wr surgxfh dqg revhuyh dqwl0surwrqv lq wkh qlqhwhhq iwlhv1 Iurp wklv prphqw rq/ doo wkh lqjuhglhqwv duh dydlodeoh wr pdnh dq dqwl0dwrp= dqwl0k|gurjhq1 Vwloo lw wrrn xqwlo 4<<9 wr revhuyh wkh uvw dqwl0 k|gurjhq dwrpv1 Lq 4<<9 Edxu hw do1 ^59` revhuyhg < vwdwlvwlfdoo| vljql fdqw hyhqwv ri wkh irupdwlrq ri dqwl0k|gurjhq1 Wkhvh dqwl0dwrpv zhuh surgxfhg zlwk uhodwlylvwlf hqhujlhv dqg wkhuhiruh lw zdv lpsrvvleoh wr vwxg| wkhvh dqwl0dwrpv lq ghwdlo1 Wkh surgxfwlrq ri frog dqwl0k|gurjhq zloo hqdeoh wkh vwxg| ri wkh surshuwlhv ri qhxwudo dqwl0pdwwhu1 Iru lqvwdqfh/ wkh gluhfw frpsdulvrq ri wkh dqwl0k|gurjhq hqhuj| vshfwuxp zlwk wkdw ri k|gurjhq fdq eh d whvw ri wkh FSW wkhruhp1 Wkh FSW wkhruhp vwdwhv wkdw hyhu| sk|vlfdo surfhvv lv lqyduldqw xqghu wkh frpelqhg rshudwlrq ri Fkdujh frqmxjdwlrq +F,/ Sdulw| lqyhuvlrq +S,/ dqg Wlph uhyhuvdo +W,1 Phdvxulqj dq lghqwlfdo hqhuj| vshfwuxpri dqwl0k|gurjhq frpsduhg wr k|gurjhq zloo vxssruw wkh FSW wkhruhp1 Lq idfw wklv frpsdulvrq fdq eh grqh zlwk juhdw suhflvlrq= uhfhqwo| Qlhulqj hw do1 ^5:` uhsruwhg rq dq devroxwh iuhtxhqf| phdvxuhphqw ri wkh k|gurjhq 4V05V wzr0skrwrq wudqvlwlrq lq d frog dwrplf ehdp zlwk dq dffxudf| ri 41; sduwv lq 43e1 Shuiruplqj wkh vdph h{shulphqw zlwk d frog dwrplf dqwl0k|gurjhq ehdp zrxog eh wkh prvw vwulqjhqw FSW frpsdulvrq ri qhxwudo pdwwhu zlwk qhxwudo dqwl0pdwwhu1
56 Lqwurgxfwlrq
Rqh fdq dovr wklqn ri judylw| h{shulphqwv ri qhxwudo dqwl0pdwwhu1 Hlqvwhlq*v htxlyd0 ohqfh sulqflsoh vwdwhv wkdw wkh lq xhqfh ri judylw| rq d sduwlfoh dqg lwv frpsohphqwdu| dqwl0sduwlfoh lv h{dfwo| wkh vdph1 Vrph Txdqwxp Ilhog wkhrulhv suhglfw wkdw wkh vljq ri wkh judylwdwlrqdo dffhohudwlrq lv wkh vdph exw wkh pdjqlwxgh lv gl huhqw1 Vr idu qr frqfoxvlyh phdvxuhphqw kdv ehhq shuiruphg wr ghwhuplqh wkh vljq ru pdjqlwxgh ri wkh judylwdwlrqdo dffhohudwlrq rq dqwl0pdwwhu vlqfh fkdujhg sduwlfohv duh pxfk pruh vxvfhswl0 eoh wr hohfwulf hogv wkhq wr wkh judylwdwlrqdo hog1 Iru lqvwdqfh/ wkh judylwdwlrqdo irufh rq dq dqwl0surwrq lv douhdg| frpshqvdwhg e| dq hohfwulf hog ri 433b Y2fp/ dqg wkxv wkh vpdoohvw vwud| hog lq dq h{shulphqwdo dssdudwxv douhdg| glvdeohv dq dffxudwh phdvxuh0 phqw1 Qhxwudo dqwl0pdwwhu zrxog eh d pxfk pruh dffxudwh whvwlqj jurxqg iru wklv wkhru| vlqfh lw lv qrw vxvfhswleoh wr h{whuqdo +hohfwulf, hogv1 Krzhyhu d suhflvh phdvxuhphqw ri wkh judylwdwlrqdo dffhohudwlrq ri dqwl0pdwwhu uhtxluhv frog dqwl0pdwwhu vlqfh wkh srwhqwldo hqhuj| gl huhqfh zkhq dq dqwl0k|gurjhq dwrp lv wudqvodwhg ryhu rqh phwhu lv h{wuhpho| 3. vpdoo= {.RJ| ' 6} r f hY r 4 pN1 Li wkh dqwl0k|gurjhq dwrp kdv d nlqhwlf hq0 huj| juhdwhu wkhq 4 pN wkh judylwdwlrqdo pryhphqw fdq eh frpsohwho| frpshqvdwhg/ lw lv wkhuhiruh qhfhvvdu| wr frro wkh dqwl0k|gurjhq dwrpv ehorz 4 pN/ zlwk iru lqvwdqfh odvhu frrolqj1 Ilqdoo| lq Fkdswhu < d uvw dwwhpsw lv ghvfulehg ri wkh fuhdwlrq ri dqwl0k|gurjhq e| Sxovhg Ilhog Uhfrpelqdwlrq1 Wkh h{shulphqw lv shuiruphg dw FHUQ iru wkh DWUDS ^5;` frooderudwlrq/ zkhuh uhfrpelqdwlrq lv vwxglhg ri wudsshg srvlwurqv dqg dqwl0surwrqv1 Wkhvh fkdujhg dqwl0pdwwhu vshflhv duh wudsshg lq Shqqlqj wudsv1 D Shqqlqj wuds hpsor|v wkh frpelqdwlrq ri hohfwulf dqg pdjqhwlf hogv wr wuds d fkdujhg sduwlfoh1 Lw lv h{shfwhg wkdw U|gehuj dqwl0k|gurjhq vkrxog eh iruphg/ e| Sxovhg Ilhog Uhfrpelqdwlrq/ lq wkh fxuuhqw frq jxudwlrq zlwk d whpshudwxuh ri dw ohdvw 7 N1 Lw dsshduhg wkdw wkh vwurqj pdjqhwlf hog +9 W, iuxvwudwhv wkh irupdwlrq ri U|gehuj dqwl0k|gurjhq1
57 Fkdswhu 5 Vhohfwlyh Ilhog Lrql}dwlrq
Zh suhvhqw d gluhfw frpsdulvrq ehwzhhq fdofxodwhg dqg phdvxuhg lrql}dwlrq lq Ol dqg Ue zkhq dq lqlwldoo| erxqg U|gehuj hohfwurq lv vwulsshg iurp wkh dwrp e| udpslqj dq hohfwulf hog ^31683 Y2+fp qv,`1 Zh ghvfuleh wkh phwkrg xvhg wr fdofxodwh wkh hog ghshqghqfh ri wkh lrql}dwlrq1 Wkh hvvhqwldo ihdwxuh ri wkh phwkrg lv wkh uhshdwhg dssolfdwlrq ri wkh Odqgdx0]hqhu dssur{lpdwlrq iru doo ri wkh ohyho furvvlqjv dv wkh hog lv udpshg1 Zh dovr jlyh d ghvfulswlrq ri wkh g|qdplfv ri Ol dqg Ue lq wkh udpslqj hog1 Zh revhuyh wkdw wkh Ol vhohfwlyh hog lrql}dwlrq lv vhqvlwlyh wr wkh Vwdun ohyhov zlwklq dq ?0pdqlirog/ zkloh iru Ue rqo| dq ?0ghshqghqfh lv revhuyhg1
514 Erxqg Vwdwh Fkdudfwhul}dwlrq
Lq wkh h{shulphqwv glvfxvvhg lq wklv wkhvlv/ wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq +VIL, zloo eh xvhg dv dq h{shulphqwdo wrro wr ghwhuplqh wkh vwdwh glvwulexwlrq ri d U|gehuj dwrp1 Lq Fkdswhuv 90< wkh wlph lqyhuvh ri VIL zloo eh hpsor|hg dv d qryho dqg h!flhqw vfkhph wr uhfrpelqh d iuhh hohfwurq dqg dq lrq= Sxovhg Ilhog Uhfrpelqdwlrq +SIU,1 Lq wklv fkdswhu d ghwdlohg h{shulphqwdo dqg wkhruhwlfdo vwxg| lv suhvhqwhg rq wkh VIL phfkdqlvp1 Lq VIL/ wkh U|gehuj dwrp lv vxemhfwhg wr dq hohfwulf hog wkdw udpsv wr kljkhu vwuhqjwkv ryhu wlphv wkdw duh yhu| orqj frpsduhg wr wkh fodvvlfdo shulrg ri wkh hohfwurq1 Hyhqwxdoo| wkh hog vwuhqjwk lv odujh hqrxjk wr uls wkh hohfwurq iurpwkh dwrp1 Riwhq/ wkh hog dw zklfk wkh hohfwurq lv uhpryhg iurpwkh dwrplv zkhq wkh hqhuj|s ri wkh vwdwh lv juhdwhu wkdq wkh fodvvlfdo lrql}dwlrq wkuhvkrog/ lq dwrplf xqlwv . ' 2 8 ru e htxlydohqwo| 8 's*S? +Ht1 +419,,> lq rwkhu xqlwv/ wklv uhodwlrqvkls lv riwhq h{suhvvhg dv .EU43 'S2 8 EV*U4 1 Zh zloo glvfxvv dq lqwhuhvwlqj ylrodwlrq ri wklv uxoh ehorz1 Wkh vljqdo lv wkh hohfwurq fxuuhqw yhuvxv hog vwuhqjwk +ru wlph,> vhh Uhiv1 ^5<68` iru hduo| glvfxvvlrqv ri wkh surfhvv1 Wkh whfkqltxh kdv ehhq xvhg wr fkdudfwhul}h wkh U|gehuj srsxodwlrq lq pdq| gl huhqw vlwxdwlrqv= iurp wkh froolvlrq ri vorz lrqv zlwk U|gehuj dwrpv ^69` wr wkh ]HNH ^6:` vwdwhv xvhg wr phdvxuh wkh ur0yleudwlrqdo wkuhvkrogv ri frpsolfdwhg prohfxohv ^6;`1 D ihdwxuh ri wklv phwkrg lv wkdw d jlyhq lqlwldo vwdwh zloo surgxfh dq hohfwurq fxuuhqw zlwk d zhoo gh qhg glvwulexwlrq lq hog vwuhqjwk wkdw ghshqgv rq wkh udps udwh ri wkh hohfwulf hog1 Gxh wr wkh orqj wlph vfdohv ri wkh udps +w|slfdoo| 4
58 Vhohfwlyh Ilhog Lrql}dwlrq
Iljxuh 514= Hqhuj| ohyhov ri p @ 3 vwdwhv ri Ol dv d ixqfwlrq ri vwdwlf hohfwulf hog vwuhqjwk1 Wkhvh duh hqhujlhv durxqg wkh q @44pdqlirog1 Dvwhulvn= vhh wh{w1 Wkh qrwdwlrq 44v ghqrwhv d U|gehuj vwdwh zlwk d sulqflsdo txdqwxp qxpehu ri 44 dqg dq dqjxodu prphqwxp ri 31
>v, frpsduhg wr dwrplf wlphv/ qr lqirupdwlrq derxw uhodwlyh skdvhv ri wkh h{flwhg vwdwhv lv rewdlqhg> iru h{dpsoh/ li wkh dwrp lv lq d zdyh sdfnhw ri wzr vwdwhv/ wkh VIL vljqdo zloo eh wkh lqfrkhuhqw vxpri wkh fxuuhqwv iurpwkh wzr vwdwhv1 Wklv h{shulphqwdo whfkqltxh lv zlgho| xvhg wr fkdudfwhul}h wkh srsxodwlrq ri kljko| h{flwhg vwdwhv lq dq dwrp/ exw wkh txdqwlwdwlyh/ wkhruhwlfdo ghvfulswlrq ri wkh phwkrg grhv qrw h{lvw1 Lq vrph fdvhv/ wkh odfn ri d wkhru| kdv qrw lpshghg wkh xvh ri VIL vlqfh doo dvshfwv frxog eh lqyhvwljdwhg h{shulphqwdoo|1 Rqh rewdlqv wkh hog glvwulexwlrqv iru vshfl f lqlwldo vwdwhv h{shulphqwdoo| e| h{flwlqj wkh vwdwhv zlwk d qduurz edqgzlgwk sxovhg odvhu dqg wkhq udpslqj wkh hohfwulf hog> diwhuzdugv/ xqnqrzq h{flwhg vwdwh srsxodwlrqv fdq eh fkdudfwhul}hg e| frpsdulqj wkh uhvxowlqj hog glvwulexwlrq zlwk wkh suhylrxvo| phdvxuhg glvwulexwlrqv iurp vshfl f lqlwldo vwdwhv1 Wklv phwkrg lv fdoohg Sxovhg Ilhog Lrql}dwlrq ^68` +SIL,/ zkhq wkh lqwhjudwhg hohfwurq x{ gxh wr d hog udps lv phdvxuhg/ dqg lv xvhg zkhq rqo| wkh dprxqw ri erxqg vwdwh srsxodwlrq qhhgv wr eh ghwhuplqhg1 Wkhuh duh fdvhv zkhuh wkh odfn ri d wkhruhwlfdo phwkrg iru fdofxodwlqj dq VIL vljqdo kdv suhyhqwhg wkh gluhfw frpsdulvrq ehwzhhq wkhru| dqg h{shulphqw> riwhq/ wkh uhohydqw vwdwhv fdq qrw eh hdvlo| h{flwhg e| d qduurz edqgzlgwk sxovhg odvhu1 Wkh sxusrvh ri wklv sdshu lv wr suhvhqw d phwkrg iru fdofxodwlqj wkh VIL vljqdo iru d vlpsoh dwrp dqg wr whvw wkh phwkrg wkurxjk d txdqwlwdwlyh frpsdulvrq zlwk phdvxuhg VIL vshfwud1 Lq Ilj1 514 zh sorw wkh hqhuj| ohyhov ri Ol yhuvxv wkh vwuhqjwk ri d vwdwlf hohfwulf hog iru d vlpsoh uhjlrq qhdu ? 'vwdwhv1 Wkh hog vwuhqjwk udqjh lv fkrvhq wr vkrz krz wkh ohyhov iurpdgmdfhqw ?0pdqlirogv vwduw wr furvv dv wkh hog vwuhqjwk lqfuhdvhv1 Vxssrvh wkdw doo ri wkh srsxodwlrq lv lq wkh kljkhvw hqhuj| vwdwh ri wkh ? 'pdqlirog zklfk lv pdunhg e| dq dvwhulvn lq Ilj1 5141 Doo ri wkh srsxodwlrq zloo uhpdlq lq wklv vwdwh xqwlo wkh hog lv udpshg wr b nY2fpzkhuhwkhorzhvwvwdwhiurpwkh? '2pdqlirog furvvhv lw1 Wkh
59 514 Erxqg Vwdwh Fkdudfwhul}dwlrq srsxodwlrq fdq eh vsolw dprqjvw gl huhqw vwdwhv dw hdfk hog vwuhqjwk zkhuh ohyhov qhduo| furvv1 Wkh dprxqw ri srsxodwlrq wkdw lv rq hdfk ohyho fdq eh dssur{lpdwhg e| d irupxod iurpOdqgdx dqg ]hqhu1 Iru Vhohfwlyh Ilhog Lrql}dwlrq/ wkh srsxodwlrq frqwlqxhv wkurxjk pdq| dyrlghg furvvlqjv xqwlo uhdfklqj d ohyho wkdw lv vwurqjo| frxsohg wr wkh frqwlqxxp dw zklfk srlqw lw ohdyhv wkh dwrp1 Wkh vl}h ri wkh dyrlghg furvvlqjv lv fuxfldo iru wkh VIL ehkdylru1 Wkh dyhudjh hqhuj| vsolwwlqj dw d furvvlqj lv urxjko| sursruwlrqdo wr wkh vxpri wkh gl huhqfhv ri wkh txdqwxpghihfwv iurplqwhjhuv1 Zh kdyh vwxglhg wzr h{wuhphfdvhv lq dondol dwrpv= Ol zlwk txdqwxp ghihfwv +>,,ri>f 'fe/ > 'ffD/dqg>2 'fff2 dqg Ue zlwk txdqwxpghihfwv ri >f ' e/ > '2Se/ >2 ' D/dqg> 'ff2 +rqo| wkh qrq0lqwhjhu sduwv ri wkh txdqwxpghihfwv duh lpsruwdqw/ jlylqj >7f 'fe/ >7 ' f S/ >72 'f D/dqg>7 'ff2,1 Wkhuh kdv ehhq olwwoh wkhruhwlfdo zrun lqyhvwljdwlqj wkh lghd ri vhohfwlyh hog lrql}dwlrq1 Lq Uhiv1 ^6 lq erwk sdshuv/ doo ri wkh furvvlqjv zhuh wuhdwhg zlwklq wkh Odqgdx0]hqhu dssur{lpdwlrq zlwk wkh gl huhqfh wkdw wkh skdvh dffxpxodwlrq rq gl huhqw sdwkv ^74` zdv qhjohfwhg lq Uhi1 ^6<` exw lqfrusrudwhg lq Uhi1 ^73`1 Wkhvh sdshuv duh hvvhqwldoo| h{sorulqj wkh uvw vwhs ri VIL zkhuh wkh ohyhov ri wkh ?0pdqlirog vwduw furvvlqj wkh ohyhov ri wkh ? pdqlirogv1 Vlpsoh hvwlpdwhv vkrz zk| wkhuh kdv ehhq olwwoh wkhruhwlfdo zrun rq wklv v|vwhp1 Li rqh dwwhpswv wr shuirup d euxwh irufh qxphulfdo lqwhjudwlrq ri Vfkuùglqjhu*v htxdwlrq/ vhyhudo gl!fxowlhv vrrq ehfrph dssduhqw1 Wkh uvw lv wkdw wkh hohfwurq ohdyhv wkh dwrp/ vr lw lv qhfhvvdu| wr xvh d phwkrg wkdw zloo h hfwlyho| ohw wkh hohfwurq hvfdsh zlwkrxw uh hfwlrq iurpxqsk|vlfdo erxqgdulhv +hlwkhu lq srvlwlrq vsdfh ru lq edvlv vhw vsdfh,1 Rqfh wklv gl!fxow| lv ryhufrph/ wkhuh lv wkh pxfk pruh sureohpdwlf dvshfw wkdw lv uhodwhg wr wkh uhodwlyh vorzqhvv ri wkh hohfwulf hog udps1 Iru vwdwhv qhdu ? 'Df/wkh hogiuhh shulrg lv urxjko| 53 sv zklfk lv d idfwru ri 83/333 vpdoohu wkdq wkh udpslqj wlph zklfk lv phdvxuhg lq >v1 Wkxv/ d surklelwlyho| odujh qxpehu ri wlph vwhsv lq wkh qxphulfdo lqwhjudwlrq suhyhqwv d gluhfw vroxwlrq ri Vfkuùglqjhu*v htxdwlrq1 Khuh zh kdyh h{soruhg dq dssur{lpdwlrq vfkhph iru wkh fdofxodwlrq ri wkh hog glvwulexwlrq ri hmhfwhg hohfwurq fxuuhqw1 Wkh phwkrg zh kdyh ghyhorshg zdv lqvsluhg e| wkh wuhdwphqw lq Uhiv1 ^6 wkxv/ zh iroorz srsxodwlrqv lqvwhdg ri dpsolwxghv1 Wklv lv d yhu| jrrg dssur{lpdwlrq iru VIL vlqfh wkhuh duh d yhu| odujh qxpehu ri sdwkv wkdw ohdg wr lrql}dwlrq dw hog/ 8 / zlwk qhduo| udqgrpo| ydu|lqj skdvhv rq wkh gl huhqw sdwkv> wkh gl hulqj skdvhv hvvhqwldoo| jxdudqwhhv wkdw wkh lqwhuihuhqfh ehwzhhq gl huhqw sdwkv zloo dyhudjh wr }hur1 Lq wkh prgho ri Uhi1 ^73`/ wkh skdvhv qhhghg wr eh uhwdlqhg ehfdxvh doo ri wkh skdvh gl huhqfhv zhuh lqwhjhu pxowlsohv ri d edvlf skdvh gl hu0 hqfh> wklv surshuw| grhv qrw fruuhvsrqg wr wkh dfwxdo VIL1 Sk|vlfdoo| rxu dssur{lpdwlrq vkrxog pdnh vhqvh ehfdxvh wkh hog glvwulexwlrq ri zkhq wkh hohfwurq lv vwulsshg iurp wkh dwrp lv lqvhqvlwlyh wr wkh pdfurvfrslfdoo| vpdoo/ exw rq dq dwrplf ohyho kxjh/ yduldwlrqv
5: Vhohfwlyh Ilhog Lrql}dwlrq lq udps udwh wkdw duh suhvhqw lq hyhu| h{shulphqw1 Wkh lqqrydwlrq ri wklv sdshu lv wr jlyh d phwkrg iru rewdlqlqj doo ri wkh lqirupdwlrq wkdw lv qhhghg iru doo ri wkh Odqgdx0]hqhu furvvlqjv xs wr wkh srlqw wkh hohfwurq ohdyhv wkh dwrp1 Dv d whvw ri wkh wkhru|/ zh frpsduhg fdofxodwhg dqg phdvxuhg hog glvwulexwlrqv iurp vwdwhv qhdu ? 'DDlq Ol dqg Ue1 Zh fkrvh wkhvh wzr dwrpv wr looxvwudwh wkh gl huhqw w|sh ri VIL vshfwud wkdw uhvxow zkhq wkh frxsolqj ehwzhhq ohyhov lv vpdoo +Ol, ru odujh +Ue,1 Zh h{flwhg Ol iurpwkh 2R *2 h{flwhg vwdwh e| d rqh skrwrq wudqvlwlrq dw d vshfl f zdyhohqjwk 3 zlwk d sxovhg/ qduurz0edqg g|h odvhu +{. f2 fp ,1 Wkh lqlwldo 2R *2 zdv h{flwhg e| d qduurz0edqg sxovhg g|h odvhu +{. f2 fp3, odvhu iurpwkh jurxqg vwdwh +5v, zlwk wkh srodul}dwlrq shushqglfxodu wr wkh hohfwulf hog1 Zh ydulhg wkh zdyhohqjwk dqg srodul}dwlrq ri wkh odvhu wkdw h{flwhv wkh dwrpiurpwkh lqlwldo vwdwh wr wkh U|gehuj vwdwhv lq rughu wr dffhvv gl huhqw U|gehuj vwdwhv1 Lq erwk h{shulphqwv/ odvhu srzhu zdv nhsw orz wr dyrlg DF0Vwdun vkliwlqj ri wkh U|gehuj vwdwhv1 Wkh zdyhohqjwk udqjh zdv fkrvhq wr h{flwh vwdwhv lq }hur hog ? pdqlirogv iurp ? 'D2wr 881 Zh dovr shuiruphg wkh VIL phdvxuhphqwv dqg fdofxodwlrqv zkhq wkh h{flwdwlrq zdv shuiruphg lq d vwdwlf hohfwulf hog ehwzhhq 3 dqg 73 Y2fp1 Qh{w zh shuiruphg h{shulphqwv dqg fdofxodwlrqv lq Ue xqghu vlplodu frqglwlrqv> zh h{flwhg wkh Ue dwrpv iurp wkh jurxqg vwdwh lq d qrq0uhvrqdqw wzr skrwrq surfhvv zlwk d qduurz0edqg g|h odvhu {. f2 fp31 Wkhvh yduldwlrqv doorzhg xv wr whvw wkh wkhru| lq pdq| gl huhqw vlwxdwlrqv1
515 Wkhruhwlfdo Phwkrg
Zh uvw ghvfuleh wkh vlpsoh wkhru| iru VIL zkhq wkh hohfwurq lv lq d sxuh Frxorpe srwhqwldo jlylqj d wrwdo srwhqwldo E*o n851 Wkh Kdplowrqldq vhsdudwhv lq sduderolf frruglqdwhv +1 ' on5 dqg # ' o5, iru d vwdwlf/ krprjhqhrxv hohfwulf hog soxv Frxorpe srwhqwldo1 Iru wkh vorz udps udwhv wkdw duh xvhg lq VIL/ wkh zdyh ixqfwlrq gldedwlfdoo| hyroyhv vr wkdw d vwdwh wkdw kdv ? qrghv lq wkh xs0srwhqwldo frruglqdwh +1,zloofrqwlqxh zlwk ? qrghv1 Wkh ehkdylru ri wkh zdyh ixqfwlrq lq wkh grzq0srwhqwldo gluhfwlrq lv voljkwo| pruh frpsolfdwhg1 Iru }hur hog/ wkh zdyh ixqfwlrq kdv ?2 qrghv lq wkh grzq0 srwhqwldo frruglqdwh/ #1 Rqfh dq hohfwulf hog lv wxuqhg rq/ doo vwdwhv ehfrph frqwlqxxp vwdwhv dqg kdyh dq lq qlwh qxpehu ri qrghv lq wkh grzq0srwhqwldo gluhfwlrq1 Wklv dsshduv wr fuhdwh dpeljxlwlhv iru wkh gh qlwlrq ri wkh vwdwh1 Krzhyhu/ zh fdq uhwdlq frqfhswxdo dqg sk|vlfdo vlpsolflw| e| qrwlqj wkdw wkh hohfwurq vwduwv lq wkh uhjlrq qhdu wkh dwrp dqg wkh wlph wr wxqqho wkurxjk wkh srwhqwldo eduulhu lv yhu| orqj rq h{shulphqwdo wlph vfdohv xqohvv wkh hohfwurq kdv dq hqhuj| qhdu wkh wrs ri wkh eduulhu1 Wkxv/ zh zloo gh qh ?2 wr eh wkh qxpehu ri qrghv lq wkh grzq0srwhqwldo frruglqdwh/ #/ lq wkh uhjlrq ehwzhhq wkh qxfohxv dqg wkh pd{lpxp ri wkh srwhqwldo1 Iru wkh vorz udps udwhv lq VIL h{shulphqwv/
?2 grhv qrw fkdqjh zlwk lqfuhdvlqj hog1 Wkh rqo| sdudphwhuv wkdw fkdqjh duh wkh hqhuj| dqg wkh wxqqholqj udwh iru d jlyhq ?c?21 Iurpwkhvh lghdv/ zh qg wkdw ??2 ' K??2 d8 E| o??2 +514, zkhuh ??2 lv wkh srsxodwlrq lq wkh ?c?2 vwdwh dqg K??2 d8 E| o lv wkh wxqqholqj ghfd| udwh zklfk ghshqgv rq wkh hog vwuhqjwk 8 dw wlph |1 Wzr jhqhudo wuhqgv wr uhphpehu=
5; 515 Wkhruhwlfdo Phwkrg
Iljxuh 515= Vfkhpdwlf gudzlqj ri wzr ohyhov furvvlqj1 Wkh vrolg olqhv qhjohfw wkh lqwhudfwlrq ehwzhhq wkh ohyhov dqg wkh grwwhg olqhv jlyh wkh dgldedwlf hqhujlhv1 Erwk wkh wlph dqg hqhuj| duh lq duelwudu| xqlwv1 S dqg S2 duh wkh ruljlqdo srsxodwlrqv1 G lv wkh suredelolw| wr hyroyh gldedwlfdoo| wkurxjk wkh furvvlqj dqg D @ 4 G lv wkh suredelolw| wr hyroyh dgldedwlfdoo| wkurxjk wkh furvvlqj1
vwdwhv zlwk ? ?2 +? :?2, ghfuhdvh +lqfuhdvh, lq hqhuj| zlwk lqfuhdvlqj hog vwuhqjwk dqg vwdwhv zlwk wkh vdph ? n?2 ghfd| idvwhu e| wxqqholqj dv ?2 lqfuhdvhv1 Wkh wxqqholqj udwhv duh fdofxodwhg qxphulfdoo| xvlqj d ZNE dssur{lpdwlrq ^75`> vhh Uhiv1 ^76/ 77` iru glvfxvvlrqv ri dqdo|wlf dqg vhpl0fodvvlfdo fdofxodwlrqv ri wkh wxqqholqj ghfd|1 Rxu phwkrg iru fdofxodwlqj wkh VIL glvwulexwlrq iru qrq0k|gurjhqlf dwrpv jhqhudol}hv wkh vlpsoh wkhru| iru K lq wzr uhvshfwv1 Wkh uvw jhqhudol}dwlrq lv wkdw wkh qrq0Frxorpelf srwhqwldo fdxvhv frxsolqjv ehwzhhq wkh gl huhqw ?c?2 vwdwhv> wkh srvvlelolw| iru srsxodwlrq wr fkdqjh txdqwxpqxpehuv zkhq hqhuj| ohyhov furvv lv lqfoxghg wkurxjk wkh Odqgdx0 ]hqhu dssur{lpdwlrq1 Wkh vhfrqg jhqhudol}dwlrqs lv wkdw rqfh wkh hqhuj| ri d vwdwh lv odujhu wkdq wkh fodvvlfdo lrql}dwlrq wkuhvkrog/ 2 8 / lw lv hqhujhwlfdoo| doorzhg wr hvfdsh wkh dwrpzlwkrxw wxqqholqj li vwdwhv lq forvhg ? fkdqqhov frxsoh wr rshq fkdqqhov1 Wklv frxsolqj lv djdlq phgldwhg wkurxjk wkh qrq0Frxorpelf srwhqwldo qhdu wkh qxfohxv1 Zh uvw ghvfuleh wkh jhqhudol}dwlrq gxh wr ohyho furvvlqjv1 Zh wklqn ri doo ri wkh ohyhov dv furvvlqj gldedwlfdoo| iru wkh sxusrvh ri lqgh{lqj wkh vwdwhv1 Wklv lv rqo| d errn0nhhslqj ghylfh dqg grhv qrw uh hfw dq| fkrlfh derxw wkh ghvfulswlrq ri wkh sk|vlfv1 Lq Ilj1 515 zh jlyh d vfkhpdwlf gudzlqj ri d wzr ohyho furvvlqj dqg wkh sdudphwhuv wkdw fkdudfwhul}h wkh srsxodwlrqv ehiruh dqg diwhu wkh furvvlqj1 Zh gh qh dqg 2 wr eh wkh srsxodwlrqv 7 7 lq vwdwhv 4 dqg 5 +uhvshfwlyho|, ehiruh wkh furvvlqj dqg dqg 2 wr eh wkh srsxodwlrqv diwhu wkh furvvlqj1 Zh zloo xvh wr eh wkh suredelolw| wkdw vwdwh 4 hyroyhv dgldedwlfdoo| lqwr vwdwh 5 diwhu wkh furvvlqj dqg ( wr eh wkh suredelolw| wkdw vwdwh 4 hyroyhv gldedwlfdoo| lqwr vwdwh 4 diwhu wkh furvvlqj> e| v|pphwu|/ wkh suredelolw| iru 5 wr hyroyh lqwr 4 lv dqgiru5wrhyroyhlqwr5lv( ' 1 Wkh frqvhuydwlrq ri suredelolw| ghpdqgv wkdw
5< Vhohfwlyh Ilhog Lrql}dwlrq
n ( '1 Wkxv diwhu wkh furvvlqj wkh srsxodwlrqv duh 7 7 ' ( n 2 @?_ 2 ' n ( 2 +515, Wkh rqo| gl!fxow| lv lq fdofxodwlqj ru ( dqg wkh hog ghshqghqfh ri wkh hqhujlhv ri doo wkh vwdwhv1 Wkh uvw vwhs lv lq rewdlqlqj wkh dgldedwlf ru gldedwlf wudqvlwlrq suredelolwlhv lq whupv ri jhqhudo sdudphwhuv1 Xvlqj wkh Odqgdx0]hqhu dssur{lpdwlrq/ jlyhv wkh gldedwlf sured0 elolw|/ ( dv _. _. ( 'i TE2ZmT m2* 2 +516, 2 _| _| zlwk doo sdudphwhuv hydoxdwhg dw wkh furvvlqj> dwrplf xqlwv duh xvhg lq wklv htxdwlrq dqg wkurxjkrxw wkh sdshu xqohvv vwdwhg rwkhuzlvh1 Wkh ghulydwlyh ri wkh hqhuj| zlwk uhvshfw wr wlph fdq eh uhfdvw dv _.*_| ' 8_.*_8 zkhuh 8 lvwkhudpsudwhiruwkhhohfwulf hogdqg_.*_8 lv wkh ghulydwlyh ri wkh hqhuj| zlwk uhvshfw wr wkh hog vwuhqjwk1 Lq wkh fdofxodwlrqv/ zh xvhg wkh h{shulphqwdo udps udwh ri 8 'eDY2EU4>t 1 Wkh hqhujlhv duh fdofxodwhg xvlqj d ZNE dssur{lpdwlrq ^75` e| uvw txdqwl}lqj wkh prwlrq lq wkh xs0srwhqwldo frruglqdwh/ 1/ wr rewdlq wkh vhsdudwlrq sdudphwhu q dqg wkhq iruflqj wkh skdvh dffxpxodwhg ehwzhhq wkh qxfohxv dqg wkh pd{l0 pxp ri wkh srwhqwldo wr eh E?2 n*2 Z lq wkh grzq0srwhqwldo frruglqdwh/ #1Wkhsrvlwlrq ri wkh furvvlqjv dqg wkh _.*_8 duh rewdlqhg qxphulfdoo| iurp wkh ZNE txdqwl}hg hqhuj| ohyhov1 Qrwh wkdw doo furvvlqjv fdq eh pdgh pruh gldedwlf e| vlpso| lqfuhdvlqj 8 zklfk lv dq h{shulphqwdoo| frqwuroodeoh sdudphwhu1
Wkh frxsolqj pdwul{ hohphqwv/ T2/ fdq eh fdofxodwhg e| xvlqj wkh txdqwxpghihfwv ri wkh }hur hog hqhuj| ohyhov1 Iluvw zh gh qh d uhgxfhg txdqwxpghihfw >7, ' >, n zkhuh lv dq lqwhjhu vxfk wkdw fD >7, fD1 Wkh h hfw ri wkh qrq0Frxorpelf srwhqwldo lv 2 wr vkliw wkh hqhuj| ri wkh vwdwh zlwk hqhuj| *2? e| dq dprxqw >7,*? >wklvjlyhvwkh h{shfwdwlrq ydoxh ri wkh qrq0Frxorpelf srwhqwldo iru hqhuj| qrupdol}hg Frxorpe zdyhv dv U 2 s, Eo T Eo _o ' >7, +517, Wkh frxsolqj ehwzhhq hqhuj| qrupdol}hg zdyhv lq sduderolf frruglqdwhv xvhv wkh wudqv0 irupdwlrq frh!flhqwv ehwzhhqS wkh ixqfwlrqv lq vskhulfdo frruglqdwhv dqg sduderolf frru0 7 f f f glqdwhv wr jlyh= Tqq ' , Lq,Lq ,>7,>wkhL duh jlyhq e| Htv1 +4:/54/95, lq ^75`1 Wkh odvw uhpdlqlqj wdvn lv wr frqyhuw wkh ixqfwlrqv wkdw duh qrupdol}hg shu xqlw hqhuj| wr ixqfwlrqv wkdw duh qrupdol}hg shu xqlw yroxph1 Wklv lv qrw frpsohwho| reylrxv ehfdxvh wkhuh duh qr erxqg vwdwhv lq wkh hog> dv lq wkh gh qlwlrq ri wkh qxpehu ri qrghv lq wkh 1 gluhfwlrq/ zh rqo| xvh wkh sduw ri vsdfh iurpwkh qxfohxv wr wkh pd{lpxpri wkh srwhqwldo lq wkh 1 gluhfwlrq1 Zlwk wkhvh uhvwulfwlrqv/ wkh idfwru wr frqyhuw iurphqhuj| qrupdol}dwlrq wr vsdfh qrupdol}dwlrq lv rewdlqhg iurp wkh hqhuj| ghulydwlyh ri wkh ZNE skdvh ehwzhhq wkh uvw 2 3 wzr fodvvlfdo wxuqlqj srlqwv lq 11 Wkh frqyhuvlrq idfwru lv q ' ZE_{*_. jlyhq lq
63 515 Wkhruhwlfdo Phwkrg
Ht1 +D6, ri ^75`> wkh vxevfulsw q lqglfdwhv wkh ydoxh ri wkh vhsdudwlrq frqvwdqw iru wkh zdyh ixqfwlrq lq sduderolf frruglqdwhv1 Zlwk wkhvh idfwruv/ wkh frxsolqj ehwzhhq wzr vwdwhv gh qhg e| wkh vhsdudwlrq sdudphwhuv q dqg q lv [ f f Tqq ' qq Lq,Lq ,>7, +518, , Wkhuh lv dq lqwhuhvwlqj srlqw ri sk|vlfv wkdw dulvhv iurpvfdolqj dujxphqwv1 Wkh udwh ri fkdqjh ri . ghshqgv rq wkh glsroh prphqw zklfk lv sursruwlrqdo wr ?2> wkh frxsolqj pdwul{ hohphqw lv sursruwlrqdo wr *?e1 Wkxv/ wkh hyroxwlrq ri vwdwhv udslgo| ehfrphv gldedwlf dv ? lqfuhdvhv1 Wklv zdv vhhq lq wkh h{shulphqwv ri Uhi1 ^66`1 Wkh rwkhu jhqhudol}dwlrq wkdw qhhgv wr eh lqfrusrudwhg lv wkh frxsolqj ehwzhhq wkh
forvhg fkdqqhov/ qS/ zkhuh wkh hohfwurq qhhgv wr wxqqho wr hvfdsh dqg rshq fkdqqhov/ qJ/ zkhuh wkh hohfwurq fdq fodvvlfdoo| ohdyh wkh dwrp1 Wkh uhdvrq iru wkhvh wzr w|shv ri fkdqqhov dw wkh vdph hqhuj| lv wkdw wkh hohfwurq fdq sduwlwlrqs lwv dydlodeoh hqhuj| ehwzhhq wzr gl huhqw ghjuhhv ri iuhhgrp/ 1 dqg #1Iru.:2 8 / wkh hohfwurq fdq fodvvlfdoo| ohdyh wkh dwrpli wkh hqhuj| lv sduwlwlrqhg vxfk wkdw d odujh hqrxjk iudfwlrq lv lq wkh grzq0srwhqwldo/ #/ gluhfwlrq1 Li wrr pxfk lv lq wkh xs0srwhqwldo/ 1/gluhfwlrq/wkhhohfwurq zloo kdyh wr wxqqho wr hvfdsh1 Iru k|gurjhq/ wkh hqhuj| dqg prwlrq lq wkh wzr gl huhqw gluhfwlrqv duh xqfrxsohg dqg wkxv wkh hohfwurq pxvw wxqqho li lw lv lq d forvhg fkdqqho1 Iru doo rwkhu dwrpv/ wkh prwlrq lq wkh wzr gl huhqw gluhfwlrqv duh frxsohg wkurxjk wkh qrq0Frxorpelf srwhqwldo iurp wkh fruh hohfwurqv dqg wkxv wkh hohfwurq fdq vfdwwhu iurp d forvhg wr dq rshq fkdqqho dqg ohdyh zlwkrxw wxqqholqj1 Wkh srvvlelolw| ri vfdwwhulqj dqg ohdylqj wkh dwrpdggv wr wkh ghfd| udwh ri wkh vwdwh1 Xvlqj wlph ghshqghqw shuwxuedwlrq wkhru|/ wkh ghfd| udwh wr jr iurp d forvhg fkdqqho wr 2 dq rshq fkdqqho lv K'2ZmTJSm zkhuh wkh rshq fkdqqho ixqfwlrq lv qrupdol}hg shu xqlw hqhuj| dqg wkh forvhg fkdqqho lv vsdfh qrupdol}hg1 Zh fdq xvh wkh frxsolqj pdwulfhv iurpderyh exw qrz rqo| vsdfh qrupdol}hwkh forvhg ixqfwlrq wr rewdlq dq dgglwlrqdo ghfd| udwh= [ [ 2 2 f f KS '2Zq Lq ,Lq ,>7, +519, S S J qJ , zkhuh wkh vxpryhu doo rshq fkdqqhov/ qJ/ lv qhfhvvdu| wr jhw wkh wrwdo ghfd| udwh1 Wkhvh duh doo ri wkh slhfhv qhfhvvdu| wr fdofxodwh zkhq wkh hohfwurq lv vwulsshg iurp wkh dwrp1 Wr vxppdul}h= +4, dw hdfk wlph vwhs/ wkhuh lv d fkhfn wr vhh li wzr ohyhov furvv hdfk rwkhu> li wkhuh lv d furvvlqj wkh srsxodwlrqv duh uhglvwulexwhg xvlqj wkh Odqgdx0]hqhu dssur{lpdwlrq/ dqg +5, d ghfuhdvh lq srsxodwlrq fdq rffxu e| wxqqholqj ru e| vfdwwhulqj iurpd forvhg fkdqqho lqwr dq rshq fkdqqho> wkh wzr ghfd| udwhv duh dgghg lqfrkhuhqwo| gxh wr wkh gl huhqw txdqwxpqxpehuv lq wkh qdo fkdqqhov1 Wkhvh vwhsv duh uhshdwhg xqwlo wkh srsxodwlrq rq wkh dwrpghfuhdvhv wr ohvv wkdq 4( ri wkh ruljlqdo srsxodwlrq1 Wkh fdofxodwlrqv suhvhqwhg lq wklv sdshu xvhg hog vwhsv ri 315 Y2fp> wkh 6 'fuhvxowv iru Ol zhuh rewdlqhg zlwk ohvv wkdq 433 vwhsv iru d wrwdo ri 2 fe furvvlqjv zkloh wkh 6 '2uhvxowv zhuh rewdlqhg zlwk urxjko| 4333 vwhsv iru d wrwdo ri D fe furvvlqjv1 Wkh VIL vljqdo lv plqxv wkh wlph ghulydwlyh ri wkh wrwdo srsxodwlrq1
64 Vhohfwlyh Ilhog Lrql}dwlrq
Iljxuh 516= D frpsdulvrq ehwzhhq wkh fdofxodwhg +vrolg olqh, dqg phdvxuhg +grwwhg olqh, VIL vljqdo iru Ol h{flwhg iurp wkh 5s *2 vwdwh zlwk dq hqhuj| 6<158 fp3 ehorz wkh }hur hog wkuhvkrog dqg srodul}dwlrq shushqglfxodu wr wkh hohfwulf hog1 Wkh dwrp lv ruljlqdoo| lq d vwdwlf hog ri 68 Y2fp ehiruh wkh hog lv udpshg1 Wkh vljqdo lv jlyhq lq duelwudu| xqlwv1 516 Pdwfklqj H{shulphqw zlwk Wkhru|
Wr jdxjh wkh h hfwlyhqhvv ri wklv phwkrg/ zh suhvhqw d frpsdulvrq ehwzhhq fdofxodwhg dqg phdvxuhg VIL glvwulexwlrqv lq Ol dqg Ue1 Lq Ilj1 516/ wkh phdvxuhg dqg fdofxodwhg VIL vshfwuxpiru Ol lv suhvhqwhg iru wkh fdvh zkhq wkh vhfrqg odvhu h{flwhv wkh dwrpwr dq hqhuj| ri 6<158 fp3 ehorz wkh }hur hog lrql}dwlrq wkuhvkrog/ lv srodul}hg shushqglfxodu wr wkh hog d{lv/ dqg wkh dwrplv lq d 68 Y2fpvwdwlf hog dw wkh h{flwdwlrq> wklv lv d w|slfdo ohyho ri djuhhphqw wkdw zdv dfklhyhg ehwzhhq wkh fdofxodwlrq dqg h{shulphqw1 Lw lv fohdu wkdw doo ri wkh ihdwxuhv duh dffxudwho| uhsurgxfhg dqg wkh dssur{lpdwlrqv zrun zhoo iru wklv dwrp1 Wkh VIL vshfwuxplv d vxshusrvlwlrq ri wkh vshfwud iurp6 gl huhqw qdo 6 v|pphwulhv= 6 'fc c 21 Lq Ilj1 517/ zh suhvhqw wkh fdofxodwhg VIL vljqdo iurp Ilj1 516 exw vhsdudwhg lqwr 60frpsrqhqwv +vrolg olqh lv 6 'f/ grwwhg olqh lv 6 '/dqg gdvkhg olqh lv 6 '2,1 Zh suhvhqw d frqwrxu sorw ri wkh fdofxodwhg VIL vljqdo yhuvxv hqhuj| dqg udps hog iru h{flwdwlrq e| d skrwrq sdudooho wr wkh hog lq Ilj1 518 dqg shushqglfxodu wr wkh hog lq Ilj1 5191 Lq erwk jxuhv/ wkh h{flwdwlrq zdv shuiruphg lq d 68 Y2fp vwdwlf hog1 Wkhvh jxuhv vkrz vrph ri wkh jhqhudo wuhqgv wkdw zh revhuyhg lq wkh VIL vshfwud1 Wkhuh duh d qxpehu ri lqwhuhvwlqj ihdwxuhv ri Iljv1 5160519 wkdw fdq eh xqghuvwrrg dw d txdolwdwlyh ohyho1 Rqh lpsruwdqw ihdwxuh lv wkdw wkh h{flwdwlrq odvhu kdv d edqgzlgwk ri urxjko| 3148 fp31 Wkxv/ wkhuh duh urxjko| 8043 Vwdun vwdwhv ri hdfk 60frpsrqhqw wkdw duh lqlwldoo| srsxodwhg1 Iru hogv ri D Y2fp/ wkh gl huhqw vwdwhv wkdw duh h{flwhg ehorqj wr gl huhqw ?0pdqlirogv dqg kdyh vxevwdqwldoo| gl huhqw glsroh prphqwv> wkxv/ wkh yduldwlrq lq wkh glylvlrq ri hqhuj| ehwzhhq wkh wzr sduderolf frruglqdwhv lv pxfk pruh
65 516 Pdwfklqj H{shulphqw zlwk Wkhru|
Iljxuh 517= D vhsdudwlrq ri wkh gl huhqw p0frpsrqhqwv ri wkh fdofxodwhg VIL vljqdo iurp Ilj1 516= vrolg olqh +p @ 3,/ grwwhg olqh +p @4,/ dqg gdvkhg olqh +p @5,1 Doo p0frpsrqhqwv kdyh wkh vdph lqlwldo fhqwudo hqhuj| dqg zlgwk1 Qrwh wkdw wkh vljqdo iru p @5glvwlqjxlvkhv wkh vhsdudwlrq ri hqhuj| ehwzhhq wkh xs0 dqg grzq0srwhqwldo gluhfwlrqv1 Wkh shdnv lq wkh p @5vshfwuxp fdq eh fodvvl hg xvlqj wkh qxpehu ri qrghv/ q/ lq wkh xs0srwhqwldo frruglqdwh dqg wkhqxpehuriqrghv/q2/ lq wkh grzq srwhqwldo frruglqdwh zlwk wkh qrwdwlrq +q>q2>q, zkhuh q @ q . q2 . mpm .4> dqrwkhu qrwdwlrq wkdw lv vrphwlphv xvhg lv wkh txdqwxp qxpehu n @ q2 q1 Zh kdyh odehoohg wkh odvw 8 shdnv dvvrfldwhg zlwk wkh p @5vwdwhv xvlqj q>q2 qrwdwlrq1 Vwduwlqj iurp wkh shdn dw 493 Y2fp wr wkh hduo| shdnv dw :3 Y2fp/ wkh vwdwhv duh +6;/43/84,/ +64/4;/85,/ +58/58/86,/ +53/64/87,/ +48/6:/88,/ +44/75/89, dqg +:/7:/8:,1 Wkh odvw wzr vwdwhv duh vwulsshg uvw dqg ryhuods hdfk rwkhu qhdu :3 Y2fp1 Dw wkh lqlwldo hog vwuhqjwk ri 68 Y2fp/ doo ri wkhvh vwdwhv duh zlwklq 315 fp3 ri hdfk rwkhu1 vxevwdqwldo wkdq wkh yduldwlrq ri wrwdo hqhuj| ri wkh gl huhqw vwdwhv1 Dqrwkhu lpsruwdqw ihdwxuh ghwhuplqlqj wkh Ol VIL vshfwud lv wkh odujh gl huhqfh lq txdqwxpghihfwv iru wkh orz0 , sduwldo zdyhv1 Wkh txdqwxpghihfwv duh >f 'fe/ > 'ffD dqg >2 'fff21 Wkh gl huhqfhv lq txdqwxpghihfwv jlyh txlwh gl huhqw ehkdylruv iru wkh gl huhqw 60vwdwhv lq wkh VIL h{shulphqw1 Wkh uhvxowv iru d qdo srodul}dwlrq sdudooho wr wkh hohfwulf hog rqo| jlyhv qdo vwdwhv ri 6 'fdqg 6 'fkdudfwhu iru wkh vsdwldo sduw ri wkh zdyh ixqfwlrq vlqfh wkh lqlwldo vwdwh kdv 6 'fdqg 6 'vsdwldo frpsrqhqwv1
Zh revhuyhg vrphzkdw gl huhqw VIL vshfwud zkhq zh xvhg wkh 2R*2 h{flwhg vwdwh dv wkh lqlwldo vwdwh1 Wklv lv ehfdxvh wkh frpsrvlwlrq ri wkh qdo 60vwdwhv fkdqjhv gxh wr wkh gl huhqw 60frpsrqhqwv ri wkh ruelwdo dqjxodu prphqwxp lq wkh 2R*21 Wkhvh frqvlghudwlrqv duh yhu| lpsruwdqw ehfdxvh wkh gl huhqw 60vwdwhv ehkdyh txlwh gl huhqwo| lq wkh VIL udpslqj1 Wkh frxsolqj pdwul{ hohphqwv rqo| ghshqg rq wkh txdqwxp ghihfw ri vwdwhv zlwk , 6>wkxv/6 'fvwdwhv fdq frxsoh wkurxjk , 'fc c 2 vfdwwhulqj exw 6 '2vwdwhv fdq rqo| frxsoh wkurxjk , '2vfdwwhulqj1 Wkh 6 'fvwdwhv jr wkurxjk doprvw hyhu| furvvlqj dgldedwlfdoo|> wkh odujh , 'ftxdqwxpghihfw surylghv
66 Vhohfwlyh Ilhog Lrql}dwlrq
Iljxuh 518= Lqwhqvlw| pds ri wkh fdofxodwhg VIL vljqdo iru Ol h{flwhg iurp wkh 5s *2 vwdwh zlwk d srodul}dwlrq sdudooho wr wkh hohfwulf hog1 Wkh dwrp lv ruljl0 qdoo| lq d vwdwlf hog ri 68 Y2fp ehiruh wkh hog lv udpshg1 vwurqj frxsolqj ehwzhhq wkh gl huhqw vwdwhv ehfdxvh wkhvh duh wkh vwdwhv wkdw vx hu prvw iurpfruh vfdwwhulqj1 Dv d uhvxow/ wkh srsxodwlrq whqgv wr vwd| rq d ihz ohyhov wkdw duh forvho| jurxshg lq hqhuj|1 Wklvs phdqv wkdw vrrq diwhu d vwdwh kdv dq hqhuj| deryh wkh fodvvlfdo lrql}dwlrq wkuhvkrog/ 2 8 / lw zloo vfdwwhu lqwr rshq fkdqqhov dqg ghfd| udslgo|1 Wkxv/ wkh 6 'fvwdwhv duh lq wkh VIL vljqdo dv d vkdus shdn dw uhodwlyho| vpdoo 8 1Wkh 6 'vwdwhv hyroyh odujho| gldedwlfdoo| exw zlwk d qrq0qhjoljleoh dgldedwlf lqwhudfwlrq dw hdfk furvvlqj1 Dowkrxjk wkh sxulw| ri wkh srsxodwlrq wkurxjk hdfk furvvlqj lv urxjko| wkh vdph dv iru 6 'f/ wkh odujh yduldwlrq lq glsroh prphqwv fdxvhv wkh wrwdo hqhuj| ri hdfk vwdwh wr ehfrph txlwh gl huhqw1 Dw hdfk furvvlqj/ wkhuh lv d qrq0qhjoljleoh suredelolw| wr pl{ zlwk vwdwhv ri gl hulqj glsroh prphqw zklfk suhyhqwv wkh wrwdo hqhuj| gl huhqfhv ehwzhhq wkh vwdwhv iurpehfrplqjdv odujh dv lq k|gurjhq1 Wkh 6 '2vwdwhv hyroyh doprvw frpsohwho|s gldedwlfdoo| dqg wkh| gr qrw vfdwwhu lqwr rshq fkdqqhov rqfh wkh hqhuj| lv deryh 2 8 1 Ehfdxvh ri wkh vpdoo txdqwxp ghihfwv iru , 2/ wkh vwdwhv rqo| ghfd| rqfh wkh hqhuj| ri wkh ?c?2 ohyho fdq fodvvlfdoo| ghfd| dw zklfk srlqw wkh hohfwurq ohdyhv yhu| udslgo|1 Wkxv/ wkh 6 '2vwdwhv jlyh d vhulhv ri shdnv dw yhu| vhsdudwhg hog vwuhqjwkv zklfk uh hfwv wkh ruljlqdo sduwlwlrqlqj ri hqhuj| lqwr wkh xs0 dqg grzq0srwhqwldo ghjuhhv ri iuhhgrpdqg qrw wkh wrwdo hqhuj| ri wkh vwdwh wkdw lv h{flwhg> wklv lv dq lqwhuhvwlqj ihdwxuh zklfk kdv qrw ehhq revhuyhg ehiruh1 Wkhuh duh d frxsoh ri ihdwxuhv lq wkh frqwrxu sorwv ri Iljv1 518 dqg 519 wkdw fdq eh lqwhusuhwhg zlwkrxw uhfrxuvh wr h{whqvlyh fdofxodwlrqv1 Wkh uvw reylrxv ihdwxuh lv wkdw wkh shdn dvvrfldwhg zlwk 6 'fvwdwhv hphujhv dw vpdoohu I dv wkh hqhuj| lqfuhdvhv1 Wklv rffxuv ehfdxvh wkh ? ohyhov lqfuhdvh zlwk lqfuhdvlqj hqhuj|> wkh 6 'fvwdwhv hyroyh doprvw sxuho| dgldedwlfdoo| dqg wkhlu hqhuj| kdugo| fkdqjhv gxulqj wkh hog udps1 Wkh 6 'fohyhov duh lrql}hg dv vrrq dv wkh hog vwuhqjwk lv odujhu wkdq *S?e dqg duh hdvlhu wr lrql}h iru odujhu ?1 Vlplodu frqvlghudwlrqv krog iru wkh 6 'ohyhov> dowkrxjk lqglylgxdo furvvlqjv duh pdlqo| gldedwlf/ wkh vkhhu qxpehu ri furvvlqjv jlyhv dq ryhudoo
67 516 Pdwfklqj H{shulphqw zlwk Wkhru|
-39.0 -38.0 -37.0 200 experiment
150
100
50
2000 theory SFI field (V/cm) 150
100
50
0 -39.0 -38.0 -37.0 term energy (cm-1)
Iljxuh 519= H{shulphqwdo dqg wkhruhwlfdo lqwhqvlw| pds ri wkh fdofxodwhg VIL vljqdo iru Ol1 Vdph sdudphwhuv dv Ilj1 518 exw iru shushqglfxodu srodul}dwlrq1 Wkh grwwhg olqh vkrzv I @+H@5,21 vsuhdglqj ri hqhuj| zlwkrxw odujh hqhuj| vkliwv1 Wkh VIL vljqdo iurpwkh 6 '2vwdwhv glvsod| d txlwh gl huhqw ihdwxuh +vhh Ilj1 519,1 Wkh 6 '2VIL frqvlvwv ri vkdus krul}rqwdo edqgv wkdw pryh wr odujhu I dv wkh hqhuj| lqfuhdvhv1 Wkh h{sodqdwlrq ri wklv skhqrphqrq lv vrphzkdw frxqwhu lqwxlwlyh1 Rqh edqg grhv qrw fruuhvsrqg wr d vlqjoh vwdwh1 Wklv fdq eh vhhq iurpwkh sduw ri wkh edqgv deryh 483 Y2fp> wkhuh lw lv fohdu wkdw hdfk edqg dfwxdoo| frqvlvwv ri vkruw krul}rqwdo edqgv wkdw vwhs xs wr kljkhu I dv wkh hqhuj| lqfuhdvhv1 Wkh h{sodqdwlrq lv wkdw hdfk edqg fruuhvsrqgv wr dq ?0pdqlirog1 Dv wkh hqhuj| lv lqfuhdvhg/ wkh vwdwh wkdw lv h{flwhg lq hdfk pdqlirog lv dw kljkhu hqhuj| +vhh Ilj1 514, dqg wkxv kdv d glsroh pruh vwurqjo| rulhqwhg wr wkh xs0srwhqwldo vlgh ri wkh dwrp> lq rwkhu zrugv/ vwdwhv zlwk pruh qrghv lq wkh xs0 srwhqwldo frruglqdwh/ 1/ duh ehlqj h{flwhg dv wkh hqhuj| lqfuhdvhv1 Wkhvh vwdwhv hyroyh gldedwlfdoo| iru 6 '2dqg wkxv duh qrw vwulsshg xqwlo yhu| kljk hog vlqfh wkh vwulsslqj hog pxvw lqfuhdvh zkhq pruh hqhuj| lv lq wkh xs0srwhqwldo frruglqdwh1 Wkh krul}rqwdo zlgwk ri wkh plql0edqgv iru 8:Df Y2fpvwhpviurpwkh odvhu edqgzlgwk dvvxphglq wkh fdofxodwlrq1 Zh suhvhqw d frpsdulvrq ehwzhhq wkh h{shulphqwdo dqg fdofxodwhg VIL vljqdo iru Ue lq d 8 Y2fpvwdwlf hog wr frqwudvw d pruhvwdqgdug vljqdo zlwk wkh Ol vljqdo+Ilj1 51:,> wkh lrql}dwlrq |lhog lv shdnhg qhdu 8 '*S?e1 Wkh Ue dwrpv duh h{flwhg iurp wkh
68 Vhohfwlyh Ilhog Lrql}dwlrq
-37.0 -36.0 -35.0 -34.0 -33.0 100 experiment 80
60
40
20
0 theory 80 SFI field (V/cm) field SFI 60
40
20
0 -37.0 -36.0 -35.0 -34.0 -33.0 term energy (cm-1)
Iljxuh 51:= H{shulphqwdo dqg wkhruhwlfdo Ue VIL |lhog dv d ixqfwlrq ri wkh whup hqhuj| ehorz wkh }hur hog lrql}dwlrq wkuhvkrog dqg dv d ixqfwlrq ri wkh VIL hog1 Wkh Ue lv h{flwhg lq d qrq0uhvrqdqw/ wzr0skrwrq wudqvlwlrq zlwk wkh odvhu srodul}hg shushqglfxodu wr wkh hohfwulf hog d{lv1 Wkh dwrp lv lq d vwdwlf 8 Y2fp hog gxulqj wkh h{flwdwlrq1 Wkh grwwhg olqh vkrzv I @+H@5,21 jurxqg vwdwh xvlqj d wzr0skrwrq/ qrq0uhvrqdqw wudqvlwlrq> wkh srodul}dwlrq ri wkh odvhu lv shushqglfxodu wr wkh hog d{lv1 Erwk 6 'fdqg 6 '2 qdo vwdwhv duh h{flwhg zlwk d udwlr ri 4=61 Iru Ue/ wkh txdqwxpghihfwv duh odujh iru , 2 dqg wkxv doo ri wkh ohyhov furvv dgldedwlfdoo| iru erwk 6 'fdqg 6 '2> wkh uhgxfhg txdqwxpghihfwv iru Ue duh
>7f 'fe/ >7 ' f S/ >72 'f D/dqg>7 'ff21 Wkxv/ iru Ue/ wkh VIL vljqdo lv qrw vhqvlwlyh wr zklfk Vwdun vwdwh lq wkh ?0pdqlirog lv h{flwhg> wkh VIL vljqdo lv rqo| vhqvlwlyh wrwkhhqhuj|riwkhvwdwh1WkhUeVILfdqehpdghwrehkdyhpruholnhwkdwiruOle| jrlqj wr kljkhu ? vwdwhv/ udpslqj wkh hog pxfk idvwhu/ ru e| xvlqj dq h{flwdwlrq vfkhph wkdw zrxog dffhvv 6 ' vwdwhv1 Xqolnh wkh Ol VIL vljqdo/ Ue rqo| vkrzv dgldedwlf lrql}dwlrq lq wklv hqhuj| udqjh dqg udps udwh1 Wkh shdn ydoxh ri 8 ghfuhdvhv dv wkh hqhuj| lqfuhdvhv ehfdxvh wkh hohfwurq lv hdvlhu wr uhpryh dv lwv elqglqj hqhuj| ghfuhdvhv1 W|slfdoo|/ wkh VIL vljqdo lv frqwdlqhg ehwzhhq E2.* 2 :8 :E.*2 2 zkhq . lv phdvxuhg iurp wkh }hur hog wkuhvkrog> dv . lqfuhdvhv/ .2 dqg 8 ghfuhdvh1
69 517 Olplwdwlrqv ri wkh Fdofxodwlrq 517 Olplwdwlrqv ri wkh Fdofxodwlrq
Zkloh rxu wkhruhwlfdo dssurdfk zrunhg zhoo iru wkh fdvhv suhvhqwhg khuh/ wkhuh duh vrph hdvlo| uhfrjql}deoh vlwxdwlrqv zkhuh wkh dssur{lpdwlrqv pd| idlo1 Iru h{dpsoh/ wkh ds0 sur{lpdwlrqv pd| idlo li wkh udpslqj hog grhv qrw kdyh d vlpsoh irup> d udpslqj hog wkdw kdv dq rvfloodwlqj frpsrqhqw frxog fdxvh wurxeoh e| kdylqj wkh skdvh rq gl huhqw sdwkv ehfrph vlpso| uhodwhg wr hdfk rwkhu +vhh dovr Fkdswhu 8,1 D pruh wurxeohvrph fdvh lv zkhq wkh khdylhu dondol dwrpv duh udpshg iurp }hur hog> wkh phwkrg suhvhqwhg khuh zrunv ehvw zkhq wkh hohfwulf hog lv vwurqj hqrxjk wr pl{ ohyhov ri gl huhqw ?0pdqlirogv1 Lq wkh phwkrg suhvhqwhg khuh/ hdfk srsxodwlrq ri d Vwdun vwdwh lv sursdjdwhg wr kljkhu hog vwuhqjwk lqfrkhuhqwo|> iru khdylhu dwrpv dw zhdn hogv/ wkhuh duh vhyhudo orz0, vwdwhv wkdw duh hvvhqwldoo| xqpl{hg zlwk wkh ?0pdqlirog dqg wkhvh vkrxog eh wuhdwhg dv d frkhu0 hqw vxshusrvlwlrq ri Vwdun vwdwhv1 Wkxv/ wkh dpsolwxghv vkrxog eh sursdjdwhg dqg qrw wkh srsxodwlrq1 Dqrwkhu gl!fxow| zlwk wkh khdylhu dondol dwrpv lv wkdw wkh vslq0ruelw lqwhudfwlrq pl{hv vwdwhv ri gl huhqw 6 dw orz hog vwuhqjwk1 Erwk gh flhqflhv fdq eh vlp0 so| {hg e| grlqj d qxphulfdo sursdjdwlrq ri wkh Vfkuùglqjhu htxdwlrq wr wkh ?0pl{lqj uhjlph dqg wkhq xvlqj wkh phwkrg ghvfulehg khuh wr rewdlq wkh VIL glvwulexwlrq1 Dv d frqwudvw/ wkh VIL ri ]HNH vwdwhv vkrxog eh vlpso| dffrpsolvkhg xvlqj wkh phwk0 rgv ghvfulehg khuh1 Wkh uhdvrq lv wkdw wkh orz dqjxodu prphqwxp vwdwhv fdq qrw eh vwurqjo| srsxodwhg iru wkh prohfxoh wr kdyh orqj olyhg U|gehuj vwdwhv1 Lq w|slfdo ]HNH vwdwhv/ wklv lv dffrpsolvkhg e| dq dssolhg ru d vwud| hohfwulf hog wkdw pl{hv wkh gl huhqw ,0vwdwhv ri dq ?0pdqlirog1 Wklv lv suhflvho| wkh vwduwlqj srlqw ri wkhvh fdofxodwlrqv1 Wkh odvw sureohplv wkdw wkh phwkrg wuhdwv hyhu| furvvlqj dv vhsdudwh dqg rqo| lqyroy0 lqj wzr ohyhov1 Wkhuh lv wkh srvvlelolw| iru 6 ohyho furvvlqjv rqfh wkh hog jhwv odujhu wkdq 2*E ?D 1 H{dplqlqj wkh hqhuj| pds iru hogv odujhu wkdq wklv fohduo| vkrz pdq| 6 dqg 7 ohyho furvvlqjv wkdw duh qrw d sulrul lvrodwhg/ dowkrxjk fohduo| wkh pdmrulw| ri furvvlqjv duh lvrodwhg 5 ohyho furvvlqjv1 Wkh huuruv gxh wr wuhdwlqj doo furvvlqjv dv lvrodwhg zloo qhhg wr eh h{dplqhg1 Lw lv rxu ihholqj wkdw pxowlsoh furvvlqjv sod| yhu| olwwoh uroh lq wkh VIL vljqdo1 Wkh uhdvrq lv wkdw lw zloo wdnh qhduo| shuihfw ghjhqhudf| ehwzhhq 6 ohyhov wr jhw dq h hfw zkhq wkh ohyhov hyroyh pdlqo| gldedwlfdoo|/ ( > exw lq wklv fdvh prvw ri wkh srsxodwlrq zloo vwd| lq wkh ruljlqdo vwdwh dqg wkxv wkh huuruv zloo eh qhjoljleoh1 Zkhq wkh suredelolw| iru dq dgldedwlf wudqvlwlrq/ / lv qrw vpdoo/ wkhq wkh srsxodwlrq grhv qrw vsuhdg idu iurpwkh dgldedwlf sdwk> wkxv prvwri wkh srsxodwlrq uhpdlqv zlwklq dq hqhuj| zlgwk +ghwhuplqhg e| wkh 5 ohyho furvvlqjv, ri wkh ruljlqdo srsxodwlrq dqg djdlq wkhuh zloo eh olwwoh huuru1
518 Glvfxvvlrq dqg Frqfoxvlrqv
Zh kdyh suhvhqwhg d gluhfw frpsdulvrq ehwzhhq phdvxuhg dqg fdofxodwhg VIL glvwulexwlrqv iru Ol dqg Ue1 Wkh frpsxwdwlrqdo phwkrg lv dq h{whqvlrq ri zhoo nqrzq whfkqltxhv1 Wkh pdlq lqqrydwlrq zdv wr xvh ZNE phwkrgv wr rewdlq wkh sdudphwhuv qhhghg lq wkh hyroxwlrq ri wkh zdyh ixqfwlrq wr wkh srlqw wkh hohfwurq ohdyhv wkh dwrp1 Zh zhuh deoh wr lqwhusuhw pdq| ihdwxuhv ri wkh vshfwuxp1 Zkhq wkh dwrp lv h{flwhg lq d vwdwlf hohfwulf hog
6: Vhohfwlyh Ilhog Lrql}dwlrq dqg wkh vwdwhv hyroyh gldedwlfdoo|/ wkh VIL phwkrg lv pxfk pruh vhqvlwlyh wr wkh glylvlrq ri hqhuj| ehwzhhq wkh wzr sduderolf frruglqdwhv wkdq wr wkh wrwdo hqhuj| ri wkh vwdwh1 Wklv zdv wkh fdvh iru Ol 6 '2vwdwhv suhvhqwhg khuh> lq wklv vlwxdwlrq/ wkh VIL phwkrg pd| eh xvhg iru wkh fkdudfwhul}dwlrq ri d vwdwh glvwulexwlrq ri wkh Vwdun ohyhov zlwklq dq ?0 pdqlirog1 Wklv kdv uhohydqfh iru ]HNH vwdwhv1 Wkh ]HNH vwdwhv dulvh wkurxjk wkh pl{lqj ri kljk0, dqg 6 vwdwhv zlwk wkh lqlwldoo| h{flwhg orz0, vwdwh> wkxv/ wkh VIL vshfwuxpri ]HNH vwdwhv vkrxog ehkdyh prvw olnh VIL ri k|gurjhq1 Dqrwkhu lpsruwdqw qglqj lv wkdw wkh fdofxodwlrq ri VIL glvwulexwlrqv lv qrw dv gl!fxow dv kdg ehhq wkrxjkw1 Wklv whfkqltxh pd| eh dssolfdeoh wr fdofxodwlqj surshuwlhv ri U|gehuj dwrpv pdqlsxodwhg e| rwkhu w|shv ri wlph ghshqghqw hogv> iru h{dpsoh/ wklv phwkrg pljkw eh xvhixo lq fdofxodwlrqv ri lrqv vfdwwhulqj iurpU|gehuj dwrpv1
6; Fkdswhu 6 WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
D vwxg| ri U|gehuj dwrpv h{srvhg wr WK} kdoi0f|foh sxovhv lv suhvhqwhg1 Wkh WK} kdoi0f|foh sxovh fdq ehvw eh ghvfulehg dv d idvw +fD sv, xqlsrodu sxovh/ iroorzhg e| d pxfk vorzhu xqlsrodu sxovh ri rssrvlwh srodulw|1 Wzr uhjlphv duh revhuyhg zkhuh U|g0 ehuj dwrpv uhdfw gl huhqw wr wkh lqwhudfwlrq zlwk wkhvh kdoi0f|foh sxovhv1 Lq wkh uvw uhjlph wkh urxqgwuls wlph ri wkh U|gehuj hohfwurq + ?, lv orqjhu wkdq wkh uvw idvw xqlsr0 odu sxovh + S,/ exw vkruwhu wkdq wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0f|foh + 6S,= S ? 6S1 Lq wkh vhfrqg uhjlph wkh urxqgwuls wlph ri wkh U|gehuj dwrp lv pxfk orqjhu wkdq wkh ixoo dv|pphwulf prqr0f|foh= ? :: 6S1 Lq wkh odwwhu uhjlph/ lrql}dwlrq vxssuhvvlrq dqg d pxfk vwurqjhu uhglvwulexwlrq lv revhuyhg1 Fodvvlfdoo| wkh revhuydwlrqv fdq eh h{sodlqhg e| wkh iroorzlqj lqwxlwlyh slfwxuh= wkh uvw idvw xqlsrodu ihdwxuh fruuh0 vsrqgv wr d vwduw nlfn ri wkh U|gehuj hohfwurq/ zkloh wkh vhfrqg xqlsrodu ihdwxuh dfwv dv d vwrs nlfn1 Wklv uhvxowv lq kdugo| dq| hqhuj| h{fkdqjh +lrql}dwlrq vxssuhvvlrq,1 Lqvwhdg dglvsodfhphqwri5>p ri wkh U|gehuj hohfwurq lv uhdol}hg/ dqg wkh U|gehuj vwdwh lv dowhuhg1
614 Kdoi0F|foh Sxovh Lrql}dwlrq
Wkh lqyhvwljdwlrq ri U|gehuj dwrpv e| kdoi0f|foh sxovhv lq wkh WK} uhjlph kdv jdlqhg zlghvsuhdg lqwhuhvw vlqfh wkh srvvlelolw| wr jhqhudwh wkhvh qhduo| xqlsrodu hohfwurpdjqhwlf zdyhv1 Wkh uvw h{shulphqwv ^7` uhyhdohg wkdw wkh lqwhudfwlrq ri U|gehuj dwrpv e| kdoi0 f|foh sxovhv fdq ehvw eh ghvfulehg dv dq lpsxovlyh nlfn/ vlqfh wkh gxudwlrq ri wkh kdoi0 f|foh sxovh +q fD sv, lv pxfk vkruwhu wkdq wkh urxqgwuls wlph ri wkh U|gehuj hohfwurq durxqg wkh qxfohxv1 Wkh fkdqjh lq prphqwxp +{T, lv jlyhq e| +dwrplf xqlwv duh xvhg/ xqohvv vwdwhg rwkhuzlvh,= U {T ' " 6E| _| +614, 3"
6< WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
Iljxuh 614= Vnhwfk ri d Nhsohu ruelw zlwk orz dqjxodu prphqwxp1 Wkh hohfwurq vshqgv prvw ri lwv wlph idu dzd| iurp wkh fruh +lqglfdwhg e| wkh wklfnqhvv ri wkh eodfn olqh,1 Forvh wr wkh qxfohxv/ kdoi0f|foh sxovh lrql}dwlrq vfdohv dv / ?2 zkloh idu dzd| iurp wkh fruh lrql}dwlrq vfdohv dv ? 1 zkhuh 6E| lvwkh+wlphydu|lqj,hohfwulf hog1Wkhfkdqjhlqprphqwxpfruuhvsrqgvwr dq hqhuj| fkdqjh ri= {. ' E2T {T nE{T 2 +615, 2 f Li wklv hqhuj| fkdqjh +{., lv juhdwhu wkdq wkh elqglqj hqhuj| ri wkh U|gehuj hohfwurq +. ' , wkh dwrpzloo lrql}h1 Lq w|slfdo h{shulphqwv/ wkh U|gehuj vwdwh lv suhsduhg 2?2 e| h{flwlqj d jurxqg vwdwh dwrpzlwk rqh ru wzr odvhuv/ uhvxowlqj lq d U|gehuj vwdwh zlwk orz dqjxodu prphqwxp +o,1 Lq vxfk d hoolswlf ruelw wkh U|gehuj hohfwurq vshqgv prvw ri lwv wlph dw wkh rxwhu srlqw ri lwv Nhsohu ruelw +vhh Ilj1 614,/ zkhuh Rf lv }hur1 Lq wkdw fdvh {. ' ' E{T 2 dqg wkxv wkh hog uhtxluhg wr lrql}h lv= 8 y {R ' 1Krzhyhu/ 2?2 2 ? zkhq wkh hohfwurq lv forvh wr wkh qxfohxv/ Rf lv yhu| odujh dqg zloo eh wkh grplqdqw whup lq Ht1 +615,= {. ' ' T {T/uhvxowlqjlq8 y {R ' 1 Dw orz hogv wkh lrql}dwlrq 2?2 f ?2 vwhpv iurp hohfwurqv qhdu wkh fruh dqg wkh lrql}dwlrq suredelolw| vfdohv dv 8 y / zkloh ?2 odujh lrql}dwlrq suredelolwlhv vfdoh dv 8 y 1 Lw kdv h{shulphqwdoo| ehhq ghprqvwudwhg ? dqg frq uphg wkdw dq lrql}dwlrq suredelolw| ri fI ri dq hqvhpeoh ri U|gehuj dwrpv vfdohv dv= 8 y / zkloh d DfI lrql}dwlrq suredelolw| vfdohv dv= 8 y ^7/78`1 fI ?2 DfI ? *2 Wkh whupkdoi0f|foh sxovh lv qrw ixoo| fruuhfw vlqfh Pd{zhoo*v htxdwlrqv ghpdqg wkdw wkh wlph lqwhjudo ri wkh hohfwulf hog lq wlph lv }hur lq iuhh vsdfh iru d sursdjdwlqj hohfwurpdjqhwlf zdyh1 Wkh WK} sxovh fdq ehvw eh ghvfulehg e| d yhu| vkruw kdoi f|foh sxovh +gxudwlrq= q fD sv,/ iroorzhg e| d pxfk vorzhu kdoi f|foh ri rssrvlwh srodulw| dqg d pxfk orzhu dpsolwxgh +w|slfdo sxovh dv|pphwu|= G ^6/79`,/ vr wkdw wkh wlph lqwhjudo ri wklv dv|pphwulf prqr0f|foh lv }hur +vhh Ilj1 615d,1 Wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0f|foh lv wkhq dv orqj dv q .f sv1 Iru U|gehuj vwdwhv zlwk d ruelwlqj wlph pxfk vkruwhu wkdq wkh gxudwlrq ri wklv vhfrqg xqlsrodu sxovh exw orqjhu wkdq wkh gxudwlrq ri wkh
73 614 Kdoi0F|foh Sxovh Lrql}dwlrq
uvw xqlsrodu sxovh/ lrql}dwlrq rffxuv gxulqj wkh uvw kdoi0f|foh ri wkh dv|pphwulf prqr0 f|foh1 Wkh lrql}dwlrq fdq wkdq eh ghvfulehg e| kdoi0f|foh sxovh lrql}dwlrq/ qhjohfwlqj wkh vhfrqg xqlsrodu ihdwxuh1 Zkhq wkh uhglvwulexwlrq ri wkhvh U|gehuj vwdwhv e| kdoi0 f|foh sxovhv lv vwxglhg lq wklv uhjlph/ wkh vhfrqg xqlsrodu ihdwxuh dfwv dv d GF r vhw iru wkh U|gehuj hohfwurq/ vr wkdw lw grhv qrw vljql fdqwo| frqwulexwh wr wkh uhglvwulexwlrq surfhvv ^7:`1
Krzhyhu/ wkh ruelwlqj wlph ri d U|gehuj vwdwh vfdohv dv ? y ? + ? '..sv/ iru ? 'Hf,/ dqg wkxv iru U|gehuj vwdwhv zlwk d vx!flhqwo| odujh sulqflsdo txdqwxpqxpehu/ wkh ruelwlqj wlph fdq ehfrph pxfk orqjhu wkdq wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0 f|foh1 Eh|rqg wklv sulqflsdo txdqwxpqxpehu/ wkh gxudwlrq ri wkh ixoo prqr0f|foh lv vkruw frpsduhgU wr wkh ruelwlqj shulrg ri wkh U|gehuj hohfwurq dqg wkh fkdqjh lq prphqwxp lv {T ' " 6E| _| r f1 Wklv zrxog uhvxow lq yhu| olwwoh hqhuj| fkdqjh ri wkh U|gehuj 3" hohfwurq1 Vxfk dq dv|pphwulf prqr0f|foh grhv qrw ohdyh wkh U|gehuj vwdwh frpsohwho| xqdi0 ihfwhg vlqfh wkh uvw xqlsrodu ihdwxuh nlfnv dq hohfwurq lq wkh gluhfwlrq ri wkh srodul}dwlrq ri wkh kdoi0f|foh sxovh/ zkloh wkh vhfrqg ghod|hg xqlsrodu sxovh vwrsv wkh hohfwurq djdlq1 Wkhuhiruh/ d glvsodfhphqw ri wkh hohfwurq suredelolw| lv lqwurgxfhg/ e| wkh idvw vwduw dqg wkh vorz vwrs nlfn ri wkh prqr0f|foh1 Iru d iuhh hohfwurq wklv glvsodfhphqw lv +6e ' e '/ lq dwrplf xqlwv,=
U U {%' " _| | 6E| _| +616, 3" 3" Lq Ilj1 615e wkh glvsodfhphqw ri dq xqdffhohudwhg hohfwurq e| dq dv|pphwulf prqr0f|foh zlwk d shdn dpsolwxgh ri 2 nY2fp+dv lv ghslfwhg lq Ilj1 615d, lv sorwwhg1 D U|gehuj hohfwurq zlwk dq ruelwlqj wlph pxfk orqjhu wkdq wkh gxudwlrq ri d kdoi0 f|foh sxovh zloo eh vljql fdqwo| glvsodfhg e| vxfk d kdoi0f|foh sxovh vlqfh wkh fkdqjh ri yhorflw| lq dq xqshuwxuehg ruelw lv qhjoljleoh rq wkh wlphvfdoh ri wkh gxudwlrq ri d kdoi0f|foh sxovh1 D glvsodfhphqw ri 418 >6 ri d iuhh hohfwurq lv fdofxodwhg iru wkh kdoi0 f|foh sxovh ri Ilj1 615d/ zklfk phdqv wkdw wkh h{shfwdwlrq ydoxh ri wkh udgldo frruglqdwh 2 tkol ri d U|gehuj hohfwurq fdq eh fkdqjhg e| dv pxfk dv 418 >6 + o:'2? $ ? ' o:'b,1 2 Lq wklv Fkdswhu zh lqyhvwljdwh wkh h hfw ri wkh vhfrqg xqlsrodu ihdwxuh ri kdoi0f|foh sxovhv lq wkhlu lqwhudfwlrq zlwk U|gehuj dwrpv/ e| vwxg|lqj wkh lrql}dwlrq dqg erxqg vwdwh uhglvwulexwlrq ri U|gehuj dwrpv vxemhfwhg wr vxfk WK} udgldwlrq1 Iru orz sulq0 flsdo txdqwxpqxpehuv + ? Hf, kdugo| dq| uhglvwulexwlrq lv revhuyhg/ dqg lrql}dwlrq suredelolwlhv duh phdvxuhg lq dffrugdqfh zlwk wkh fodvvlfdo lrql}dwlrq odzv1 D vwurqj lrq0 l}dwlrq vxssuhvvlrq/ dqg erxqg vwdwh uhglvwulexwlrq lv revhuyhg iru U|gehuj vwdwhv zlwk kljk sulqflsdo txdqwxpqxpehuv + ?::Hf,1 D fodvvlfdo prgho lv suhvhqwhg lq zklfk wkh lrql}dwlrq ehkdylru dqg erxqg vwdwh uhglvwulexwlrq ri U|gehuj vwdwhv e| wkhvh dv|pphwulf prqr0f|fohv lv txdolwdwlyho| h{sodlqhg1
74 WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
principal quantum number principal quantum number
40 58 69 77 85 49 38 32 2000 a c 1500
1000 A=-B
500 power (arb. un.) (arb. power electric field (V/cm) 0
0 20406080
b 1.2 m) µ 0.9
0.6
0.3 displacement ( displacement 0.0 0 2040608001234 time (ps) frequency (THz)
Iljxuh 615= d= D WK} kdoi0f|foh sxovh frqvlvwv ri d vkruw xqlsrodu ihdwxuh/ iroorzhg e| d pxfk vorzhu xqlsrodu ihdwxuh ri rssrvlwh srodulw|1 Rq wkh wrs d{lv wlph +wkh U|gehuj ruelwwlqj wlph, lv frqyhuwhg lqwr d sulqflsdo txdqwxp | * qxpehu= q @ 2Z 1 e= D iuhh hohfwurq lv glvsodfhg e| pruh wkdq 4=5 plilw lv h{srvhg wr wkh kdoi0f|foh sxovh ri Ilj1 615d +dpsolwxgh= 5 nY2fp,1 f= Irxulhu wudqvirup ri wkh sxovhvkdsh ghslfwhg lq Ilj1 615d1 Rq wkh wrs d{lv iuhtxhqf| lv frqyhuwhg lqwr d sulqflsdo txdqwxp qxpehu= k @ H @ 1 2?2 615 H{shulphqwdo Uhdol}dwlrq
Wkh suhsdudwlrq ri U|gehuj dwrpv lq Ol zdv grqh lq d vlplodu h{shulphqwdo frq jxudwlrq dv ghvfulehg lq Fkdswhu 51 Wkh vhwxs lv ghslfwhg lq Ilj1 6161 D wkhupdo ehdp ri jdv0 skdvh olwklxpdwrpv/surgxfhg e| d uhvlvwlyho| khdwhg ryhq/ zdv gluhfwhg lq ehwzhhq wzr fdsdflwru sodwhv/ wr surylgh d krprjhqhrxv hohfwulf hog1 D kroh +> 4313 pp, lq wkh fhqwhu ri wkh dqrgh sodwh/ zdv fryhuhg e| d julg wr plqlpl}h glvwruwlrqv rq wkh hohfwulf hog1 Wklv hqdeohg wkh ghwhfwlrq ri lrql}hg hohfwurqv/ rq d Plfur Vskhuh Sodwh ghwhfwru orfdwhg 813 fpdzd| iurpwkh dqrgh sodwh1 Wkh fdwkrgh sodwh zdv frqqhfwhg wr d sxovh jhqhudwru/ zklfk frxog udps wkh yrowdjh lq d zhoo gh qhg wlph1 Wkh dqrgh sodwh zdv frqqhfwhg wr jurxqg1 Wkh xqirfxvhg rxwsxw ri wzr/ qduurzedqg/ g|h odvhuv zhuh frolqhdu gluhfwhg lq ehwzhhq wkh sdudooho fdsdflwru sodwhv rq wr wkh olwklxpdwrpvlq furvvhg ehdpduudqjhphqw +vhh Ilj1 616,1 Wkh uvw odvhu h{flwhg wkh olwklxpdwrpviurpwkh jurxqg vwdwh wr wkh 2R ohyho +S.fb. qp,/ zkloh wkh vhfrqg odvhu +q .ff qp, zdv iuhtxhqf| grxeohg wr h{flwh olwklxp dwrpv iurp wkh 2R ohyho wr d zhoo gh qhg U|gehuj vwdwh1 Wkh zdyhohqjwk ri wkh vhfrqg h{flwlqj odvhu frxog eh vfdqqhg lq rughu wr h{flwh gl huhqw U|gehuj vwdwhv1 Kdoi0f|foh WK} udgldwlrq zdv surgxfhg e| looxplqdwlqj d eldvhg JdDv vhplfrqgxfwru
75 616 H{shulphqwdo Uhvxowv
Iljxuh 616= Vnhwfk ri wkh h{shulphqwdo vhw0xs1 zdihu zlwk d vkruw +q Df iv, odvhu sxovh +q Hff qp,/ ruljlqdwhg iurp d Wl=Vdsskluh fklushg sxovh dpsol hu v|qfkurql}hg wr wkh g|h odvhuv1 Wklv udgldwlrq zdv doljqhg froolqhdu zlwk wkhrswlfdoodvhuehdpv/rqwrwkhU|gehujdwrpv1Wkhshdnydoxhriwkhhohfwulf hogri wkh kdoi0f|foh udgldwlrq/ zkhq lw uhdfkhv wkh U|gehuj dwrpv lv sursruwlrqdo wr wkh eldv yrowdjh ryhu wkh zdihu1 Wkh kdoi0f|foh sxovh uhdfkhg wkh U|gehuj dwrpv dssur{lpdwho| 833 qv diwhu wkh h{flwdwlrq e| wkh vhfrqg qduurzedqg odvhu1 Lrql}dwlrq dqg vwdwh uhglvwulexwlrq kdv ehhq prqlwruhg zlwk wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq ^5/83` +VIL/ Fkdswhu 5,1 Wklv whfkqltxh pdnhv xvh ri wkh idfw wkdw hyhu| U|gehuj vwdwh kdv d hohfwulf hog vwuhqjwk dvvrfldwhg zlwk lw iru zklfk lw zloo lrql}h= 8 ' k 1 Wklv hog vwuhqjwk fdq eh fdoleudwhg +ghwhuplqlqj k, e| h{flwlqj vshfl f ?e U|gehuj vwdwhv e| d qduurzedqg odvhu dqg ghwhuplqlqj wkh hog uhtxluhg wr lrql}h wkh U|gehuj vwdwh1 Li rqh udpsv wkh vwdwlf hohfwulf hog lq wlph +udpslqj wkh yrowdjh rq wkh fdwkrgh sodwh, dqg prqlwruv dw zklfk wlph lrql}dwlrq rffxuv rqh fdq ghgxfh wkh erxqg vwdwh glvwulexwlrq ri dq dwrplf v|vwhp1 Wkh lqwhjudwhg hohfwurq x{ gxh wr hog lrql}dwlrq lv d phdvxuh iru wkh dprxqw ri erxqg vwdwh srsxodwlrq1
616 H{shulphqwdo Uhvxowv
D WK} lrql}dwlrq fxuyh iru d U|gehuj vwdwh zlwk d sulqflsdo txdqwxpqxpehu ri ? '.f lv ghslfwhg lq Ilj1 617d1 Wkh uhfrughg V0fxuyh lv d w|slfdo vljqdwxuh ri WK} lrql}dwlrq1 Lq Ilj1 617e wkh fruuhvsrqglqj VIL wudfhv duh ghslfwhg zklfk vkrz wkdw pdlqo| ghsohwlrq ri wkh lqlwldoo| suhsduhg vwdwh rffxuv/ zlwk olwwoh uhglvwulexwlrq1 Wr ydolgdwh wkdw wkh lrql}dwlrq frxog eh ghvfulehg e| lpsxovlyh nlfnlqj ri wkh U|gehuj hohfwurq dzd| iurp wkh qxfohxv/ dgglwlrqdo WK} lrql}dwlrq fxuyhv zhuh uhfrughg iru U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ohvv wkdq ? '.f1 Ilj1 617f vkrzv krz wkh WK} lrql}dwlrq suredelolw| ri U|gehuj dwrpv vfdohv iru wkh ? 'D / S/dqg.f U|gehuj vwdwhv1 Fohduo| wkh
76 WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
n=90 n=75 n=68 n=63 1.0 no THz 50 % ionization b 4000 c -3/2 a 1000 V/cm n 0.8 2000 V/cm 10 % ionization 3500 V/cm -2 3000 n 0.6 50%
0.4 2000 ionized fraction SFI yield (arb. un.) 0.2 bias voltage (V) 1000 10% 0.0 0 500 1000 1500 2000 2500 3000 3500 0 0 1020304050 50 55 60 65 70 75 bias voltage (V) SFI field (V/cm) principal quantumnumber (n)
Iljxuh 617= H{shulphqwdo WK} lrql}dwlrq gdwd iru U|gehuj vwdwhv zlwk d urxqgwuls wlph vkruwhu wkdq wkh gxudwlrq ri wkh dv|pphwulf prqr0f|foh= ? ? 6S1 d= Dq h{shulphqwdo WK}0lrql}dwlrq fxuyh iru d U|gehuj vwdwh zlwk q @:31 Wkh wzr duurzv ghqrwh zkdw hogvwuhqjwk lv uhtxluhg wr lrql}h 43( dqg 83( ri wkh U|gehuj dwrpv1 e= Wkuhh VIL wudfhv rewdlqhg diwhu h{srvlqj U|gehuj dwrpv wr d WK} kdoi0f|foh sxovh ri q @:3iru wkuhh gl huhqw dpsolwxghv ri wkh kdoi0f|foh sxovh1 f= H{shulphqwdoo| revhuyhg lrql}dwlrq suredelolwlhv iru U|gehuj vwdwhv ri q @86/ 94/dqg:31 Wkh rshq grwv fruuhvsrqg wr 83( lrql}d0 wlrq suredelolw|/ zkloh wkh forvhg grwv fruuhvsrqg wr dq lrql}dwlrq suredelolw| ri 43(1 Wkh 43( dqg 83( lrql}dwlrq suredelolw| forvho| iroorz d +vrolg olqh= ?2 I @ f / zlwk f @:=3 43S Y2fp, dqg +grwwhg olqh= I @ f / f ?2 f ? *2 Df ? *2 S zlwk fDf @4=9 43 Y2fp, vfdolqj odz uhvshfwlyho|1
8 q +43( lrql}dwlrq, dqg 8 q +83 ( lrql}dwlrq, vfdolqj odzv duh uhwulhyhg1 Wkh 43( ?2 ? *2 lrql}dwlrq suredelolw| ghshqghqf| fdq eh wwhg e|= 8 ' S /zlwkS '.ffS T*S6/ f ?2 f zkloh wkh 83( lrql}dwlrq suredelolw| fdq eh wwhg e|= 8 ' S /zlwkS 'S fS Df ? *2 Df T*S61DudwlrriSf 'eD lv rewdlqhg/ lq jrrg djuhhphqw zlwk wkh udwlr ghwhuplqhg iurp SDf S Sf 2fff uhi1 ^7` +wkhuh d udwlr ri ' S 'ef zdv revhuyhg,1 SDf fDff
Iru wkhvh U|gehuj vwdwhv/ wkh urxqgwuls wlph + ? '2Z? , ri wkh U|gehuj hohfwurq udqjhv iurp 22 sv +? 'D ,wrD2 sv +? '.f,/ zklfk lv vkruwhu wkdq wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0f|foh + 6S,/ exw pxfk orqjhu wkdq wkh gxudwlrq ri wkh uvw xqlsrodu ihdwxuh + S, lq WK} kdoi0f|foh sxovhv +vhh Ilj1 615d, ^7`/ dqg wkhuhiruh wkh lrql}dwlrq fdq eh xqghuvwrrg dv wuhdwlqj wkh WK} sxovh dv d wuxh kdoi0f|foh lpsxovlyh nlfn1 Lq wklv vwxg| zh irfxv rq wkh uhjlph zkhuh wkh gxudwlrq ri wkh vhfrqg xqlsrodu ihdwxuh dfwv lpsxovlyh dv zhoo1 Wklv phdqv wkdw wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0f|foh vkrxog eh pxfk vkruwhu wkdq wkh urxqgwuls wlph ri wkh U|gehuj hohfwurq= 6S ?1Lqwklvuhjlphlwlv h{shfwhg wkdw wkh lrql}dwlrq phfkdqlvp ri U|gehuj vwdwhv zlwk wkhvh kdoi0f|foh sxovhv lv dowhuhg e| wkh vhfrqg vorzhu xqlsrodu ihdwxuh1 Wklv zrxog fruuhvsrqg wr U|gehuj vwdwhv ri ?::Hf + ? '..sv,/ vlqfh wkh gxudwlrq ri wkh zkroh dv|pphwulf prqr0f|foh lv dv orqj dv q .f sv +vhh Ilj1 615d,1 Lq Ilj1 618d wkh lrql}dwlrq suredelolw| lv sorwwhg yhuvxv wkh eldv yrowdjh ri wkh vhpl0 frqgxfwlqj zdihu iru d U|gehuj vwdwh zlwk d sulqflsdo txdqwxpqxpehu ri ? ' D
+ ? ' .sv,1 Wzr vwulnlqj uhvxowv duh dssduhqw1 Iluvwo|/ lw lv qrw srvvleoh wr dfklhyh
77 617 Fodvvlfdo Fdofxodwlrqv d ffI lrql}dwlrq suredelolw| +wkh pd{lpxp uhfrughg lrql}dwlrq suredelolw| zdv :8(,1 Vhfrqgo|/ wkhuh lv d vwurqj ghyldwlrq ri wkh fodvvlfdo lrql}dwlrq vfdolqj odz/ vlqfh iru orz lrql}dwlrq suredelolwlhv ohvv shdn dpsolwxgh lv uhtxluhg iru lrql}dwlrq wkdq suhglfwhg e| wkh fodvvlfdo vfdolqj odzv +ghqrwhg e| wkh grwv lq Ilj1 618d,1 D U|gehuj vwdwh zlwk d sulqflsdo txdqwxpqxpehu juhdwhu wkdq ? 'Sf+elqglqj hqhuj|= . ' ' e f3e d1x1, 2?2 kdv douhdg| vrph suredelolw| wr eh lrql}hg e| d vlqjoh kljk iuhtxhqf| skrwrq ri wkh kdoi0 f|foh sxovh +4 WK} ' 63 fp3 ' . f3e d1x1/ vhh dovr Ilj1 615f,1 Wkhuhiruh/ wkh revhuydwlrq wkdw orzhu dpsolwxghv duh uhtxluhg ri wkh kdoi0f|foh sxovh wkdq suhglfwhg e| wkh fodvvlfdo vfdolqj odzv fdq eh h{sodlqhg e| wkh idfw wkdw zh duh vwxg|lqj lrql}dwlrq lq wkh rqh0skrwrq lrql}dwlrq uhjlph iru wkhvh kljk U|gehuj vwdwhv +?:.f,dvrssrvhg wr wkh pxowl0skrwrq uhjlph iru U|gehuj vwdwhv zlwk d sulqflsdo txdqwxp qxpehu vpdoohu wkdq ? '.f/ iurpzklfk wkh fodvvlfdo vfdolqj odzv zhuh ghgxfhg1 Lw grhv krzhyhu/ qrw h{sodlq wkh lrql}dwlrq vxssuhvvlrq +vhh vhfwlrq 618,1 Lq Ilj1 618e wkuhh VIL wudfhv duh ghslfwhg iru ? ' DU|gehuj dwrpv h{srvhg wr kdoi0 f|foh sxovhv ri gl huhqw dpsolwxghv +eldv yrowdjh= 583 Y2fp/ 833 Y2fp/ dqg 5333 Y2fp,1 Wkh VIL wudfh rewdlqhg zlwk qr WK} vkrzv wkh lqlwldo vwdwh glvwulexwlrq1 Dssduhqwo|/ iru wkhvh kljk ? vwdwhv/ uhglvwulexwlrq wr pdlqo| kljkhu ?0vwdwhv rffxuv/ lqvwhdg ri lrql}dwlrq1 Qrwlfh wkdw dovr pruh ghhso| erxqg vwdwhv duh fuhdwhg1 Wklv vljql fdqw uhglvwulexwlrq lv qrw revhuyhg zkhq zh vwduw rxw zlwk U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ehorz ? '.fdv vkrzq lq Ilj1 617e/ lqglfdwlqj wkdw wkh uhglvwulexwlrq rffxuv gxh wr wkh lpsxovlyh fkdudfwhu ri wkh vhfrqg vorzhu xqlsrodu ihdwxuh lq kdoi0f|foh sxovhv1 Wkh vkdsh ri wkh VIL wudfh rewdlqhg e| h{srvlqj U|gehuj dwrpv wr d kdoi0f|foh sxovh ri 833 Y2fp/ zdv qrw vljql fdqwo| dowhuhg zkhq wkh dpsolwxgh ri wkh kdoi0f|foh sxovh zdv lqfuhdvhg +xs wr 5333 Y2fp,1 WK} lrql}dwlrq fxuyhv iru U|gehuj vwdwhv ri gl huhqw ? +?:.f, duh ghslfwhg lq Ilj1 618f/ vkrzlqj wkdw lrql}dwlrq vxssuhvvlrq lv vwurqjhu iru U|gehuj vwdwhv zlwk d kljkhu sulqflsdo txdqwxpqxpehu1 Pruhryhu d fohdu glvdjuhhphqw lv revhuyhg ehwzhhq wkh h{0 shulphqwdoo| ghwhuplqhg lrql}dwlrq suredelolw| dqg wkh lrql}dwlrq suredelolw| suhglfwhg e| wkh fodvvlfdo vfdolqj odzv +Ilj1 618g,/ dffrxqwlqj iru wkh uvw xqlsrodu ihdwxuh rqo|1 Lq wkh qh{w vhfwlrq zh glvfxvv d fodvvlfdo prgho zklfk txdolwdwlyho| h{sodlqv wkh lrql}dwlrq vxssuhvvlrq dqg uhglvwulexwlrq wr kljkhu U|gehuj vwdwhv e| dv|pphwulf prqr0f|foh sxovhv1
617 Fodvvlfdo Fdofxodwlrqv
Fodvvlfdo fdofxodwlrqv zhuh shuiruphg/ wdnlqj lqwr dffrxqw wkh vhfrqg vorz xqlsrodu ihdwxuh lq kdoi0f|foh sxovhv/ wr xqghuvwdqg wkh revhuydwlrqv1 Wkh htxdwlrqv ri prwlrq ri d U|gehuj hohfwurq durxqg d qxfohxv lq d wlph ydu|lqj hog zhuh vroyhg e| wkh Uxqjh0 Nxwwd qxphulfdo lqwhjudwlrq phwkrg1 Wkh lrql}dwlrq suredelolw| ri d kdoi0f|foh sxovh ri d {hg dpsolwxgh zdv fdofxodwhg e| ghwhuplqlqj wkh hqhuj| ri d U|gehuj hohfwurq diwhu lqwhudfwlrq zlwk wkh kdoi0f|foh sxovh/ iru ydulrxv vwduwlqj wlphv ri wkh kdoi0f|fohsxovh gxulqj rqh Nhsohu ruelw wlph1 Wkh suredelolw| lv wkhq ghwhuplqhg e| wkh vxp ri doo wkh ruelwvzklfkuhvxowhglqlrql}dwlrq+.:f,/ glylghg e| wkh qxpehu ri gl huhqw vwduwlqj
78 WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
limitn=135 n=114 n=103 n=96 1.0 a b no THz 250 V/cm 0.8 500 V/cm 2000 V/cm 0.6 n-3/2
0.4 SFI yield (arb. un.) (arb. yield SFI
ionization probability 0.2 n-2 0.0 0 500 1000 1500 2000 02468 bias voltage (V) SFI field (V/cm)
1.0 50 % ionization c 4000 d -3/2 n 0.8 10 % ionization -2 3000 n ility 0.6
2000 0.4
ionization probab ionization 0.2
Iljxuh 618= H{shulphqwdo WK} lrql}dwlrq gdwd iru U|gehuj vwdwhv zlwk d urxqgwuls wlph + ? @ 6:4 sv, pxfk orqjhu wkdq wkh gxudwlrq ri wkh ixoo dv|p0 phwulf prqr0f|foh= ? AA 6S1 d= WK} lrql}dwlrq fxuyh iru d U|gehuj vwdwh ri q @4681 Iru wkhvh kljk q0vwdwhv lw lv lpsrvvleoh wr dfklhyh 433( lrql}d0 wlrq1 Wkh wzr grwv +, ghqrwh zkdw dpsolwxgh lv uhtxluhg/ suhglfwhg e| wkh fodvvlfdo lrql}dwlrq odzv/ wr rewdlq d 43( dqg 83( lrql}dwlrq suredelolw|1 e= Wzr VIL wudfhv rewdlqhg diwhu h{srvlqj U|gehuj dwrpv wr d WK} kdoi0f|foh sxovh ri q @468iru wzr gl huhqw dpsolwxghv ri wkh kdoi0f|foh sxovh1 Wkh grwwhg olqh ghslfwv wkh VIL wudfh zkhq wkh U|gehuj dwrpv zhuh qrw h{srvhg wr WK} udgldwlrq1 f= WK}0lrql}dwlrq fxuyhv iru qA:3/ vkrzlqj wkdw lrql}dwlrq lv vxssuhvvhg iru kljkhu U|gehuj vwdwhv1 g= Wkh h{shulphqwdoo| ghwhuplqhg 43( dqg 83( lrql}dwlrq suredelolwlhv frpsduhg wr wkh fodvvlfdo vfdolqj odzv +I y /dqgI y ,1 D vwurqj ghyldwlrq lv revhuyhg iru U|gehuj fI ?2 DfI ? *2 vwdwhv zlwk qA:31
79 617 Fodvvlfdo Fdofxodwlrqv
1.0 50% ionization n=43
-3/2 calculated electric field (V/cm) n=34 n 8000 0.8 n=26 10% ionization n-2 6000 0.6
4000 0.4
2000 ionization probability 0.2
a b 0.0 0 0 2500 5000 7500 25 35 45 calculated electric field (V/cm) principal quantum number
Iljxuh 619= Fdofxodwhg lrql}dwlrq sredelolwlhv iru U|gehuj vwdwhv zlwk d urxqgwuls wlph vkruwhu wkdq wkh gxudwlrq ri wkh ixoo dv|pphwulf prqr0f|foh= ? ? 6S1 d= Lrql}dwlrq suredelolwlhv iru U|gehuj vwdwhv zlwk dq ruelwwlqj wlph pxfk vkruwhu wkdq wkh gxudwlrq d ixoo WK} dv|pphwulf prqr0f|foh/ exw orqjhu wkdq wkh gxudwlrq ri wkh uvw xqlsrodu ihdwxuh lq d WK} kdoi0f|foh sxovh1 e= Wkh 43( dqg 83( lrql}dwlrq sursdelolwlhv/ ghwhuplqhg iurp wkh fdofxodwlrqv/ frpsduhg wr wkh fodvvlfdo vfdolqj odzv +I y /dqgI y ,1 fI ?2 DfI ? *2 wlphv41 Lq Ilj1 619d wkh fdofxodwhg lrql}dwlrq suredelolw| lv sorwwhg iru vhyhudo U|gehuj vwdwhv +, '2, zlwk d sulqflsdo txdqwxpqxpehu ri= ? '2S/ e/dqge e| d kdoi0 f|foh sxovh zklfk hqyhorsh lv ghslfwhg lq Ilj 615d1 Lghqwlfdo lrql}dwlrq fxuyhv zhuh fdofxodwhg/ zkhq wkh vdph fdofxodwlrqv zhuh shuiruphg zlwk d wuxh kdoi0f|foh sxovh +rqo| xvlqj wkh uvw idvw kdoi0f|foh dv wkh wlph ydu|lqj hog lq wkh fdofxodwlrqv, lqvwhdg ri wkh dv|pphwulf prqr0f|foh ri Ilj1 615d1 Wklv vkrzv wkdw iru U|gehuj vwdwhv zlwk d vx!flhqwo| orz sulqflsdo txdqwxpqxpehu +vr wkdw ? 6S,/ wkh vhfrqg vorz xqlsrodu ihdwxuh grhv qrw vljql fdqwo| frqwulexwh lq wkh lrql}dwlrq surfhvv1 Iurpwkh fdofxodwhg WK} lrql}dwlrq fxuyhv zh ghwhuplqhg wkh hog uhtxluhg wr rewdlq d 43( dqg 83( lrql}dwlrq suredelolw|/ dqg wkh fodvvlfdo vfdolqj odzv zhuh uhwulhyhg +vhh Ilj1 619,1 Li wkh vdph prgho lv dssolhg wr d U|gehuj vwdwh zlwk ? ' D +, '2,/ d gl huhqw lrql}dwlrq ehkdylru lv rewdlqhg1 Gxh wr wkh vhfrqg xqlsrodu ihdwxuh/ lrql}dwlrq lv vwurqjo| vxssuhvvhg1 Wklv fdq eh vhhq lq Ilj1 61:d zkhuh d fdofxodwhg lrql}dwlrq fxuyh e| wkh dv|pphwulf prqr0f|foh +dv ghslfwhg lq Ilj1 615d, lv frpsduhg wr wkh fdofxodwhg lrql}dwlrq fxuyh e| d wuxh kdoi0f|foh sxovh +IZKP fD sv,1 Iru d iuhh hohfwurq wkh hqhuj| h{fkdqjh lv }hur/ dqg wkxv lw lv xqghuvwrrg wkdw lrql}dwlrq lv vxssuhvvhg1 Wkh vpdoo lrql}dwlrq
4 Wklv lv lghqwlfdo wr shuiruplqj d fdofxodwlrq zkhuh wkh vwduwlqj wlph ri wkh kdoi0f|foh sxovh lv {hg exw wkh hohfwurq vwduwv dw gl huhqw srvlwlrqv lq lwv Nhsohu ruelw/ zkhuh wkh lrql}dwlrq suredelolw| lv wkhq rewdlqhg e| vxpplqj doo wkh ruelwv zklfk uhvxowhg lq lrql}dwlrq zhljkwhg e| wkh h{shfwdwlrq ydoxh ri wkh vwduwlqj srvlwlrq ri hdfk lqglylgxdo ruelw1
7: WK} Lrql}dwlrq ri Kljk U|gehuj Vwdwhv
simulated SFI spectra 1.0 a c no THz 0.8 1000 V/cm 2000 V/cm
0.6
0.4 yield (arb. un.)
Ionization probability Ionization 0.2
0.0 0 500 1000 1500 2000 02468 calculated electric field (V/cm) SFI field strength (V/cm)
Iljxuh 61:= d= Fdofxodwhg WK} lrql}dwlrq fxuyhv iru d U|gehuj vwdwh zlwk d sulqflsdo txdqwxp qxpehu ri q @ 468 +o @5,1 Wkh urxqgwuls wlph ri vxfk d U|gehuj vwdwh lv pxfk orqjhu + ? @6:4sv, wkdq wkh gxudwlrq ri wkh dv|pphwulf prqr0f|foh1 Grwwhg olqh= fdofxodwhg WK} lrql}dwlrq iru d wuxh kdoi0f|foh sxovh1 Vrolg olqh= fdofxodwhg WK} lrql}dwlrq zlwk d sxovhvkdsh dv ghslfwhg lq Ilj1 6151 e= Fdofxodwhg uhglvwulexwlrq ri d q @ 468/ o @8U|gehuj vwdwh dv d ixqfwlrq ri wkh dpsolwxgh ri wkh dv|pphwulf prqr0f|foh1 Wkh rshq grwv uh hfw wr zklfk dyhudjh sulqflsdo txdqwxp qxpehu uhglvwulexwlrq rffxuv/ zkloh wkh frqwrxu judsk uh hfw wkh dfwxdo vwdwh glvwulexwlrq1 f= Vlpxodwhg VIL vshfwud iurp wkh vwdwh +uh0,glvwulexwlrq rewdlqhg e| wkh fdofxodwlrqv1 Qrwlfh wkh yhu| jrrg djuhhphqw zlwk wkh h{shulphqwdo uhvxowv ghslfwhg lq Ilj1 618e1 suredelolw| frphv iurp wkh idfw wkdw wkh yhorflw|U ri wkh hohfwurq lq lwv ruelw durxqg wkh qxfohxv lv wlph ghshqghqw dqg wkxv {. ' " 6E| _| lv qrw h{dfwo| }hur uhvxowlqj lq 3" vrph lrql}dwlrq1 Fodvvlfdo fdofxodwlrqv zhuh xvhg wr ghgxfh lq zkdw pdqqhu wkh ruelw ri wkh U|gehuj vwdwh lv dowhuhg/ vlqfh wkh vxssuhvvlrq ri lrql}dwlrq lv txdolwdwlyho| ghvfulehg fodvvlfdoo|1 Wklv fdq eh grqh e| fdofxodwlqj wkh lqwhudfwlrq ri d U|gehuj vwdwh zlwk d kdoi0f|foh sxovh dqg ghwhuplqlqj wkh hqhuj| glvwulexwlrq ri wkh U|gehuj vwdwh diwhuzdugv1 Lq Ilj1 61:e wkh fdofxodwhg uhglvwulexwlrq ri d ? ' D U|gehuj vwdwh lv ghslfwhg1 Dq dyhudjh uh0 glvwulexwlrq wr kljkhu U|gehuj vwdwhv lv revhuyhg1 Wkh VIL vshfwuxpzdv vlpxodwhg +Ilj1 61:f, iru d {hg dpsolwxgh ri wkh kdoi0f|foh sxovh vwduwlqj irup wkh fdofxodwhg vwdwh +uh0,glvwulexwlrq1 Wklv zdv grqh e| frqyhuwlqj wkh sulqflsdo txdqwxpqxpehu ri d U|gehuj vwdwh lqwr d hog vwuhqjwk iru zklfk wkh vshfl f U|gehuj vwdwh zrxog hog lrql}h +8 ' k ,1 Wkhvh vlpxodwlrqv uhsurgxfh wkh h{shulphqwdo revhuydwlrqv yhu| dffxudwho| ?e +frpsduh Ilj1 61:f zlwk Ilj1 618e,1 Iurp wkh h{shulphqwdo VIL wudfhv lw lv ghgxfhg wkdw zlwk d eldv yrowdjh ri 5333 Y uhglvwulexwlrq rffxuv wr U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ri ? ' 2ff1 Wkh h{shfwdwlrq ydoxh ri wkh udgldo frruglqdwh ri wkh lqlwldo ? ' D U|gehuj vwdwh lv o:'2?2 '2 >p/ dqg iru d U|gehuj vwdwh ri ? '2ffwklv h{shfwdwlrq ydoxh lv= o:'e2 >p1 Wkhuhiruh/ d U|gehuj vwdwh ri ? ' D lv glvsodfhg e| dq dv|pphwulf prqr0f|foh zlwk d eldv yrowdjh ri 5333 Y2fp e| q 2 >p1
7; 618 Glvfxvvlrq dqg Frqfoxvlrqv 618 Glvfxvvlrq dqg Frqfoxvlrqv
Lq wklv Fkdswhu lw lv ghprqvwudwhg wkdw U|gehuj dwrpv zlwk d kljk sulqflsdo txdqwxp qxpehu +?::Hf, duh urexvw djdlqvw lrql}dwlrq e| kdoi0f|foh sxovhv1 Lqvwhdg ri frp0 sohwh lrql}dwlrq/ uhglvwulexwlrq wr kljk U|gehuj vwdwhv lv revhuyhg1 Qrîo hw do1 ^7;` revhuyhg d vlplodu h hfw zkhq wkh| h{srvhg U|gehuj dwrpv wr ihz0f|foh +q D f|fohv, plfurzdyh udgldwlrq +7 JK}, zlwk dq dpsolwxgh ef odujhu wkdq uhtxluhg wr lrql}h wkh lqlwldo vwdwh1 Lqvwhdg ri lrql}lqj wkh U|gehuj dwrpv/ srsxodwlrq wudsslqj lq kljk q0vwdwhv zdv re0 vhuyhg1 Wkh revhuydwlrqv suhvhqwhg lq wklv Fkdswhu forvh wkh jds ehwzhhq kdoi0f|foh sxovh lrql}dwlrq ri U|gehuj vwdwhv zlwk ? .f/ dqg ihz0f|foh plfurzdyh lrql}dwlrq1 Wklv h{shulphqw dovr uhodwhv wr wkh vwxg| ri lrql}dwlrq e| vkruw/ idu0lqiuduhg odvhu sxovhv e| Krrjhquddg hw do1 ^7<`1 Wkdw vwxg| ghprqvwudwhg wkdw lrql}dwlrq ri U|gehuj vwdwhv lq wkh rqh0skrwrq uhjlph zdv vxssuhvvhg iru sxovh gxudwlrqv vkruwhu wkdq wkh ruelw shulrg ri wkh U|gehuj hohfwurq1 Wklv zdv h{sodlqhg vhpl0fodvvlfdoo|= wkh zdyhixqfwlrq ri d U|gehuj hohfwurq shuirupv d Nhsohu0olnh ruelw durxqg wkh qxfohxv1 Rqo| wkh zdyhixqfwlrq qhdu wkh fruh fdq eh lrql}hg e| wkh odvhu sxovh1 Vlqfh qrw doo ri wkh zdyhixqfwlrq sdvvhv qhdu wkh fruh iru d odvhu sxovh pxfk vkruwhu wkdq wkh Nhsohu ruelwlqj wlph/ wkh zdyhixqfwlrq idu iurpwkh fruh lv vwdeoh djdlqvw lrql}dwlrq1 Wkh vdphvhpl0fodvvlfdo h{sodqdwlrq fdqqrw eh dssolhg wr wkh revhuydwlrqv uhsruwhg lq wklv fkdswhu/ vlqfh wkh lrql}dwlrq ri U|gehuj dwrpv e| kdoi0f|foh sxovhv lv xqghuvwrrg dv lpsxovlyho| nlfnlqj wkh hohfwurq dzd| iurp wkh qxfohxv1 Wkhuhiruh/ lrql}dwlrq fdq vwloo rffxu hyhq zkhq wkhuh lv qr zdyhixqfwlrq qhdu wkh fruh1 Dq lqwxlwlyh phfkdqlvp iru wkh lrql}dwlrq vxssuhvvlrq lv suhvhqwhg lq zklfk wkh kdoi0 f|foh sxovh fdq ehvw eh ghvfulehg e| d idvw vwduw nlfn dqg d vorz vwrs nlfn ri rssrvlwh srodulw| dqg orzhu dpsolwxgh1 Lqvwhdg ri nlfnlqj wkh U|gehuj hohfwurq dzd| iurp wkh qxfohxv/ wkh kdoi0f|foh sxovh lqgxfhv d qhz U|gehuj ruelw lq zklfk wkh h{shfwdwlrq ydoxh ri wkh udgldo frruglqdwh ri wkh U|gehuj hohfwurq lv dowhuhg1 Lq rwkhu zrugv= wkh U|gehuj hohfwurq lv glvsodfhg1 Wklv rqo| krogv lq wkh uhjlph zkhuh wkh wlph gxudwlrq ri wkh dv|pphwulf prqr0f|foh lv vkruwhu wkdq wkh urxqgwuls wlph ri wkh U|gehuj hohfwurq1 Lq wklv uhjlph srsxodwlrq wudqvihu pdlqo| wr kljk U|gehuj vwdwhv lv suhglfwhg e| fodvvlfdo fdofxodwlrqv lq djuhhphqw zlwk h{shulphqwdo revhuydwlrqv1 Wkh vlpxodwhg VIL vshfwud iurp wkh fdofxodwhg vwdwh glvwulexwlrq zhuh lq yhu| jrrg djuhhphqw zlwk wkh h{shulphqwdo VIL vshfwud1 Lw zdv h{shulphqwdoo| dqg wkhruhwlfdoo| ghprqvwudwhg wkdw d ? ' DU|gehuj vwdwh fdq eh glvsodfhg e| dv pxfk dv 2 >p1 Uhglvwulexwlrq ri U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ri ? 'Dfe| vorz xqlsrodu +< qv IZKP, hohfwulf hog sxovhv/ lv glvfxvvhg lq Fkdswhu 81 Wkhuh lw lv ghprqvwudwhg wkdw hyhq xqlsrodu ihdwxuhv lq wkh qdqrvhfrqg uhjlph fdq kdyh d vwurqj h hfw rq U|gehuj vwdwhv zlwk d uhodwlyho| orz sulqflsdo txdqwxpqxpehu/ dqg wkxv wkdw lq prvw fdvhv rqh fdqqrw qhjohfw wkh prqr0f|foh qdwxuh ri kdoi0f|foh sxovhv1
7<
Fkdswhu 7 Irufhg Dxwrlrql}dwlrq
Lq wklv fkdswhu zh uhsruw rq wkh dxwrlrql}dwlrq g|qdplfv ri wkh 8g:g grxeo| h{flwhg vwdwh lq edulxp lq d vwdwlf hohfwulf hog1 Wkh gl huhqw h{shulphqwv dqg wkhru| vkrz Vwdun ehdwlqjv lq wkh dxwrlrql}dwlrq surfhvv1 Lw dovr dsshduhg wkdw wkh wrwdo vslq ri wkh wzr ydohqfh hohfwurqv/ sod|v d pdmru uroh lq wkh lrql}dwlrq g|qdplfv1 Devruswlrq vshfwurvfrs| uhyhdohg wkh lrql}dwlrq g|qdplfv qhdu wkh fruh/ zkloh dq dwrplf vwuhdn fdphud zdv xvhg wr uhfrug wkh wlph0ghshqghqw hohfwurq hplvvlrq/ surelqj wkh zdyh ixqfwlrq zkhq lw lv idu iurp wkh fruh1 Fdofxodwlrqv edvhg rq Pxowl0fkdqqho Txdqwxp Ghihfw Wkhru| duh frpsduhg wr h{shulphqwdo gdwd dqg zh duh deoh wr suhglfw wkh vlqjohw0wulsohw pl{lqj1
714 Lqwurgxfwlrq wr Irufhg Dxwrlrql}dwlrq
Dq dwrplq d grxeo| h{flwhg vwdwh kdv wzr hohfwurqv srsxodwlqj ohyhov gl huhqw iurpwkh jurxqg vwdwh1 Wkhvh h{flwhg vwdwhv fdq frxsoh wr vwdwhv lq zklfk rqh hohfwurq kdv uhod{hg wr wkh jurxqg vwdwh dqg wkh rwkhu fduulhv doo wkh hqhuj|1 Li wkh wrwdo hqhuj| vkduhg e| wkh wzr hohfwurqv h{fhhgv wkh elqglqj hqhuj|/ wkh vhfrqg hohfwurq lv irufhg wr hvfdsh> wkh grxeo| h{flwhg vwdwh kdv ghfd|hg e| dxwrlrql}dwlrq lqwr d jurxqg vwdwh lrq soxv d iuhh hohfwurq1 Li wkh wrwdo hqhuj| lv ohvv wkdq wkh elqglqj hqhuj|/ wkh grxeo| h{flwhg vwdwh fdq rqo| frxsoh wr erxqg U|gehuj vwdwhv1 Krzhyhu/ lq wkh suhvhqfh ri d vx!flhqwo| vwurqj hohfwulf hog vxfk U|gehuj vwdwhv frxsoh wr frqwlqxxpvwdwhv> wkh hohfwulf hog lqwurgxfhv d vdggoh srlqw lq wkh fruh srwhqwldo ryhu zklfk wkh hohfwurqv fdq hvfdsh +vhh Ilj1 714,1 Wkh surfhvv e| zklfk wkh grxeo| h{flwhg vwdwh frxsohv wr d U|gehuj vwdwh/ zklfk lq wxuq frxsohv wr wkh hog0lqgxfhg frqwlqxxp/ lv nqrzq dv irufhg dxwrlrql}dwlrq ^84` +vhh dovr Ht1 +4143,,1 Lq wklv fkdswhu zh lqyhvwljdwh wkh g|qdplfv ri vxfk d irufhg dxwrlrql}dwlrq surfhvv lq wkh dondolqh hduwk dwrpedulxpwr ohduq pruhderxw wkh frpsoh{ hohfwurq g|qdplfvri d ghfd|lqj wzr hohfwurq v|vwhp1 Vwduwlqj iurp wkh jurxqg vwdwh +9v2, wkh 8g:g grxeo| h{flwhg vwdwh lv odvhu0h{flwhg yld wkh 8g9s odvhu0h{flwhg lqwhuphgldwh vwdwh1 Zh vwxglhg wkh g|qdplfv ri wkh frxsolqj wr wkh 9v"& U|gehuj vhulhv iroorzhg e| wkh lrql}dwlrq ri wkh U|gehuj Vwdun vwdwhv1 Wkh dssurdfk ri rxu vwxg| lv wkuhhirog1 Iluvw zh shuiruphg d kljk uhvroxwlrq vshfwurvfrs| vwxg|1 Wklv frqyhqwlrqdo phdqv ri vwxg|lqj wkh v|vwhp ^85/ 86`
84 Irufhg Dxwrlrql}dwlrq
6s27d 5d7d Ω 6s26d 567 nm 5d6p
413 nm E ground state: 6s6s r modified Coulomb potential
Iljxuh 714= Wkh surfhvv ri irufhg dxwrlrql}dwlrq dv vwxglhg lq Ed1 D grxeo| h{flwhg vwdwh lv fuhdwhg e| phdqv ri wzr frqvhfxwlyh odvhu sxovhv1 Wkh grxeo| h{flwhg vwdwh +8g:g, frxsohv vwurqjo| wr wkh 9vqg U|gehuj vwdwhv wkurxjk frq0 jxudwlrq lqwhudfwlrq1 Wkhvh vwdwhv lq wxuq duh frxsohg wr d frqwlqxxp lq d vwurqj hohfwulf hog dqg fdq wkhuhiruh dxwrlrql}h1
|lhogv g|qdplfdo lqirupdwlrq htxlydohqw wr rswlfdo sxps0sureh vwxglhv zlwk vkruw odvhu sxovhv ^87`1 Lq vxfk d sxps0sureh vwxg| wkh sxps sxovh fuhdwhv d U|gehuj zdyhsdfnhw/ [/ dqg diwhu d ghod| wlph d vhfrqg zdyhsdfnhw lv odxqfkhg e| wkh sureh sxovh1 Wkh lqwhuihuhqfh ri wkh wzr zdyhsdfnhwv lv phdvxuhg1 Vlqfh wkh U|gehuj zdyhsdfnhw [ lv d surmhfwlrq ri wkh jurxqgvwdwh zdyh ixqfwlrq rq wkh U|gehuj vwdwhv/ wkh odxqfkhg zdyh sdfnhw [E| 'f lv qhdu wkh fruh1 Dv d uhvxow erwk vshfwurvfrs| dqg sxps0sureh h{0 shulphqwv |lhog lqirupdwlrq rq wkh orz dqjxodu prphqwxp fkdudfwhu ri wkh zdyhsdfnhw qhdu wkh fruh1 Zlwk khos ri wkh uhfhqwo| ghyhorshg dwrplf vwuhdn fdphud zh duh deoh wr phdvxuh wkh rxwjrlqj hohfwurq x{ zlwk d slfrvhfrqg uhvroxwlrq dqg wkxv sureh wkh hohf0 wurqlf zdyh ixqfwlrq qhdu wkh vdggoh srlqw1 Ilqdoo| zh dssolhg d yhuvlrq ri Pxowl0fkdqqho TxdqwxpGhihfw Wkhru| +PTGW, ^75/ 888:` ghvfulelqj wkh g|qdplfvsurehg e| erwk w|shv ri h{shulphqwv dffxudwho|1 Zh uhsruw rq wzr uhpdundeoh qglqjv rq wkh irufhg dxwrlrql}dwlrq g|qdplfv ri wkh edulxp8g:g vwdwh1 Iluvw/ erwk wkh vshfwurvfrs| dqg wkh hohfwurq hplvvlrq gdwd vkrzhg d ehdwlqj ri wkh dxwrlrql}dwlrq surfhvv1 Wkh dqjxodu prphqwxp ghjhqhudf| lv oliwhg e| wkh hohfwulf hog1 Wkh uhvxowlqj Vwdun vwdwhv duh frkhuhqwo| h{flwhg/ |lhoglqj dq rvfloodwlrq ri wkh dqjxodu prphqwxp +Vwdun ehdwlqj, ^8;/ 9;`1 Krzhyhu/ wkh g|qdplfv dv vhhq zlwk erwk whfkqltxhv lv qrw wkh vdph vlqfh wkh| sureh gl huhqw sduwv ri wkh zdyh ixqfwlrq1 Vhfrqgo|/ wkh qdwxuh ri wkh g|qdplfv lv vrphzkdw pruh frpsoh{ wkdq vnhwfkhg deryh vlqfh dovr wkh vslq ri wkh wzr hohfwurqv lv lqyroyhg1 Wkh vslq ri wkh rxwjrlqj hohfwurq lv dqwl sdudooho ru sdudooho wr wkh vslq ri wkh hohfwurq zklfk lv lq wkh jurxqg vwdwh Edn +9v,1 Zh qg wkdw wkh g|qdplfv ri hohfwurq hplvvlrq lq wkh wzr vslq fkdqqhov lv gudpdwlfdoo| gl huhqw1 Zkloh gluhfw hmhfwlrq ri wkh hohfwurq uhvxowv prvwo| lq d vlqjohw vwdwh/ wkh wulsohw hplvvlrq lv grplqdqw iru orqjhu wlphv1
85 715 Iuhtxhqf| Grpdlq H{shulphqwv 715 Iuhtxhqf| Grpdlq H{shulphqwv
Erwk h{shulphqwv zhuh shuiruphg lq d ydfxxp fkdpehu zlwk d edfnjurxqg suhvvxuh ri 813433. Wruu1 Lq rxu vshfwurvfrs| h{shulphqw/ uhyhdolqj wkh hohfwurq g|qdplfv qhdu wkh fruh/ zh srsxodwhg d grxeo| h{flwhg vwdwh lq edulxpe| phdqv ri wzr qduurzedqg sxovhg g|h odvhuv lq d vwdwlf hohfwulf hog1 Wkh uvw sxovh/ zlwk d fhqwudo zdyhohqjwk ri 74617 qp dqg srodul}dwlrq sdudooho wr wkh hohfwulf hog/ h{flwhg jurxqg vwdwh hohfwurqv lq edulxpwr d 8g9s lqwhuphgldwh vwdwh1 Wkh 8g:g shuwxuehu uhjlrq zdv h{flwhg e| d vhfrqg qv sxovh zlwk d fhqwudo zdyhohqjwk qhdu 89: qpdqg d edqgzlgwk ri 314 fp31Wkhsrodul}dwlrq ri wklv sxovh zdv hlwkhu fkrvhq wr eh sdudooho ru shushqglfxodu wr wkh hohfwulf hog1 Dq dwrplf edulxpehdpzdv surgxfhg e| d uhvlvwlyho| khdwhg ryhq1 Wkh edulxpdwrpvzhuh h{flwhg ehwzhhq wzr sdudooho fdsdflwru sodwhv 4313 pp dsduw1 Wkh hohfwurqv/ fuhdwhg e| wkh dxwrlrql}dwlrq surfhvv/ duh sxvkhg wkurxjk wkh julg lq wkh dqrgh sodwh wrzdugv d vhw ri Pxowl Fkdqqho Sodwhv1 E| vfdqqlqj wkh vhfrqg odvhu ryhu wkh 8g:g shuwxuehu dw d fhuwdlq hog vwuhqjwk zh rewdlqhg wkh hohfwurq |lhog dv ixqfwlrq ri wkh ghwxqlqj iurpwkh shuwxuehu1 Fduh lv wdnhq qrw wr vdwxudwh wkh vshfwud zlwk wrr pxfk srzhu/ w|slfdoo| wkh srzhu ri wkh vhfrqg odvhu zdv nhsw ehorz q5Z2fp21 Lq Ilj1 715 +wrs, d w|slfdo devruswlrq vshfwuxplv ghslfwhg1 Wkh vkdus ihdwxuhv duh wkh uhvrqdqfhv dulvlqj iurpwkh Vwdun vwdwhv lq wkh 9v "& fkdqqhov/ zkloh wkh ryhudoo eurdg ihdwxuh lv gxh wr wkh frxsolqj ehwzhhq wkh 9v fkdqqhov dqg wkh 8g:g shuwxuehu dqg fdq eh ghvfulehg e| d Idqr sur oh ^99` zlwk dq dv|pphwu| sdudphwhu +t, ri 2D1 Wkh zlgwk ri wklv eurdg ihdwxuh +r48 fp3 IZKP, lv uhsuhvhqwlqj wkh frxsolqj vwuhqjwk ehwzhhq wkh shuwxuehu dqg wkh U|gehuj vhulhv1 Wkh srvlwlrqv ri wkh gl huhqw uhvrqdqfhv iurpwkh 9v "& fkdqqhov fdq eh uhodwhg wr srvlwlrqv ri wkh yhu| eoxh Vwdun vwdwhv ^87` ri orzhu o|lqj q0 pdqlirogv +dv orz dv q @ 55/ iru 4933 Y2fp,1 Wkh uhdvrq wkdw zh duh rqo| vhhlqj wkh eoxh vwdwhv lv ehfdxvh wkh zdyh ixqfwlrq ri wkhvh vwdwhv lv orfdol}hg idu iurpwkh vdggoh srlqw/ khqfh wkhvh vwdwhv duh orqj olyhg dv rssrvhg wr uhg vwdwhv zklfk lrql}h lqvwdqwdqhrxvo|1 D ixuwkhu lqyhvwljdwlrq ri Ilj1 715 dovr vkrzv wkdw wkh uhvrqdqfhv lq wkh 9v fkdqqhov dsshdu dv glsv +zlqgrz uhvrqdqfhv, rq wkh eoxh vlgh +{.:f, ri wkh shuwxuehu dqg dv shdnv rq wkh uhg vlgh ri wkh shuwxuehu1 Wklv lv gxh wr wkh lqwhuihuhqfh ehwzhhq hohfwurq zdyhv iurpwkh gl huhqw fkdqqhov lq wkh frqwlqxxpfkdqqho1 D wkhruhwlfdo fdofxodwlrq lv ghslfwhg dqg wkh wkhru| lv lq h{fhoohqw djuhhphqw zlwk h{shulphqw1 Wr frqqhfw wklv devruswlrq vshfwurvfrs| h{shulphqw wr wkh U|gehuj hohfwurq g|qdplfv/ zh pxowlso| dq devruswlrq vshfwuxpzlwk d Jdxvvldq zlwk d zlgwk dqg d fhqwudo iuhtxhqf| fruuhvsrqglqj wr wkh zlgwk ri d vkruw eurdgedqg odvhu sxovh1 Wkh Irxulhu Wudqvirupri wkh dfklhyhg vshfwuxpvkrzv wkh uhfxuuhqfh vshfwuxplq zklfk zh fdq vhh Vwdun ehdwv gxh wr wkh frkhuhqw vxshusrvlwlrq ri wkh 9v"& Vwdun vwdwhv1 Lq Ilj1 715 +erwwrp, d Irxulhu Wudqvirup lv ghslfwhg iru d Jdxvvldq sxovh zlwk d fhqwudo zdyhohqjwk ri 8991:: qpdqg d sxovh gxudwlrq ri :18 sv1 Fohduo|/ d ehdwlqj sdwwhuq lv uhvroyhg zklfk lv lqyhuvho| sursruwlrqdo wr wkh hqhuj| vhsdudwlrq ri wkh gl huhqw Vwdun vwdwhv +lq dwrplf xqlwv,= ' 2Z 1 {.
86 Irufhg Dxwrlrql}dwlrq
1600 V/cm; perpendicular polarization red middle blue (a)
electron yield (arb. units) (arb. yield electron -20 -10 0 10 20 (b) ∆E (cm-1) (0)> ψ
(t)| ψ <
0 102030405060 time (ps)
Iljxuh 715= +d, Lrql}dwlrq vljqdo dv d ixqfwlrq ri wkh ghwxqlqj ri wkh vhfrqg qduurzedqg odvhu sxovh1 Wkh edulxp dwrpv zhuh h{flwhg zlwk d srodul}dwlrq shushqglfxodu wr d vwdwlf hohfwulf hog ri 4933 Y2fp1 Wkh hqhuj| lv zlwk uhvshfw wr wkh }hur hog srvlwlrq ri wkh 8g:g vwdwh +74;74199 fp3,1 Wkh pdunhuv uhg/ plggoh/ eoxh zloo eh xvhg dv d uhihuhqfh lq Ilj1 6 dqg 81 Wkh erog yhuwlfdo duurzv ghqrwh wkh srvlwlrq ri wkh : eoxhvw Vwdun vwdwhv ri q@55/ vkrzlqj zlqgrz uhvrqdqfhv rq wkh eoxh vlgh ri wkh shuwxuehu/ zkhuh wkh duurzv olqh xs zlwk ydooh|v lq wkh h{shulphqwdo vshfwuxp1 Wkh vkdus uhvrqdqfh dw q 56 fp3 lv gxh wr d voljkw +314 (, vwurqwlxp frqwdplqdwlrq ri wkh edulxp vdpsoh1 Qrwh wkh h{fhoohqw pdwfk zlwk wkhru| +grwwhg olqh,1 +e, Irxulhu Wudqvirup ri d frqyroxwhg vshfwuxp zlwk d zlgwk ri 813 fp3 dqgdghwxqlqjri0913fp3 +ghqrwhg e| wkh Jxdvvldq fxuyh lq wkh xsshu judsk,1 716 Wlph Grpdlq H{shulphqwv
Lq rughu wr phdvxuh wkh hohfwurq hplvvlrq ri wkh irufhg dxwrlrql}dwlrq surfhvv/ zh kdyh xvhg dq dwrplf vwuhdn fdphud ^9:` zlwk slfrvhfrqg uhvroxwlrq1 Wkh sulqflsoh lv dv iroorzv dqglvvnhwfkhglqIlj17161Edulxpdwrpvduhh{flwhglqdfurvvhgehdpduudqjhphqw ehwzhhq wzr sodwhv +vhsdudwlrq @ 4313 pp, ryhu zklfk wkh vwdwlf hog lv dssolhg1 Wkh vhfrqg sodwh kdv d volw sdudooho wr wkh ehdpgluhfwlrq wkurxjk zklfk wkh hohfwurqv fdq ohdyh wkh lqwhudfwlrq uhjlrq1 Ehklqg wklv sodwh d vzhhslqj hohfwulf hog lv fuhdwhg +v|qfkurql}hg zlwk wkh odvhu sxovh, ehwzhhq wzr gh hfwlrq sodwhv/ shushqglfxodu wr wkh suhylrxv sodwh vhw dqg shushqglfxodu wr wkh gluhfwlrq ri wkh hohfwurq x{1 Wklv hohfwulf hog w|slfdoo| vzhhsv iurp0318 nY wr .318 nY lq 833 sv1 Wkhuhiruh hohfwurqv duulylqj dw gl huhqw wlphv lq wkh gh hfwlrq uhjlrq h{shulhqfh d gl huhqw yrowdjh dqg duh uhfrughg rq d gl huhqw srvlwlrq rq d vhw ri Pxowl Fkdqqho Sodwhv lq frpelqdwlrq zlwk d skrvskru vfuhhq zklfk lpdjhv wkh gh hfwhg hohfwurqv1
87 716 Wlph Grpdlq H{shulphqwv
Rydberg atoms
CCD camera
deflection plates channel plates phosphor screen
laser excitation
Iljxuh 716= Wkh dwrplf vwuhdn fdphud vhwxs1 D grxeo| h{flwhg vwdwh lq Ed dwrpv lv fuhdwhg e| phdqv ri d qv g|h odvhu dqg d vkruw sv g|h odvhu +vhh wh{w,1 Gxh wr wkh suhvhqfh ri d vwurqj hohfwulf hog/ Irufhg Dxwrlrql}dwlrq rffxuv1 Wkh hplwwhg hohfwurqv duh dffhohudwhg wr wkh uljkw lq wkh jxuh dqg duulyh ehwzhhq wzr gh hfwlrq sodwhv1 Rqh ri wkh gh hfwlrq sodwhv fdq eh udslgo| fkdujhg e| d fdsdflwru/ wuljjhuhg e| rswlfdoo| vzlwfklqj d slhfh ri JdDv1 Wkh wlph gl huhqfh ehwzhhq hohfwurqv duulylqj ehwzhhq wkh gh hfwlrq sodwhv lv wkxv frqyhuwhg lqwr d gh hfwlrq dqjoh1 Wkh hohfwurqv vwulnh d Pxowl Fkdqqho Sodwh vhw dqg wkh uhvxowlqj vljqdo lv ghwhfwhg e| d Skvrskru vfuhhq1 D FFG fdphud lv xvhg wr uhfrug wkh oljkw ri wkh skrvskru vfuhhq1
Wklv h{shulphqw lqyroyhg wkh lqyhvwljdwlrq ri wkh vdph grxeo| h{flwhg erxqg vwdwh/ zlwk wkh vdph h{flwdwlrq vfkhph dv lq wkh devruswlrq vshfwurvfrs| h{shulphqw/ h{fhsw wkdw wkh vhfrqg qduurzedqg sxovh lv uhsodfhg e| d slfrvhfrqg sxovh zlwk d wxqdeoh fhqwudo iuhtxhqf|1 Wkh uhfrughg dxwrfruuhodwlrq zlgwk ri wkh dpsol hg sxovhv +833 >a/43K},ri 43 + 4, sv fruuhvsrqglqj wr d sxovh gxudwlrq ri : + 31:, sv lqglfdwhv wkdw wkh sxovhv duh qhdu wudqvirupolplwhgjlyhq wkh vshfwudo zlgwk ri 8 + 4, fp31 Wkh vwuhdn fdphud h{shulphqw lq lwv wxuq uhyhdov lqirupdwlrq rq zkhq wkh zdyhsdfnhw lv idu iurpwkh fruh dqg wkh dwrphplwvhohfwurq x{1 Lq Ilj1 717 wkuhh gl huhqw hohfwurq hplvvlrq wudfhv + oohg flufohv, duh ghslfwhg dw wkh vdph hog vwuhqjwk +4933 Y2fp, exw iru gl huhqw ydoxhv ri wkh fhqwudo zdyhohqjwk ri wkh lrql}lqj eurdgedqg sxovh1 Qrwh wkdw wkh hohfwurq hplvvlrq lv qrw lqvwdqwdqhrxv/ zklfk frxog eh h{shfwhg gxh wr wkh uhodwlyho| vwurqj frxsolqj ehwzhhq wkh shuwxuehu dqg wkh vwuxfwxuhg frqwlqxxp+d frxsolqj ri D S63 fruuhvsrqgvwrdfrxsolqjwlphrifH Rr,1 Lqvwhdg Vwdun ehdwlqjv duh uhvroyhg hvshfldoo| wr wkh uhg vlgh ri wkh shuwxuehu1 Lw dsshduv wkdw wkh lrql}dwlrq g|qdplfv vwurqjo| ghshqgv rq zklfk zlqj ri wkh shuwxuehu rqh lv h{flwlqj= uhfxuuhqfhv duh vwurqjhvw zkhq rqh lv ghwxqhg iurpwkh shuwxuehu dqg wkh ryhudoo vwuxfwxuh lv vwurqjo| lq xhqfhg e| wkh fhqwudo zdyhohqjwk ri wkh lrql}lqj sxovh1 Dw wkh fhqwhu ri wkh shuwxuehu wkhuh vhhpv wr eh qr h hfw ri dqjxodu uhfxuuhqfhv dqg wkh vwuhdn wudfh vhhpv wr iroorz dq prqrwrqlf ghfd|1 Dw wkhvh wkuhh iuhtxhqf| srvlwlrqv zh kdyh shuiruphg Irxulhu Wudqvirupdwlrqv iurp wkh vshfwurvfrs| gdwd lq Ilj1 715/ dqg wkh uhvxowv duh ghslfwhg lq Ilj1 717 +vrolg olqh,1 Wkh
88 Irufhg Dxwrlrql}dwlrq
1600 V/cm; perpendicular polarization
blue
02040 middle
electron flux (arb. units) (arb. flux electron 02040 red
02040 time (ps)
Iljxuh 717= Wkuhh hohfwurq hplvvlrq wudfhv + oohg flufohv, wdnhq zlwk d :14 sv sxovh dw srvlwlrqv lq wkh iuhtxhqf| grpdlq fruuhvsrqglqj zlwk wkh odehov lq jxuh 7151 Uhg kdv d ghwxqlqj ri 04413 fp3 / plggoh d ghwxqlqj ri 415 fp3/ dqg eoxh d ghwxqlqj ri 4313 fp3 zlwk uhvshfw wr wkh shuwxuehu1 Hdfk wudfh lv frpsduhg wr wkhru| +grwwhg olqh,1 Dovr Irxulhu Wudqvirupv duh ghslfwhg +vrolg olqhv, dw wkh fruuhvsrqglqj srvlwlrqv lq wkh iuhtxhqf| grpdlq1 vwurqjhu uhfxuuhqfhv rq wkh uhg vlgh ri wkh shuwxuehu duh gxh wr wkh vkdus uhvrqdqfhv frpsduhg wr wkh zlqgrz uhvrqdqfhv rq wkh eoxh vlgh1 Wklv h hfw fdq dovr eh vhhq lq wkh Irxulhu Wudqvirupvshfwud1 Zh kdyh qrz surehg wkh zdyhixqfwlrq ri d wzr hohfwurq v|vwhperwkqhduwkhfruhdqgzkhqlwlvqhduwkhvdggohsrlqwzkhuhlwfdqdxwrlrql}h gxhwrwkh hog1Qrwhwkdwwkhuhfxuuhqfholihwlphlvqrwwkhvdphdvwkholihwlphghgxfhg iurphohfwurq hplvvlrq1 Wklv lv sduwlfxoduo| fohdu dw wkh eoxh vlgh/ zkhuh wkh rswlfdo sxps0 sureh h{shulphqw vxjjhvwv wkdw wkh olihwlph lv pxfk vkruwhu wkdq wkh vwuhdn wudfhv vkrz1 Lq idfw wkhvh phdvxuhphqwv vkrz wkdw wkh hohfwurq lv vwloo erxqg +vwloo vljqdo wr frph lq hohfwurq hplvvlrq, exw qrw qhdu wkh fruh +qr pruh vljqdo lq uhfxuuhqfh vshfwuxp,1 Zh dovr vwxglhg wkh h hfw ri fkdqjlqj wkh vdggoh srlqw srvlwlrq1 Ehfdxvh vwurqj hohfwulf hogvduhxvhgwkhvdggohsrlqwlvidudzd|iurpwkhuhohydqw9v"& vwdwhv lq hqhuj|/ dqg wkh ghwxqlqj ri wkh odvhu zklfk h{flwhv wr wkh 8g:g shuwxuehu kdv d qhjoljleoh h hfw rq wkh srvlwlrq lq hqhuj| ri wkh fuhdwhg zdyhsdfnhw deryh wkh vdggoh srlqw1 Wkhuhiruh rqh fdq lqyhvwljdwh wkh h hfw ri wkh vwdwlf hohfwulf hog +wkdw lv= wkh srvlwlrq ri wkh vdggoh
89 717 Pxowl0Fkdqqho Txdqwxp Ghihfw Wkhru|
02040
1600 V/cm
02040 1550 V/cm
electron flux (arb. units) (arb. flux electron 02040 1450 V/cm
02040 time (ps)
Iljxuh 718= Wkuhh hohfwurq hplvvlrq wudfhv zlwk }hur ghwxqlqj exw wdnhq zlwk gl huhqw hohfwulf hog vwuhqjwkv/ iru shushqglfxodu srodul}dwlrq1 Wkh hog0 vwuhqjwk lv nqrzq zlwk d 43( dffxudf|1 srlqw, dqg wkh ghwxqlqj lqghshqghqwo|1 Wkh hog dw zklfk wkh qq59 Vwdun vwdwhv duh dw wkh vdggoh srlqw lv :35 Y2fp+ 8 ' , dqg rqh zrxog h{shfw wkdw lw zloo eh kdughu iru S?e wkh zdyhsdfnhw wr hvfdsh ryhu wkh vdggohsrlqw/ dv wkh hog ghfuhdvhv wrzdugv wklv ydoxh1 Lq Ilj1 718 wklv h hfw lv lqghhg revhuyhg= wkh hohfwurq x{ h{whqgv rxw wr pxfk odwhu wlphv zkhq wkh shuwxuehu lv h{flwhg lq d hog zklfk eulqjv wkh shuwxuehu forvhu wr wkh vdggoh srlqw1 Dovr zh revhuyh wkdw hyhq wkrxjk zh duh h{flwlqj dw wkh fhqwhu ri wkh shuwxuehu/ uhfxuuhqfhv duh vwduwlqj wr dsshdu dw 4773 Y2fp/ zkloh dw kljkhu hog vwuhqjwkv wkh vwuhdn wudfhv dw wklv srvlwlrq vkrz d prqrwrqlf ghfd|1
717 Pxowl0Fkdqqho Txdqwxp Ghihfw Wkhru|
Wklv vhulhv ri h{shulphqwv zdv dovr vxssruwhg e| wkhru| dqg lq Ilj1 717 hdfk vwuhdn wudfh + oohg flufohv, lv frpsduhg wr wkh fdofxodwlrq +grwwhg olqh,1 Fohduo| zh kdyh vkrzq krz srzhuixo wkh wkhru| lv lq uhsurgxflqj wkh gdwd iurpwkh wzr h{shulphqwv1 Wkh fdofxodwlrqv duh edvhg rq wkh Pxowl0fkdqqho Vwdun Wkhru| ghyhorshg lq Uhi1 ^89/8:/8<`/ zklfk duh dovr ghvfulehg lq Fkdswhu 51 Wklv irupxodwlrq xvhv wkh ZNE wuhdwphqw ri wkh Vwdun sureohp
8: Irufhg Dxwrlrql}dwlrq
red middle
singlet singlet
triplet electron flux (arb. units) (arb. flux electron triplet
02040 02040 time (ps)
Iljxuh 719= Wkh wzr sdqhov vkrz wkh fdofxodwhg fkdudfwhu ri wkh hohfwurq x{ dw gl huhqw hqhujlhv +odehov ri jxuh 5,1 Fohduo| vlqjohw0wulsohw pl{lqj lv revhuyhg/ hvshfldoo| iru wkh uhg fdvh1 ghyhorshg e| Kduplq ^75/88` wr rewdlq wkh glsroh pdwul{ hohphqwv dqg wkh zdyh ixqfwlrq idu iurpwkh qxfohxv1 Zlwk wklv lqirupdwlrq dqg wkh dv|pswrwlf irupri wkh zdyh ixqfwlrq/ zh fdofxodwh wkh wlph0ghshqghqw x{ ri hohfwurqv zkhq wkh v|vwhp lv h{flwhg e| d sxovhg odvhu1 Suhylrxv +qrqg|qdplfdo, wkhruhwlfdo lqyhvwljdwlrqv ri qrq0dondol dwrpv lq h{whuqdo hogv duh ghvfulehg lq Uhiv1 ^84/ 9398`1 Wkh fdofxodwlrq surfhhgv lq wzr vwdjhv1 Lq wkh uvw vwdjh/ zh rewdlq wkh }hur0 hog glsroh pdwul{ hohphqwv dqg N0pdwulfhv iru Ed e| voljkwo| prgli|lqj wkh uhvxowv iurp dq U0pdwul{ fdofxodwlrq lq OV0frxsolqj ^8<`1 Wkh vslq0ruelw h hfwv duh lqfrusrudwhg e| xvlqj dq OV wr mT iudph wudqvirupdwlrq iru wkh glsroh pdwul{ hohphqwv dqg wkh N0pdwulfhv dqg xvlqj wkh h{shulphqwdo wkuhvkrog hqhujlhv wr rewdlq wkh }hur0 hog U|gehuj vwdwhv dw wkh fruuhfw hqhujlhv1 Lq wkh vhfrqg vwdjh/ wkh zdyh ixqfwlrqv lq vskhulfdo frruglqdwhv duh wudqviruphg lqwr sduderolf frruglqdwhv ^75/ 88` wr dffrxqw iru wkh h hfwv iurp wkh hohfwulf hog lq d qrqshuwxuedwlyh pdqqhu1 Wkh wlph0ghshqghqw x{ ri hohfwurqv lqwr wkh vwuhdn fdphud lv vlpxodwhg e| vxshusrvlqj wkh hqhuj|0ghshqghqw zdyh ixqfwlrqv zlwk wkh dssursuldwh frh!flhqwv zklfk duh wkh glsroh pdwul{ hohphqwv dqg wkh hqhuj|0ghshqghqw dpsolwxgh iru wkh skrwrq ^89/ 8:`1 Lq d suhylrxv lqyhvwljdwlrq ^84` ri wkh vdph v|vwhp d vlpsohu prgho jdyh txdqwlwdwlyh djuhhphqw gxh wr orzhu uhvroxwlrq dqg wkh dssolfdwlrq ri kljkhu hog vwuhqjwkv zklfk lqgxfhg udslg hog lqgxfhg lrql}dwlrq1 Zlwk wkh khos ri wklv h{whqghg wkhru| zh duh qrz deoh wr sureh wkh h hfw ri pl{lqj zklfk frxog qrw eh uhwulhyhg iurpwkh h{shulphqwv1 Zh irfxvhg hvshfldoo| rq wkh vlqjohw0 wulsohw pl{lqj ri wkh 9v"& fkdqqhov1 Wkh wzr uhohydqw fkdqqhov duh ghqrwhg dv wkh 9vqg (2 dqg wkh 9vqg (2 fkdqqho1 Lq Ilj1 719 d vxusulvlqj h hfw lv vkrzq1 Wkh wzr judskv vkrz wkh fdofxodwlrqv ri wkh hohfwurq x{ zlwk hlwkhu vlqjohw ru wulsohw fkdudfwhu1 Lw dsshduv
8; 718 Glvfxvvlrq dqg Frqfoxvlrqv wkdw hyhq wkrxjk li rqh lqlwldoo| h{flwhv pdlqo| vlqjohw fkdudfwhu +uhg srvlwlrq,/ qhduo| doo wkh hohfwurq x{ frplqj rxw dw odwhu wlphv lv gxh wr pl{lqj ri vlqjohw fkdudfwhu lqwr wulsohw/ zkloh wkh vlqjohw fkdudfwhu ghfd|v doprvw lqvwdqwdqhrxvo|1 Dssduhqwo| rqo| wkh vkdus uhvrqdqfhv kdyh d orqj hqrxjk olihwlph wr dftxluh vxevwdqwldo pl{lqj1 Wkhuhiruh dw wkh shuwxuehu/ zkhuh wkh ghfd| lv uhodwlyho| idvw/ wkh vlqjohw0wulsohw pl{lqj lv vwurqjo| vxssuhvvhg1 Wkh h hfw lv wkh vwurqjhvw wr wkh uhg vlgh ri wkh shuwxuehu zkhuh lq wkh iuhtxhqf| vshfwuxpwkh vkdushvw uhvrqdqfhv zhuh vhhq1
718 Glvfxvvlrq dqg Frqfoxvlrqv
Lq frqfoxvlrq/ zh kdyh phdvxuhg wkh surfhvv ri irufhg dxwrlrql}dwlrq erwk lq wkh wlph0 dv lq wkh iuhtxhqf|0grpdlq1 Erwk h{shulphqwv uhyhdohg frpsohphqwdu| g|qdplfdo lqirupd0 wlrq/ zklfk frxog eh lqwhuolqnhg e| shuiruplqj Irxulhu Wudqvirupdwlrqv1 Vwdun ehdwlqjv duh revhuyhg lq erwk h{shulphqwv/ hyhq wkrxjk zh lqlwldoo| h{flwh d ghhso| erxqg grxeo| h{flwhg vwdwh +8g:g,1 Wkhruhwlfdo fdofxodwlrqv |lhoghg jrrg djuhhphqw iru erwk h{shu0 lphqwv1 Wkhuhiruh zh zhuh deoh wr xvh wkhru| dv d wklug wrro wr vwxg| wkh g|qdplfv lqyroyhg lq wkh irufhg dxwrlrql}dwlrq surfhvv1 Lq sduwlfxodu zh irfxvhg rq wkh h hfw ri wkh vlqjohw0wulsohw pl{lqj1 Lw dsshduv wkdw vlqjohw fkdudfwhu lrql}hv doprvw lpphgldwho| zkloh wkh ghfd| dw odwhu wlphv kdv pdlqo| wulsohw fkdudfwhu1
8<
Fkdswhu 8 Iuxvwudwhg Euhdnlqj
Zh uhsruw rq wkh revhuydwlrq ri vwdelol}dwlrq ri odvhu0h{flwhg uxelglxp Vwdun dwrpv deryh wkh fodvvlfdo lrql}dwlrq olplw zlwk wkh khos ri vkruw +< qv, xqlsrodu hohfwulf hog sxovhv1 Glsslqj wkh hog grzq iurp 73 Y2fp wr 3 Y2fp dqg edfn wr 73 Y2fp 63 qv diwhu wkh skrwrh{flwdwlrq lqwr wkh frqwlqxxp/ |lhogv d odujh erxqg vwdwh srsxodwlrq1
814 U|gehuj Dwrpv lq Wlph0Ghshqghqw Hohfwulf Ilhogv
Lq wklv Fkdswhu zh ghprqvwudwh wkdw wkh lrql}dwlrq ri d odvhu0h{flwhg U|gehuj vwdwh fdq eh iuxvwudwhg e| dq h{whuqdo wlph0ydu|lqj hohfwulf hog1 Iuxvwudwhg lrql}dwlrq kdv d forvh uhvhpeodqfh wr wkh uhfrpelqdwlrq ri d iuhh hohfwurq dqg dq lrq/ vlqfh d qhz erxqg vwdwh lv pdgh iurp d fodvvlfdoo| xqerxqg v|vwhp1 Lq idfw wklv vwxg| zdv shuiruphg dv d slorw vwxg| iru wkh ghyhorsphqw ri d qryho dqg frqwuroodeoh uhfrpelqdwlrq vfkhph dv glvfxvvhg lqFkdswhu9/:/dqg;1 Wkh ehkdylru ri U|gehuj dwrpv lq idvw rvfloodwlqj hohfwulf hogv kdv ehhq vwxglhg h{0 whqvlyho| e| vhyhudo jurxsv ^74/9<:8`1 Hvshfldoo|/ wkh lrql}dwlrq ehkdylru zlwk plfurzdyh hohfwulf hog sxovhv kdv ehhq ri lqwhuhvw1 Iru lrql}dwlrq ri U|gehuj dwrpv lq d vwdwlf hog/ wkh fruuhvsrqglqj hohfwulf hog 8 lv jlyhq e| 8 ' / dw plfurzdyh iuhtxhqflhv lrql}d0 S?e wlrq douhdg| rffxuv dw hogv dv orz dv 8 ' ^:7` +dwrplf xqlwv duh xvhg xqohvv vwdwhg ?D rwkhuzlvh,1 Lq d plfurzdyh hog vxffhvvlyh Odqgdx0]hqhu furvvlqjv ehwzhhq d Vwdun vwdwh iurpd fhuwdlq q0pdqlirog wr d Vwdun vwdwh iurp rqh kljkhu o|lqj q0pdqlirog fdxvhv wkh lrql}dwlrq wr rffxu1 Rqfh lq wkh frqwlqxxpvxffhvvlyh Odqgdx0]hqhu wudqvlwlrqv fdq vwloo rffxu zlwklq wkh olihwlph ri wkh frqwlqxxp vwdwhv +urxwh D lq Ilj1 814,1 Wkh txhvwlrq qrz ulvhv li wkh lqyhuvh surfhvv fdq dovr rffxu= zrxog lw eh srvvleoh wr lqgxfh erxqg vwdwhv zlwk plfurzdyh hogv vwduwlqj rxw lq d +vwdwlf, hog lqgxfhg frqwlqxxpdqg pdnh d Odqgdx0]hqhu furvvlqj wr pruh ghhso| erxqg vwdwhv e| kdoi ri d f|foh ri wkh plfurzdyh hog +urxwh E lq Ilj1 814,1 Dqg li wklv lv srvvleoh= grhv d plfurzdyh hog sod| dq lpsruwdqw uroh zkhq wkh hohfwurq lv lq wkh hog lqgxfhg frqwlqxxpB Ehqvn| hw do1 ^:;` uhsruwhg rq vlplodu uhfrpelqdwlrq vfkhphv xvlqj kdoi f|foh sxovhv lq wkh vxe0
94 Iuxvwudwhg Euhdnlqj
-30 n=60
) A
-1 -35 ? -40 B
-45 term energy (cm energy term
n=50 -50 4 F=1/16n
0 102030405060 field (V/cm)
Iljxuh 814= Vwdun0pds ri uxelglxp/ rqo| wkh orzhvw dqg kljkhvw n0vwdwhv ri hdfk q0pdqlirog duh vkrzq1 Wkh grwwhg olqh ghslfwv wkh srvlwlrq ri wkh fodvvlfdo lrql}dwlrq olplw1 Lq wkh h{shulphqwv wkh dwrpv duh skrwr h{flwhg deryh wkh hog lrql}dwlrq lqgxfhg wkuhvkrog dqg diwhu d {hg ghod| d xqlsrodu hog sxovh lv dssolhg/ zklfk glsv wkh hog grzq dqg edfn xs djdlq zlwklq < qv1 Wkh txhvwlrq ulvhv lq zkdw pdqqhu wkh lrql}lqj vwdwhv duh d hfwhg= wzr wudmhfwrulhv +D dqg E, duh vxjjhvwhg wr sod| d uroh1 slfrvhfrqg +WK}, uhjlph +Fkdswhu 6,1 Lq wklv fkdswhu zh uhsruw rq wkh uhpdundeoh qglqj wkdw dfwxdoo| xqlsrodu sxovhv lq wkh qdqrvhfrqg uhjlph fdq eh xvhg wr uhfrpelqh dq hohfwurq lq wkh hog lqgxfhg frqwlqxxpzlwk lwv sduhqw lrq1 Iru wkh WK} h{shulphqwv uhsruwhg lq Uhi1 ^:;` wkh kdoi0f|foh sxovh lv pxfk vkruwhu wkdq wkh NhsohuU ruelw shulrg dqg wkh dfwlrq ri wkh sxovh fdq eh ghvfulehg dv d prphqwxp nlfn= {R ' " 8_|1Iru 3" wkh qdqrvhfrqg hog sxovh uhsruwhg khuh/ wkh sxovhv duh uhodwlyho| vorz dqg d ghvfulswlrq lq whupv ri ohyho furvvlqjv vhhpv wr eh pruh dssolfdeoh1 Wkh vwxg| ri qryho vfkhphv wr uhfrpelqh iuhh sduwlfohv lv lqwhuhvwlqj iurp wkh srlqw ri ylhz wkdw wkhuh kdv vwloo qrw ehhq irxqg dq h!flhqw zd| wr uhfrpelqh dq lrq zlwk dq hohfwurq1
815 H{shulphqwdo Uhdol}dwlrq
Vfkhpdwlfdoo| wkh h{shulphqwdo surfhgxuh zh xvh lv dv iroorzv +vhh dovr Ilj1 815,= uvw zh h{flwh jdv0skdvh uxelglxpdwrpvzlwk dq ;0qv odvhu sxovh deryh wkh fodvvlfdo hog lqgxfhg vdggohsrlqw +8 ' ,/ wkhq zh dsso| dq xqlsrodu sxovh e| zklfk zh krsh wr S?e lqgxfh erxqg vwdwhv/ dqg qdoo| zh xvh Sxovhg Ilhog Lrql}dwlrq ^5/ 68` +SIL/ Fkdswhu 5, wr ghwhuplqh wkh erxqg iudfwlrq1 E| lqfuhdvlqj wkh hohfwulf hog judgxdoo| rqh fdq lrql}h d kljko| h{flwhg dwrpgxh wr wkh vxssuhvvlrq ri wkh lrql}dwlrq olplwe| wkh vwdwlf hohfwulf hog/ dqg wkh dprxqw ri erxqg vwdwh srsxodwlrq fdq eh ghwhuplqhg1 D wkhupdo dwrplf uxelglxpehdp+surgxfhg e| d uhvlvwlyho| khdwhg ryhq, lv srlqwhg lq ehwzhhq wzr
95 815 H{shulphqwdo Uhdol}dwlrq
Iljxuh 815= d= H{shulphqwdo frq jxudwlrq1 Uxelglxp lv h{flwhg lqehwzhhq wzr sdudooho fdsdflwru sodwhv1 Wkh fdwkrgh sodwh lv frqqhfwhg wr d vorz sxovh jhqhudwru iru SIL ghwhfwlrq +vhh wh{w,1 Wkh dqrgh sodwh lv frqqhfwhg wr d idvw sxovhjhqhudwru zlwk wkh dlg ri idvw frd{ldo olqhv1 e= Wlplqj vfkhph ri wkh h{shulphqw= dw w@3 d qv/ qduurzedqg/ odvhu sxovh lv xvhg wr h{flwh U|gehuj vwdwhv lq wkh ylflqlw| ri wkh vdggohsrlqw lq uxelglxp lq d vwdwlf hog ri 73 Y2fp1 Diwhu 63 qv wkh hog lv glsshg grzq wr }hur hog dqg edfn xs djdlq wr 73 Y2fp zlwklq < qv1 Diwhu q:83 qv dq hohfwulf hog udps lv dssolhg wr ghwhuplqh wkh iudfwlrq ri wkh h{flwhg vwdwh srsxodwlrq wkdw lv vwdelol}hg lq d erxqg vwdwh1 fdsdflwru sodwhv +gldphwhu= 83 pp/ wklfnqhvv= 4 pp,/ vhsdudwhg e| 4313 pp1 Wkh Ue dwrpv duh h{flwhg lq d qrq0uhvrqdqw wzr0skrwrq surfhvv e| phdqv ri d qduurzedqg +{b f2 fp3, g|h0odvhu sxovh deryh wkh fodvvlfdo lrql}dwlrq olplw lq d vwdwlf hog ri 73 Y2fp +vhh Ilj1 815d,1 Wkh sodwh ixuwkhvw dzd| iurpwkh ghwhfwru +d vhw ri plfur vskhuh sodwhv, lv frqqhfwhg wr d er{ wkdw jhqhudwhv wkh +vorz, yrowdjh udps iru wkh sxovhg hog lrql}dwlrq ghwhfwlrq+0733Ylq833qv,vxshulpsrvhgrqdqr vhwri073Y1Wkhsodwhforvhvwwrwkh ghwhfwru +wkh dqrgh sodwh, lv frqqhfwhg wr wkh KS ;474d sxovh jhqhudwru/ zklfk surgxfhv wkh < qv +IZKP, xqlsrodu sxovhv/ wkh dpsolwxgh ri zklfk frxog eh wxqhg iurp 4133 wr 83133 Y1 Wkurxjk wklv sodwh d kroh +gldphwhu= 43 pp, lv guloohg/ zklfk lv fryhuhg e| d julg wr plqlpl}h wkh glvwruwlrq rq wkh hohfwulf hog1 Dssur{lpdwho| 68 qv +yduldeoh, diwhu h{flwdwlrq/ wkh hog lv udpshg grzq wr 3 Y2fp dqg edfn xs wr 7313 Y2fp zlwklq < qv1 Ulqjlqj zdv plqlpl}hg e| pdwfklqj wkh lpshgdqfh ri wkh sxovh jhqhudwru wr wkh dqrgh sodwh e| xvlqj idvw frd{ldo olqhv frqqhfwhg rq wzr rssrvlwh vlghv ri wkh fdsdflwru sodwh +vhh Ilj1 815d,1 Rqh frd{ldo olqh zdv gluhfwo| frqqhfwhg wr wkh KS ;474d sxovh jhqhudwru zkloh wkh rwkhu zdv xvhg dv d prqlwru olqh wr phdvxuh wkh sxovh sur ohv dqg fdoleudwh wkh dpsolwxghv/ xvlqj dq dssursuldwh whuplqdwlrq +83 l,1 Dssur{lpdwho| :83 qv diwhu h{flwdwlrq/ wkh hog lv lqfuhdvhg wr 733 Y2fplq 833 qv wr hog lrql}h wkh erxqg vwdwhv fuhdwhg e| odvhu0h{flwdwlrq1 Wkh sdudphwhuv ydulhg dffxudwho| lq wklv h{shulphqw zhuh wkh iuhtxhqf| ri wkh g|h odvhu/ zklfk skrwr0h{flwhg uxelglxpdwrpv/dqg wkh ghod| ri wkh hog sxovh uhodwlyh wr wkh odvhu sxovh1
96 Iuxvwudwhg Euhdnlqj
1.0 delay time 30 ns
0.8
0.6 A
B 0.4 bound fraction bound 0.2 C
0.0 -40 -39 -38 -37 -36 -35 -34 term energy (cm-1)
Iljxuh 816= Erxqg vwdwh srsxodwlrq dv ixqfwlrq ri wkh iuhtxhqf| ri odvhu1 Wkh xqlsrodu sxovh zdv dssolhg 63 qv diwhu odvhu h{flwdwlrq1 Erwk srodul}dwlrqv ri wkh odvhu hog zlwk uhvshfw wr wkh vwdwlf hohfwulf hog duh vkrzq +rshq flufohv= sdudooho srodul}dwlrq/ rshq wuldqjohv= shushqglfxodu srodul}dwlrq,1 Wkh vrolg olqh uhsuhvhqwv wkh lqwhjudwhg SIL vljqdo dv d ixqfwlrq ri wkh zdyhohqjwk ri wkh h{flwlqj odvhu zkhq qr xqlsrodu hog sxovh lv dssolhg1 Wkh odehov D +H@06:17 fp3,/ E +H@06915 fp3,/ F +H@0691; fp3, duh pdunhuv zklfk zloo eh uhihuuhg wr odwhu rq1 Wkh yhuwlfdo grwwhg olqh ghslfwv zkhuh wkh fodvvlfdo lrql}dwlrq olplw lv dw 73 Y2fp1 816 H{shulphqwdo Uhvxowv= Iuxvwudwhg Lrql}dwlrq
Lq Ilj1 816 wkh rshq wuldqjohv dqg flufohv vkrz wkh uhfrpelqhg iudfwlrq/ iru shushqglfxodu dqg sdudooho srodul}dwlrq ri wkh odvhu0h{flwdwlrq zlwk uhvshfw wr wkh vwdwlf hohfwulf hog ri 73 Y2fp/ zkhq 63 qv diwhu h{flwdwlrq zh dsso| dq xqlsrodu sxovh zklfk glsv wkh hog grzq wr 3 Y2fpdqg edfn xs djdlq wr 73 Y2fpdv d ixqfwlrq ri wkh whuphqhuj|1 Lq d vwdwlf hohfwulf hog ri 7313 Y2fpwkh skrwrlrql}dwlrq wkuhvkrog lv orzhuhg e| 06;1: fp3/ wkhuhiruh vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ri 87 ru kljkhu lrql}h/ vlqfh wkh| duh deryh wkh hog0lqgxfhg vdggoh srlqw lq wkh prgl hg Frxorpe srwhqwldo1 Lq Ilj1 816 zh vkrz wkh uhfrughg erxqg vwdwh vljqdo dv d ixqfwlrq ri wkh zdyhohqjwk ri wkh h{flwlqj g|h odvhu lq d vwdwlf hohfwulf hog ri 7313 Y2fpzlwkrxw dq hohfwulf hog nlfn +vrolg olqh,1 D vkdus vwhs lv revhuyhg lq wkh SIL vljqdo dv d ixqfwlrq ri wkh zdyhohqjwk ri wkh h{flwlqj odvhu1 Dovr wkh srvlwlrq ri wklv vwhs djuhhv zlwk wkh wkhruhwlfdoo| suhglfwhg ydoxh ri wkh wkuhvkrog H @ H 1 Krzhyhu/zkhqzhudpswkh hoggrzqdqgedfnxsdjdlq f S?e diwhu h{flwdwlrq zlwk d odvhu sxovh zlwk d srodul}dwlrq shushqglfxodu wr wkh hohfwulf hog/ lw dsshduv wkdw zh duh deoh wr uhfrpelqh iuhh vwdwhv wr erxqg vwdwhv1 Ilj1 816 ghslfwv wklv h hfw= wkh vwhs ixqfwlrq vkdsh dw wkh srvlwlrq ri wkh vdggoh srlqw lq wkh vwdwlf hohfwulf hog fdvh wrwdoo| glplqlvkhv zkhq diwhu h{flwdwlrq lq d vwdwlf hohfwulf hog d xqlsrodu sxovh lv dssolhg/ lqglfdwlqj wkdw zh duh lqghhg deoh wr lqgxfh erxqg vwdwhv iurpvwdwhv deryh wkh hog lqgxfhg vdggoh srlqw1 Qrwh wkdw iru wkh shushqglfxodu fdvh/ hyhq iru h{flwdwlrq ri vwdwhv 8 fp3 deryh wkh vdggoh srlqw/ d erxqg iudfwlrq ri dw ohdvw 314 lv uhfrughg1
97 817 H{shulphqwdo Uhvxowv= Olihwlph Phdvxuhphqwv
time delay 30 ns 0.4
0.2 bound fraction bound
0.0 20 25 30 35 amplitude (V/cm)
Iljxuh 817= Erxqg iudfwlrq dv d ixqfwlrq ri wkh xqlsrodu sxovh dpsolwxgh1 Wkh xqlsrodu sxovh zdv dssolhg 63 qv diwhu odvhu h{flwdwlrq ri U|gehuj vwdwhv zlwk d whup hqhuj| ri H @ 6:=7 fp3 +srvlwlrq D lq Ilj1 816 ,1
Lq Ilj1 817 wkh erxqg iudfwlrq lv sorwwhg yhuvxv wkh dpsolwxgh ri wkh xqlsrodu sxovh iru d {hg zdyhohqjwk +srvlwlrq D lq Ilj1 816,/ vkrzlqj wkdw iru dpsolwxghv orzhu wkdq 58 Y2fp qr uhfrpelqdwlrq rffxuv1 Iru dpsolwxghv kljkhu wkdq 5: Y2fp surqrxqfhg rvfloodwlrqv duh revhuyhg1 Lq vhfwlrq 818 zh glvfxvv krz lqwhuihulqj sdwkzd|v lq wkh Vwdun0pds +vhh Ilj1 814, fdq |lhog vxfk rvfloodwlrqv1
817 H{shulphqwdo Uhvxowv= Olihwlph Phdvxuhphqwv
Zh duh deoh wr h{wudfw lqirupdwlrq rq wkh olihwlph lqyroyhg lq wkh uhfrpelqdwlrq surfhvv/ zkhq zh { wkh zdyhohqjwk wr d ydoxh zklfk h{flwhv wkh uxelglxpdwrpvderyh wkh vdggoh srlqw dqg vfdq wkh ghod| wlph ri wkh xqlsrodu sxovh zlwk uhvshfw wr wkh wlph ri h{flwdwlrq1 Lq Ilj1 818 wkh erxqg iudfwlrq dv d ixqfwlrq ri wkh wlph ghod| iru gl huhqw ydoxhv ri wkh zdyhohqjwk ri wkh lrql}lqj odvhu lv ghslfwhg1 Zh djdlq fdq fohduo| vhh wkdw wkh olihwlphv ri wkh sdudooho h{flwhg vwdwhv duh vxevwdqwldoo| vkruwhu wkdq wkh olihwlphv lq wkh shushqglfxodu fdvh ^:<`1 Krzhyhu/ hyhq zhoo deryh wkh vdggoh srlqw wkhuh duh vwloo vwdwhv zklfk kdyh vxusulvlqjo| orqj olihwlphv iru erwk wkh sdudooho dqg iru wkh shushqglfxodu fdvh1 Wklv fdq eh xqghuvwrrg zlwk wkh khos ri vhpl0fodvvlfdo dujxphqwv= lq wkh fdvh ri sdudooho srodul}dwlrq hdfk vfdwwhuzdyh hyroyhv sduwldoo| wrzdugv wkh vdggoh srlqw +dorqj wkh srodul}dwlrq d{lv/ p@3,/ zkloh iru shushqglfxodu srodul}dwlrq qrw pxfk vfdwwhu zdyh wudyhov wrzdugv wkh vdggohsrlqw +pdlqo| p@5,1
818 Ruljlq ri wkh Rvfloodwlrqv
Rvfloodwlrqv zhuh revhuyhg +vhh Ilj1 818, iru xqlsrodu sxovh dpsolwxghv kljkhu wkdq 5: Y2fp1 Ehorz zh zloo glvfxvv wzr srvvleoh prghov ghvfulelqj wkhvh rvfloodwlrqv txdolwd0
98 Iuxvwudwhg Euhdnlqj
0.6 C; parallel B; perpendicular A; perpendicular 0.4
0.2 SFI signal (arb. un.) 0.0 10 20 30 40 50 60 70 80 90 time (ns)
Iljxuh 818= Wkh wkuhh wudfhv vkrz wkh erxqg vwdwh srsxodwlrq dv d ixqfwlrq ri wkh wlph ghod| ri wkh xqlsrodu hog sxovh zlwk uhvshfw wr wkh lrql}lqj odvhu sxovh1 Wkh odehov D/ E/ F fruuhvsrqg wr wkh pdunhuv lq Ilj18161 Wudfhv D dqg E uhsuhvhqw gdwd wdnhq zlwk shushqglfxodu srodul}dwlrq/ zkloh wudfh F uhsuhvhqwv gdwd wdnhq zlwk sdudooho srodul}dwlrq1 wlyho|1 Wkh uvw prgho dffrxqwv iru wkh skdvh dffxpxodwlrq ri lqglylgxdo Vwdun vwdwhv1 Gxulqj dq dyrlghg furvvlqj wkh zdyhixqfwlrq +[E| , zlwk dq dpsolwxgh S/fdqehvsolw 2 2 2 xs lqwr wzr vwdwhv zlwk wkh zdyhixqfwlrqv= @[E| dqg _[2E| +zlwk @ n _ ' S /vhh Ilj1 819,1 Vlqfh wkh hqhuj| ohyhov duh wlph ghshqghqw lq d wlph ydu|lqj hohfwulf hog +.E| ' n 8 E| ?&/zkhuh? lv wkh sulqflsdo txdqwxpqxpehu dqg & wkh sduderolf 2?2 2 txdqwxp qxpehu,/ wkh wzr zdyhixqfwlrqv dffxpxodwh wkhlu rzq dprxqw ri skdvh +,= 3.| 3 [E| 'e ' e 1 Li lq d dgglwlrqdo furvvlqj wkh wzr vwdwhv phhw djdlq/ wkh| fdq ghvwuxfwlyho| ru frqvwuxfwlyho| lqwhuihuh1 Frqvwuxfwlyh lqwhuihuhqfh rffxuv zkhq wkh skdvh gl huhqfh lv dq lqwhjhu pxowlsoh ri 2Z/ zkloh ghvwuxfwlyh lqwhuihuhqfh rffxuv zkhq wkh skdvh gl huhqfh lv dq lqwhjhu pxowlsoh ri Z ^:9`1 Zkhq wkh dpsolwxgh lv ydulhg lq wklv h{shulphqw/ wkh udps udwh +_8 , lv ydulhg/ dqg wkxv wkh dprxqw ri skdvh froohfwhg e| wkh _| gl huhqw vwdwhv lv ydulhg1 D urxjk hvwlpdwlrq ri wkh skdvh gl huhqfh gxh wr furvvlqjv lq wkh Vwdun0pds iru vwdwhv zlwk d sulqflsdo txdqwxp qxpehu ri ? 'Df/ fdq eh grqh zlwk wkh iroorzlqj h{suhvvlrq/ e| wdnlqj rqo| lqwr dffrxqw wkh uhgghvw +& ' ?,dqgwkheoxhvw +& ' ?, vwdwhv ri wzr dgmdfhqw ?0pdqlirogv=
{8 {8 2?2 { '{.{| r e {8?& 'S +814, 2 7 7 zlwk {8 wkh hohfwulf hog gl huhqfh ehwzhhq wzr frqvhfxwlyh furvvlqjv +r f Y2fp,/ dqg 7 wkh vohz udwh ri wkh hohfwulf hog sxovh1 Iru d vohz udwh ri ef TS63?r3 wklv skdvh gl huhqfh lv 316 udg1 Shdnv +frqvwuxfwlyh lqwhuihuhqfh, duh uhwulhyhg zlwk d shulrg ri {8 r 2 Y2fp+vhh Ilj1 818,/ wklv zrxog fruuhvsrqg wr d skdvh gl huhqfh ri 9 udg zklfk lv yhu| forvh wr 2Z/ zkhuh zh zrxog h{shfw frqvwuxfwlyh lqwhuihuhqfh djdlq1 Zh wkhuhiruh sursrvh wkdw wkh rvfloodwru| ehkdylru frxog eh gxh wr lqwhuihuhqfh h hfwv lq wkh Vwdun0pds lqgxfhg e| dyrlghg furvvlqjv1
99 818 Ruljlq ri wkh Rvfloodwlrqv
-1.95 1.0 a level 1 level 1 ∆φ b -2.00 level 2 a.u.) -4 -2.05
0.5
interference -2.10
-2.15 populated fraction populated binding energy (x10 -2.20 level 2 0.0 0 4 8 12 16 20 0 4 8 12 16 20 time (ns) time (ns)
Iljxuh 819= Lqwhuihuhqfh e| d grxeoh Odqgdx0]hqhu furvvlqj1 d= Wkh grwwhg dqg vrolg olqh ghslfw wkh hqhuj| ghshqghqfh ri wzr gl huhqw vwdwhv dv d ixqfwlrq ri wlph1 Dq lqlwldo vwdwh +w, vsolwv xs lqwr wzr vwdwhv lq wkh uvw furvvlqj= d +w, dqg e 2+w,1 Wkh skdvh gl huhqfh +!, ri wkh wzr vwdwhv uhvxowv lq frqvwuxf0 wlyh ru ghvwuxfwlyh lqwhuihuhqfh zkhq wkh vwdwhv phhw djdlq diwhu wkh vhfrqg furvvlqj1 e= Srsxodwlrq ri wkh wzr vwdwhv dv d ixqfwlrq ri wlph/ ghwhuplqhg e| lqwhjudwlqj wkh Vfkuùglqjhu htxdwlrq +vhh wh{w, iru dq xqlsrodu sxovh dpsolwxgh ri 68 Y2fp1
Wr ydolgdwh wklv k|srwkhvlv wkh wlph ghshqghqw Vfkuùglqjhu htxdwlrq zdv lqwhjudwhg iru d wzr ohyho prgho lq zklfk wkh wzr lqglylgxdo ohyhov lqwhudfw= Y[E| | ' O[E| '.[E| c zlwk= O 'E.E| /2 Y| /2 .2E|
/zkhuh$ lv wkh frxsolqj ehwzhhq ohyho dqg ohyho / zkloh . lv wkh +wlph ghshqghqw, hqhuj| ri vwdwh 1 Wkh frxsolqj fdq eh hvwlpdwhg zlwk= / ' B6 /zlwkB wkh devroxwh ?e 6 ydoxh ri wkh txdqwxpghihfw + , ' 6,1 Iru uxelglxp B2 'f D/ zklfk ohdgv wr d frxsolqj ri q f3H dwrplf xqlwv1 Lq wkh prgho wkh wzr ohyhov zhuh wkh plggoh Vwdun vwdwh +& 'f, ri ? 'D/ w/ dqg wkh uhgghvw Vwdun vwdwh +& ' ? n,ri? 'D2/ zklfk kdyh dq dyrlghg furvvlqj dw q b Y2fp1 D Jdxvvldq sxovh vkdsh ri < qv gxudwlrq +IZKP, zdv xvhg wr ghvfuleh wkh wlph ghshqghqfh ri wkh hohfwulf hog1 Wkh hqhuj| ghshqghqfh ri wkh vwdwhv dv d ixqfwlrq ri wlph lv ghslfwhg lq Ilj1 819d iru wkh wzr vwdwhv iru dq xqlsrodu sxovh dpsolwxgh ri 68 Y2fp1 Dw w@3 wkh kljk hqhuj| vwdwh lv srsxodwhg dqg zh fdofxodwh wkh srsxodwlrq glvwulexwlrq ri wkh wzr vwdwhv diwhu dsso|lqj wkh xqlsrodu sxovh +vhh Ilj1 819e,1 Lq Ilj1 81:d wkh srsxodwlrq glvwulexwlrq dv d ixqfwlrq ri wkh dpsolwxgh lv sorwwhg1 Fohdu rvfloodwlrqv duh uhwulhyhg uhyhdolqj wkdw wkh h{shulphqwdoo| revhuyhg prgxodwlrqv frxog eh gxh wr lqwhuihuhqfh lq wkh Vwdun pds1 Lw vkrxog eh qrwhg wkdw wkh wzr0ohyho prgho lv dq ryhu vlpsol fdwlrq ri wkh h{shulphqw/ vlqfh idu pruh Vwdun vwdwhv duh lqyroyhg1 Wkh vhfrqg prgho lv edvhg rq wkh Odqgdx0]hqhu wkhru| +vhh dovr Fkdswhu 5, dqg dffrxqwv iru doo wkh Vwdun ohyhov iurp ? 'efwr ? 'Sflq wkh Vwdun pds1 Iluvw zh fuhdwh d Odqgdx0]hqhu julg ghwhuplqhg e| wkh hqhuj| ghshqghqfh ri Vwdun ohyhov ri vhyhudo q0 pdqlirogv zlwk uhvshfw wr hohfwulf hog +vhh Ilj1 814,1 Dw w@3/ zh vwduw rxw zlwk srsxodwlqj
9: Iuxvwudwhg Euhdnlqj
model 2 model 1 0.6 1.0 ω=2x10-9 a.u. level 1 ω=4x10-9 a.u. a.u.
-4 -9 0.4 ω=8x10 a.u.
0.5
0.2 populated fraction populated
level 2
a E<1.99x10 with fraction b 0.0 0.0 30 32 34 36 38 0 5 10 15 20 25 amplitude (V/cm) amplitude (V/cm)
Iljxuh 81:= Uhvxowv ri wkh wzr prghov glvfxvvhg lq wkh wh{w wr h{sodlq wkh rvfloodwlrqv lq Ilj1 8171 d= fdofxodwhg vwdwh glvwulexwlrq ri d wzr ohyho v|vwhp lq d wlph ydu|lqj hohfwulf hog/ xvlqj wkh Vfkuùglqjhu htxdwlrq1 e= Fdofxodwhg iudfwlrq ri wkh lqlwldo srsxodwlrq zklfk hqgv xs ehorz dq hqhuj| ri 4=<<433e d1x1/ xvlqj wkh Odqgdx0]hqhu dssur{lpdwlrq/ iru wkuhh gl huhqw ydoxhv ri wkh frxsolqj vwuhqjwk $1 rqh vshfl f vwdwh +? 'D/dqg& ' D $ . ' be f3e d1x1,lqdqhohfwulf hogri5: Y2fp1 Zkhq wkh hog lv ydulhg/ ohyho furvvlqjv ehwzhhq Vwdun vwdwhv zloo rffxu1 Zh gh qh
dqg 2 wr eh wkh srsxodwlrqv lq vwdwh 4 dqg 5 uhvshfwlyho| ehiruh d furvvlqj dqg dqg 2 wkh srsxodwlrqv diwhu d furvvlqj1 Zh zloo xvh wr eh wkh suredelolw| vwdwh 4 hyroyhv dgldedwlfdoo| lqwr vwdwh 5 diwhu wkh furvvlqj/ dqg ( wkh suredelolw| wkdw vwdwh 4 hyroyhv gldedwlfdoo| lqwr vwdwh 4 diwhu wkh furvvlqj1 Wkxv diwhu wkh furvvlqj wkh srsxodwlrqv duh=
' ( n 2 dqg 2 ' n ( 2
Wkh suredelolw| iru vwdwh 5 wr hyroyh lq vwdwh 4 lv / dqg iru vwdwh 5 wr hyroyh lq vwdwh 5 lv ( ' 1 Wkh suredelolw| iru d gldedwlf furvvlqj lv ghwhuplqhg e| wkh Odqgdx0]hqhu dssur{lpdwlrq= _. _. ( 'i TE2Z m/ m2 * 2 2 _| _|
_. zlwk _. wkh ghulydwlyh ri wkh Vwdun hqhuj| wr wlph= _. ' ?c& ' ?& _8 1 _| _| _| 2 _| Vxfk d fdofxodwlrq lv shuiruphg iru vhyhudo dpsolwxghv ri wkh xqlsrodu sxovh1 Diwhu hdfk fdofxodwlrq wkh srsxodwlrq zlwk dq hqhuj| ohvv wkdq . ' bb f3e d1x1 +wkxv pruh ghhso| erxqg wkdq wkh lqlwldo vwdwh, lv ghwhuplqhg1 Lq Ilj1 81:e wkh ghwhuplqhg srsxodwlrq +zlwk . bb f3e d1x1, lv sorwwhg dv d ixqfwlrq ri wkh dpsolwxgh iru dq xqlsrodu sxovh ri < qv +IZKP,1 Djdlq d prgxodwhg vljqdo lv uhwulhyhg/ exw wklv wlph qrw gxh wr lqwhuihuhqfh h hfwv ri wkh Vwdun vwdwhv1 Lqvwhdg wkh prgxodwlrq rffxuv gxh wr gl huhqw sdwkzd|v lq wkh Vwdun pds iru gl huhqw dpsolwxghv ri wkh xqlsrodu sxovh1
9; 819 Fulwlfdo Vohz Udwh 819 Fulwlfdo Vohz Udwh
Zh kdyh vkrzq wkdw d idvw hog nlfn gulyhv d vxevwdqwldo sduw ri wkh srsxodwlrq/ lqlwldoo| deryh wkh vdggohsrlqw dqg iuhh wr lrql}h/ edfn lqwr erxqg vwdwhv1 Hvshfldoo| lq wkh fdvh ri shushqglfxodu srodul}dwlrq zh dfklhyhg h!flhqw uhfrpelqdwlrq suredelolwlhv1 Wkh olihwlphv ri vwdwhv lq wkh hog lqgxfhg frqwlqxxp wkdw zhuh h{flwhg zlwk oljkw srodul}hg shushqglfxodu wr wkh hohfwulf hog duh rq wkh rughu ri whqv ri qdqrvhfrqgv zkloh wkh wlphv zhuh vkruwhu iru sdudooho srodul}dwlrq/ dowkrxjk vwloo lq wkh qdqrvhfrqg uhjlph1 Lq whupv ri Odqgdx0]hqhu furvvlqj +vhh dovr Fkdswhu 5, wkh revhuyhg h hfwv fdq rqo| eh xqghuvwrrg li zh iroorz sdwk E lq Ilj1 8141 Wklv phdqv wkdw zh duh shuiruplqj h{shulphqwv lq wkh gldedwlf uhjlph/ lpso|lqj wkdw wkh vohz udwh +{8 , ri rxu xqlsrodu sxovhv lv juhdwhu {| wkdq wkh fulwlfdo vohz udwh iru d gldedwlf sdvvdjh iurpd vwdwh l wr d vwdwh m1 Wklv fulwlfdo vohz udwh +VSo|, fdq eh fdofxodwhg zlwk wkh khos ri wkh iroorzlqj irupxod ^5`= /2 E?3e 2 7 ' f 2 ' ?3f +815, So| 2 YE. . *Y8 ? zkhuh /f lv wkh vl}h ri wkh dyrlghg furvvlqj dqg Y.*Y8 lv wkh ghulydwlyh ri wkh whup hqhuj| ri d fhuwdlq vwdwh dv d ixqfwlrq ri wkh hog1 Wkh frxsolqj /f fdqehzulwwhqdv / ' B6 /zkhuhB lv wkh devroxwh ydoxh ri wkh txdqwxpghihfw B +rqo| wdnlqj lqwr f ?e 6 , dffrxqw wkh frqwulexwlrq iurpwkh orzhvw , vwdwh= , ' 6,1 Li zh lqwurgxfh wkh idfwru 7 7So| +zkhuh V lv wkh vohz udwh ri wkh sxovhv xvhg lq rxu h{shulphqw, zh qg wkdw lq rxu fdvh +dw ? 'DD,wklvidfwrulv 7 ' e ETS63?r3 'ef / zklfk lqghhg sodfhv rxu 7So| f h{shulphqwv lq wkh gldedwlf uhjlph1 Zh zrxog olnh wr vwuhvv wkdw wkh SIL vljqdo fohduo| vkrzv wkdw zh lqgxfh erxqg vwdwhv iurpfodvvlfdoo| iuhh vwdwhv/ dqg wkdw wkh h hfwv vhhq lq wkh h{shulphqw duh qrw gxh wr olihwlph hqkdqfhphqw ri fodvvlfdoo| iuhh vwdwhv1 Krzhyhu zh glg revhuyh wkdw zlwk dp0 solwxghv orzhu wkdq 58 Y2fpzh zhuh qrw deoh wr lqgxfh erxqg vwdwhv1 Dssduhqwo| iru wkrvh dpsolwxghv wkh vohz udwh lv ehorz 7So| dqg qr gldedwlf sdvvdjh fdq eh pdgh1 Zkhq zh xvh odvhu udgldwlrq zklfk lv srodul}hg sdudooho wr wkh hohfwulf hog/ fuhdwlqj p @ fc uhfrpelqdwlrq lv vwurqjo| uhgxfhg1 Vwloo wkhuh lv 43 shufhqw ri wkh lqlwldo srsxodwlrq zklfk lv ehlqj uhfrpelqhg dw 06: fp3/5fp3 deryh wkh vdggohsrlqw1 Wkh olihwlph ri wkh vwdwhv skrwrh{flwhg zlwk sdudooho srodul}dwlrq lv frqvlghudeo| vkruwhu dqg wkxv d vpdoohu iudfwlrq vxuylyhv wkh 63 qv zdlwlqj wlph +h1j1 Eurhuv hw do1 ^:<`,1 Ehvlghv/ wkh 6 'ffkdudfwhu lqgxfhv odujhu dyrlghg furvvlqjv wkdq lq wkh fdvh ri shushqglfxodu sr0 odul}dwlrq +fuhdwlqj pdlqo| 6 '2,/ zklfk dovr pdnhv lw kdughu wr fuhdwh erxqg vwdwhv e| Odqgdx0]hqhu furvvlqjv1
81: Frqqhfwlrq wr Rwkhu H{shulphqwv
Ohw xv qrz uhfrqvlghu d plfurzdyh lrql}dwlrq h{shulphqw lq d vwdwlf hohfwulf hog= li diwhu d fhuwdlq vhw ri f|fohv ri d vlqjoh plfurzdyh sxovh/ d vxevwdqwldo sduw ri wkh ruljlqdoo| erxqg srsxodwlrq lv surprwhg wr wkh hog lqgxfhg frqwlqxxp/ lw zloo vwloo qrw lrql}h gxh
9< Iuxvwudwhg Euhdnlqj
-40
4 1/16n
-50
-60 )
-1 n = 40
-70
-80
-90 term energy (cm
-100
-110 0 50 100 150 200 250 Field (V/cm)
Iljxuh 81;= Vfkhpdwlf uhsuhvhqwdwlrq ri wkh h{shulphqw shuiruphg e| Ehqvn| hw do1 ^:;`1 D eurdgedqg rswlfdo sxovh lv xvhg wr h{flwh vwdwhv deryh wkh vdggohsrlqw lq d vwdwlf hohfwulf hog ri 545 Y2fp1 Diwhu dsso|lqj d kdoi f|foh sxovh ri derxw 418 nY/ wkh| zhuh deoh wr revhuyh erxqg vwdwhv lqgxfhg e| wkh WK} udgldwlrq1 Lq wklv fkdswhu zh dujxh wkdw wkh lqhylwdeoh vhfrqg kdoi f|foh/ fdq dovr sod| d vljql fdqw uroh/ ehfdxvh ri dgglwlrqdo uhglvwulexwlrq ri vwdwhv deryh wkh vdggoh0 srlqw diwhu wkh uvw xqlsrodu ihdwxuh/ d hfwlqj wkh uhfrpelqdwlrq vljqdo1 wr wkh uhodwlyho| orqj olihwlphv lqyroyhg1 Wkhuhiruh wkh Vwdun vwdwhv vwloo lqgxfh Odqgdx0 ]hqhu furvvlqjv lq wkh plfurzdyh hog uhvxowlqj lq Deryh Wkuhvkrog Lrql}dwlrq +DWL, ^;3` ehkdylru1 Deryh wkuhvkrog plfurzdyh lrql}dwlrq h{shulphqwv zhuh douhdg| shuiruphg e| Jdoodjkhu hw do1 ^;4/;5` lq wkh qrq0shuwxuedwlyh uhjlph zkhuh wkh lqwhqvlwlhv iurp rswlfdo DWL h{shulphqwv zhuh vfdohg grzq wr wkh plfurzdyh uhjlph1 Khuh/ zh vxjjhvw wkdw hyhq pxfk orzhu lqwhqvlwlhv ri plfurzdyh hogv lq d vwdwlf hohfwulf hog douhdg| vx!fh dv dq dowhuqdwlyh zd| wr lqgxfh DWL1 Dqrwkhu srlqw zruwk qrwlqj lv wkdw zh kdyh vhhq dq h hfw ri xqlsrodu sxovhv dv orqj dv < qv1 Jhqhudo xqlsrodu sxovh h{shulphqwv duh shuiruphg lq wkh vxe0slfrvhfrqg uhjlph/ zkhuh WK} kdoi0f|foh sxovhv zlwk dq dpsolwxgh ri wkh rughu ri 4 nY duh jhqhudwhg e| looxplqdwlqj eldvhg vhplfrqgxfwru zdyhuv zlwk d srzhuixo ihpwrvhfrqg odvhu sxovh ^;6`1 Ehdulqj lq plqg wkdw wklv kdoi0f|foh sxovh sursdjdwhv wkurxjk ydfxxp/ lw fdq qrw eh d uhdo kdoi f|foh sxovh e| Pd{zhoo*v odzv1 Lw vkrxog dw ohdvw kdyh dqrwkhu kdoi f|foh ri rssrvlwh srodulw| vr wkdw wkh sxovh kdv }hur lpsxovh1 Jhqhudoo|/ rqh vxssrvhv wkdw wklv vhfrqg xqlsrodu ihdwxuh kdv d zlgwk dw ohdvw dq rughu ri pdjqlwxgh odujhu wkdq wkh uvw dqg wkhuhiruh d pxfk orzhu dpsolwxgh/ wkxv frqwulexwlqj wr plqru h hfwv lq wkh dfwxdo h{shulphqw +d ghwdlohg vwxg| ri wkh h hfw ri wkh vhfrqg xqlsrodu ihdwxuh ri WK} sxovhv lv suhvhqwhg lq Fkdswhu 6,1 Krzhyhu zh kdyh vkrzq wkdw xqlsrodu sxovhv zlwk uhodwlyho| orqj zlgwkv dqg vpdoo dpsolwxghv fdq h hfw h{flwhg vwdwhv wr d juhdw h{whqw1 Ehorz zh dujxh wkdw vxfk d vhfrqg xqlsrodu ihdwxuh fdq frqwulexwh wr wkh uhfrpel0
:3 81: Frqqhfwlrq wr Rwkhu H{shulphqwv qdwlrq h hfwv revhuyhg lq wkh h{shulphqwv shuiruphg e| Ehqvn| hw do1^:;`lqwkhWK} uhjlph1 Lq wkrvh h{shulphqwv d eurdgedqg odvhu sxovh +{. 'ffp3, zdv xvhg wr h{flwh vwdwhv deryh wkh vdggoh srlqw lq d vwdwlf hog ri derxw 533 Y2fp1 Wkh| zhuh deoh wr uh0 frpelqh 8 shufhqw ri wkh jhqhudwhg h{flwhg vwdwhv zlwk wkh khos ri d WK} 8 nY kdoi0f|foh sxovh ghod|hg rq wkh rughu ri slfrvhfrqgv uhodwlyh wr wkh skrwrlrql}lqj odvhu sxovh1 Judsk0 lfdoo| wkh h{flwdwlrq vfkhph lv ghslfwhg lq Ilj1 81;1 Diwhu wkh uvw idvw xqlsrodu ihdwxuh uhglvwulexwlrq kdv rffxuuhg ri wkh h{flwhg vwdwhv1 Sduw ri wkhvh uhglvwulexwhg vwdwhv zloo eh yhu| forvh wr wkh vdggoh0srlqw zlwk srvlwlyh hqhuj|1 Wkh iudfwlrq ri wkh uhglvwulexwhg srsxodwlrq mxvw deryh wkh vdggoh0srlqw zloo ghshqg rq wkh hqhuj| wudqvihu ri wkh zdyh0 sdfnhw fuhdwhg e| wkh uvw idvw xqlsrodu ihdwxuh dqg wkxv e| wkh h{dfw wlplqj ri wkh ghod| ri wkh kdoi0f|foh sxovh1 Wkhvh vwdwhv zloo qrw frqwulexwh wr wkh uhfrpelqdwlrq vljqdo iru shuihfw xqlsrodu kdoi0f|foh sxovhv1 Edvhg rq wkh h{shulphqwv suhvhqwhg lq wklv fkdswhu zh eholhyh wkdw wklv vpdoo sruwlrq ri wkh srsxodwlrq lq wkh frqwlqxxp fdq ehfrph erxqg e| wkh vorzhu vhfrqg xqlsrodu ihdwxuh ri wkh WK} udgldwlrq1 Lq rwkhu zrugv/ gxh wr wkh vhfrqg vorzhu xqlsrodu ihdwxuh wkhuh lv vrph suredelolw| wkdw wkhvh vwdwhv zloo eh uhglvwulexwhg wr qhjdwlyh hqhuj|/ vr wkdw lw grhv frqwulexwh wr wkh erxqg vwdwh vljqdo1 Frqvlghu iru lqvwdqfh uhglvwulexwhg vwdwhv +diwhu wkh uvw idvw xqlsrodu ihdwxuh, lq wkh ylflqlw| ri= 0 '2.*.S@ 0419; +vfdohg hqhuj|/ vhh Ilj1 81;,/ zklfk fruuhvsrqgv lq rxu h{shulphqw wr d whup hqhuj| ri 0651: fp31 Zh hvwlpdwh wkh gxudwlrq +63 sv, dqg dpsolwxgh +483 Y2fp, ri wkh vhfrqg xqlsrodu ihdwxuh lq wkh h{shulphqwv ri Ehqvn| hw do1 e| uhtxlulqj wkdw wkh wrwdo lpsxovh vkrxog eh }hur/ dqg wkdw wkh gxudwlrq ri wkh vorzhvw vhfrqg xqlsrodu ihdwxuh lv uhvwulfwhg e| wkh sodwh vhsdudwlrq ryhu zklfk wkh vwdwlf hohfwulf hog lv dssolhg1 Wkh iudfwlrq 7 7So| +dw ? ' D,lvqrzDfff ETS63?r3 ' Dfff/ dqg wkhuhiruh wkhlu vhfrqg xqlsrodu ihdwxuh pdlqo| lqgxfhv gldedwlf ehkdylru/ mxvw dv lq rxu h{shulphqwv1 Rqh fdq vfdoh wkh gxudwlrq ri wkh vhfrqg ihdwxuh lq wkh sxovh ri wkh h{shulphqwv ri Ehqvn| hw do1 wr rxu q vwdwhv dv iroorzv= {8 vfdohv dv q3f/ zkloh {8 vfdohv dv q3e/wkhuhiruh{| vfdohv dv qS1Wklv {| phdqv wkdw d sxovh ri 63 sv gxudwlrq dw ? ' Dzrxog fruuhvsrqg wr d sxovh ri 318 qv dw ? 'DD/ zklfk lv lq idfw qrw idu r iurprxu frqglwlrqv1 Ixuwkhu h{shulphqwv duh uhtxluhg wr ghwhuplqh wkh uroh ri wkh vorz ihdwxuh lq wklv w|sh ri uhfrpelqdwlrq h{shulphqwv1 Lq vxppdu|/ zh kdyh revhuyhg uhfrpelqdwlrq ri Vwdun dwrpv e| xqlsrodu hog sxovhv1 Olihwlphv lq wkh rughu ri qdqrvhfrqgv kdyh ehhq phdvxuhg lpso|lqj wkdw Odqgdx0]hqhu wudqvlwlrqv lq wkh hog lqgxfhg frqwlqxxpduh srvvleoh lq d plfurzdyh hog/ jlylqj ulvh wr DWL1 Rvfloodwlrqv zhuh revhuyhg zkhq wkh dprxqw ri uhfrpelqhg srsxodwlrq zdv +h{shulphqwdoo|, uhfrughg dv d ixqfwlrq ri wkh xqlsrodu sxovh dpsolwxgh1 Wzr prghov duh suhvhqwhg zklfk jlyh d srvvleoh h{sodqdwlrq iru wkh revhuyhg rvfloodwlrqv1 D vxjjhvwlrq lv pdgh rq wkh frqwulexwlrqv ri qrq0xqlsrodu ihdwxuhv rq kdoi0f|foh WK} uhfrpelqdwlrq h{shulphqwv1
:4
Fkdswhu 9 Sxovhg Ilhog Uhfrpelqdwlrq
Zh suhvhqw d qryho dssurdfk wr wkh suhsdudwlrq ri qhxwudo +dqwl0,pdwwhu1 Wkh vfkhph lv edvhg rq uhfrpelqdwlrq ri d iuhh hohfwurq dqg dq lrq/ dqg fdq eh frqvlghuhg dv wkh wlph lqyhuvh ri sxovhg hog lrql}dwlrq1 Zh kdyh rewdlqhg surplvlqj uhvxowv rq uxelglxp= dw orz ghqvlwlhv douhdg| h!flhqflhv ri 316 ( zhuh rewdlqhg1 Wklv lv rughuv ri pdjqlwxgh pruh wkdq kdv ehhq dfklhyhg lq suhylrxv uhfrpelqdwlrq vwxglhv1
914 D Qryho Uhfrpelqdwlrq Vfkhph
Wkh uhfrpelqdwlrq ri dq dqwl0surwrq zlwk d srvlwurq lv rqh ri wkh kxugohv lq wkh surfhvv ri pdnlqj qhxwudo dqwl0k|gurjhq dwrpv1 H{lvwlqj uhfrpelqdwlrq vfkhphv iru wkh irupdwlrq ri qhxwudo dwrpv vxfk dv glhohfwurqlf uhfrpelqdwlrq ^53/ ;7;;` dqg glvvrfldwlyh uhfrpel0 qdwlrq ^;<` fdqqrw eh xvhg gxh wr wkh devhqfh ri lqwhuqdo vwuxfwxuh ri wkh +dqwl0,surwrq1 Uhfrpelqdwlrq ri d surwrq dqg dq hohfwurq wr irup dq dwrp lv rqo| srvvleoh zkhq d wklug erg| wdnhv dzd| wkh h{fhvv hqhuj| ri wkh fdswxuhg hohfwurq +vhh dovr Fkdswhu 4,1 Wklv wklug erg| fdq eh d vshfwdwru/ lq zklfk fdvh wklv phfkdqlvp lv nqrzq dv wkuhh erg| uhfrpelqdwlrq +WEU, ^44/ 53`1 Lq rughu wr dfklhyh vl}hdeoh uhfrpelqdwlrq udwhv WEU lv vwxglhg lq kljk ghqvlw| sodvpdv dw orz whpshudwxuhv +7 N, ^44`1 Zkhq wklv wklug erg| lv d skrwrq/ wklv phfkdqlvp lv nqrzq dv udgldwlyh uhfrpelqdwlrq +UU, ^48`1 UU fdq eh vwlpxodwhg e| d odvhu0 hog +Vwlpxodwhg Udgldwlyh Uhfrpelqdwlrq/ VUU ^494;`, dqg eh0 frphv pruh h!flhqw iru orzhu odvhu iuhtxhqflhv +vfdolqj dv D3 , dqg whpshudwxuh ri wkh sodvpd*v1 Dqrwkhu uhfrpelqdwlrq vfkhph/ wkdw uholhv rq fkdujh h{fkdqjh zlwk srvlwurq0 lxpzdv vxjjhvwhg e| H1D1 Khvvhov hw do1 ^<3`1 Wkh| suhglfw d kljk uhfrpelqdwlrq udwh exw vr idu wklv vfkhph lv qrw uhdol}hg lq sudfwlfh1 Lq wklv Fkdswhu zh suhvhqw d wklug dqg h!flhqw phfkdqlvp iru wkh uhfrpelqdwlrq ri iuhh hohfwurqv zlwk iuhh lrqv/ xvlqj sxovhg hohfwulf hogv +D 314JK},1Wkhvfkhphlv vfkhpdwlfdoo| vnhwfkhg lq wkh xsshu sdqho ri Ilj1 9141 Dq lrq lv vlwxdwhg lq d vwdwlf hohfwulf hog1 Wkh vwdwlf hohfwulf hog prgl hv wkh Frxorpe srwhqwldo vxfk wkdw d vdggoh srlqw lv fuhdwhg +Ilj1 914d,1 Li dq hohfwurq sdvvhv ryhu wkh vdggoh srlqw lq wkh prgl hg Frxorpe srwhqwldo/ lw zloo wdnh d vpdoo/ exw qrw qhjoljleoh/ dprxqw ri wlph wr uhwxuq wr wkh vdggoh srlqw dqg hvfdsh iurpwkh lrq +Ilj1 914d,1 Li wkh vwdwlf hog lv wxuqhg r +Ilj1 914e, ehiruh
:6 Sxovhg Ilhog Uhfrpelqdwlrq
a b c e-
E A+ z
0.003 d
0.002
0.001 efficiency# ( Rb* / # Rb+ )
0.000 -15 -10 -5 0 5 10 15 closing pulse delay (ns)
Iljxuh 914= Vfkhpdwlf uhsuhvhqwdwlrq ri wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph= +d,= Dq lrq dzdlwv lq d vwdwlf hohfwulf hog dq hohfwurq/ zklfk lv ghfho0 hudwhg dqg kdv lwv wxuqlqj srlqw dw wkh lrq1 +e,= Zkhq wkh hohfwurq lv dw wkh wxuqlqj srlqw/ wkh hohfwulf hog lv txlfno| wxuqhg r 1 +f,= Li wkh hog lv wxuqhg r gxulqj wkh wxuqlqj ri wkh hohfwurq/ d erxqg vwdwh lv iruphg1 +g,= H{shulphq0 wdoo| revhuyhg h!flhqf| +qxpehu ri uhfrpelqhg dwrpv glylghg e| wkh qxpehu ri iuhh Ue lrqv, dv d ixqfwlrq ri wkh ghod| + , ri wkh txlfn wxuqr +418 Y2fp wr 315 Y2fp lq 413 qv,1
:7 915 H{shulphqwdo Uhdol}dwlrq wkh hohfwurq uhwxuqv wr wkh vdggoh srlqw/ lw zloo uhpdlq erxqg lq d kljko| h{flwhg vwdwh +Ilj1 914f,1 Lq wkh h{shulphqwv uhsruwhg lq wklv fkdswhu wkh hohfwurqv vwduw rxw zlwk d nlqhwlf hqhuj| ri 31:8 hY dqg duh ghfhohudwhg e| d vwdwlf hohfwulf hog ri 418 Y2fp/ vxfk wkdw wkh hohfwurqv kdyh wkhlu wxuqlqj dw wkh srvlwlrq ri d uxelglxplrq vrxufh1 Wkh wlph uhtxluhg iru wkh hohfwurq wr wudyho iurpwkh vdggoh srlqw/ wr wkh uxelglxpqxfohxv/ dqg edfn wr wkh vdggoh srlqw lv urxjko| 4 qv iru wkh hogv dqg hqhujlhv xvhg lq wklv h{shulphqw1 Lq Ilj1 914g wkh h{shulphqwdoo| ghwhuplqhg h!flhqf| +qxpehu ri uhfrpelqhg uxelglxp dwrpv glylghg e| wkh qxpehu ri iuhh uxelglxp lrqv, ri wklv vfkhph lv ghslfwhg dv d ixqfwlrq ri wkh ghod| ri wkh idvw hog wxuq r 1 Wklv ghod| lv zlwk uhvshfw wr wkh wlph zkhq wkh iuhh hohfwurq kdv lwv wxuqlqj srlqw lq wkh hohfwulf hog1 Fohduo|/ d pd{lpxp qxpehu ri uhfrpelqdwlrq hyhqwv lv uhfrughg dw }hur ghod|1 Qrwh wkdw h!flhqflhv xs wr f f3 duh rewdlqhg1 Zh zloo vkrz wkdw wklv vfkhph ri Sxovhg Ilhog Uhfrpelqdwlrq +SIU, fdq zrun iru dq| dwrp1 SIU grhv qrw uho| rq fruh0vfdwwhulqj/ dulvlqj iurp txdqwxp ghihfwv ri qrq0 k|gurjhqlf dwrpv ^5`1 Dv zh vkrz odwhu/ wkh SIU vfkhph surgxfhv dq dwrp lq d U|gehuj vwdwh/ d vwdwh zlwk d kljk sulqflsdo txdqwxpqxpehu + q r 2ff,^5`1SIUfdqehylhzhgdv wkh lqyhuvh surfhvv ri Sxovhg Ilhog Lrql}dwlrq ^5/68` +glvfxvvhg lq Fkdswhu 5,/ lq zklfk d sxovhg hohfwulf hog lrql}hv d U|gehuj vwdwh1 Wkh odwwhu surfhvv lv xvhg lq dwrplf sk|vlfv wr ghwhuplqh wkh sulqflsdo txdqwxp qxpehu ri d U|gehuj vwdwh ^63`/ dqg lq sk|vlfdo fkhp0 lvwu| lw irupv wkh edvlv ri ]HNH0vshfwurvfrs| ^6:/ 6;`/ ghwhuplqlqj wkh skrwrlrql}dwlrq srwhqwldo dqg yleudwlrqdo vwuxfwxuh ri odujh prohfxohv1
915 H{shulphqwdo Uhdol}dwlrq
Wkh SIU vfkhph zdv h{shulphqwdoo| uhdol}hg dv iroorzv= d sxovhg hohfwurq vrxufh ^<4` zdv fuhdwhg e| skrwrlrql}lqj olwklxpdwrpvlq d vwdwlf hohfwulf hog ri 4183 Y2fp/zlwk d sxovhg +< qv gxudwlrq, qduurzedqg +{b 315 fp3, g|h odvhu +rshudwlqj dw 63 K},1 W|slfdoo| hohfwurq sxovhv ri < qv gxudwlrq/ zlwk derxw ED 2 fe hohfwurqv lq d yroxph ri 3135 pp zhuh surgxfhg1 Wkh hohfwulf hog lv fuhdwhg e| wzr sdudooho fdsdflwru sodwhv +vhsdudwlrq= 4313 pp, ryhu zklfk d yrowdjh lv dssolhg +Ilj1 915d,1 Wkh lrql}lqj odvhu sxovh lv irfxvvhg wr d gldphwhu ri 83 >p wr plqlpl}h wkh hqhuj| vsuhdg ri wkh fuhdwhg hohfwurq sxovhv1 Diwhu lrql}dwlrq/ wkh iuhh hohfwurqv duh sxvkhg wrzdugv wkh dqrgh sodwh +frqqhfwhg wr jurxqg, wkurxjk zklfk d vpdoo kroh lv guloohg/ fryhuhg e| d julg1 Diwhu sdvvlqj wkurxjk wkh dqrgh/ wkh hohfwurqv hqwhu d hog0iuhh uhjlrq ri 4813 pp/ diwhu zklfk dqrwkhu vhw ri sdudooho fdsdflwru sodwhv +zlwk vpdoo krohv/ fryhuhg e| d julg, lv vlwxdwhg1 Vlqfh wkh qdo sodwh lv rq 04183 Y wkh hohfwurqv wxuq durxqg kdoizd| ehwzhhq wkhvh sodwhv/ vhsdudwhg e| 4313 pp1 Lq wklv uhjlrq d forxg ri uxelglxp lrqv lv dzdlwlqj wkh hohfwurqv1 Wr plqlpl}h wkh vsuhdg ri wkh hohfwurqv gxulqj wkhlu wudyho wrzdugv wkh lrqv lq gluhfwlrqv shushqglfxodu wr wkh gluhfwlrq ri sursdjdwlrq/ d pdjqhwlf hog zdv lpsohphqwhg/ sdudooho wr wkh gluhfwlrq ri sursdjdwlrq +E5 @ 518 pW,1 W|slfdoo| ED 2 f Ue lrqv zhuh surgxfhg lq d yroxph ri 513 pp 1 Wkh lrqv zhuh surgxfhg e| skrwrlrql}lqj uxelglxp dwrpv lq d vwdwlf hohfwulf hog ri 4183 Y2fp/ 83 qv ehiruh wkh olwklxp dwrpv zhuh lrql}hg/
:8 Sxovhg Ilhog Uhfrpelqdwlrq
A Photoionized electrons Rb ions detector
y
x z -1.50 V 0.00 V SFI-field quick turnoff
τ
B
Iljxuh 915= d= H{shulphqwdo vhwxs1 D vwdwlf hohfwulf hog ri 4183 Y2fp sxvkhv hohfwurqv wrzdugv wkh uxelglxp lrq uhjlrq/ zkhuh wkh lrqv dzdlw wkh hohfwurqv lq dq rssrvlwh hohfwulf hog1 Wkh fdwkrgh sodwh lv frqqhfwhg wr d idvw sxovh jhqhudwru vr wkh hog fdq eh wxuqhg ri zlwklq 317 qv wr < qv1 Wkh dqrgh sodwh lv frqqhfwhg wr d vorz sxovh jhqhudwru iru VIL ghwhfwlrq1 e= Wlplqj vfkhph ri wkh h{shulphqw1 Wkh judsk vkrzv wkh hohfwulf hog dv d ixqfwlrq ri wlph lq wkh lrq uhjlrq dqg zkhq wkh hohfwurqv dqg lrqv zhuh fuhdwhg e| skrwrlrql}dwlrq1 lq d wzr0skrwrq surfhvv1 Wkh iuhtxhqf| grxeohg rxwsxw ri d Qg=\DJ odvhu zdv xvhg iru wklv wzr0skrwrq surfhvv +5{865 qp,/ uhvxowlqj lq lrql}hg hohfwurqv zlwk dq lqlwldo yhorflw| ri e fD p2v1 Wkhuhiruh/ doo wkh hohfwurqv ruljlqdwlqj iurp lrql}hg uxelglxp dwrpv kdyh ohiw wklv lqwhudfwlrq uhjlrq dw wkh wlph wkh olwklxp skrwrhohfwurqv duh fuhdwhg1 Qrwh wkdw wkh khdy| uxelglxplrqv duh yluwxdoo| vwdqglqj vwloo gxulqj rxu h{shulphqw + {, @4>p lq 433 qv,1 Wkh vkdsh ri wkh lrq forxg lv 9 pp lq wkh }0 dqg {0gluhfwlrq/ dqg 93 >plq wkh |0gluhfwlrq1 Lq wkh lrq vrxufh uhjlrq wkh hohfwurqv duh ghfhohudwhg e| wkh hohfwulf hog ri 4183 Y2fp/ dqg kdyh wkhlu wxuqlqj srlqw dw wkh srvlwlrq ri wkh lrq forxg1 Dw wkdw wlph wkh hog lv wxuqhg r e| glsslqj wkh yrowdjh rq wkh fdwkrgh sodwh iurp04183 Y wr 03153 Y1 Wkh hohfwulf hog wxuq r lv uhdol}hg e| frqqhfwlqj dq lpshgdqfh pdwfkhg/ idvw sxovh jhqhudwru wr wkh fdwkrgh sodwh1 Gl huhqw sxovh jhqhudwruv zhuh xvhg wr vwxg| wkh h hfw ri gl huhqw idoo wlphv ri wkh hohfwulf hog +<3( $ 43( lq 317 qv/ 413 qv/ <13 qv uhvshfwlyho|,1
:9 916 H{shulphqwdo Uhvxowv dqg Fodvvlfdo Ghvfulswlrq
Wkh qxpehu ri Ue lrqv lv nhsw orz zlwk uhvshfw wr wkh qxpehu ri iuhh hohfwurqv wr suhyhqw wkh h hfw ri wudsslqj wkh hohfwurqv lq wkh dwwudfwlyh srwhqwldo ri wkh lrqv1 Iru D f lrqv lq d vskhuh zlwk d yroxph ri 513 pp / wkh hohfwurqv ihho dq dwwudfwlyh hog ri 443 pY2fp dw wkh hgjh ri wklv vskhuh1 Vxfk d orz ghqvlw| sodvpd lv wkhuhiruh qrw vwdeoh zkhq wkh lrq uhjlrq lv eldvhg diwhu wkh txlfn wxuq r wr dq hohfwulf hog ri 533 pY2fp1 Wkh h{shulphqwv zhuh shuiruphg lq d ydfxxp fkdpehu zlwk d edfnjurxqg suhvvxuh ri Df3. Wruu1
916 H{shulphqwdo Uhvxowv dqg Fodvvlfdo Ghvfulswlrq
Prvw uhfrpelqdwlrq surfhvvhv duh fkdudfwhul}hg e| furvv0vhfwlrqv1 Lq rxu SIU vfkhph lw lv pruh dssursuldwh wr jlyh wkh yroxph lq zklfk wkh hohfwurq kdv wr eh dw wkh prphqw ri wkh txlfn wxuq r wr uhfrpelqh zlwk wkh lrq1 Zh gh qh wkh lqwhudfwlrq yroxph T?| dv wkh yroxph ri vsdfh iru zklfk dq hohfwurq zlwk dq lqlwldo yhorflw| +3/3/y5, zloo uhfrpelqh zlwk wkh lrq diwhu wkh hohfwulf hog lv udpshg grzq wr 533 pY2fp> lw lv qrw qhfhvvdu| wr xvh d glvwulexwlrq lq yhorflw| gxh wr wkh yhu| orz h hfwlyh whpshudwxuh ri wkh hohfwurq vrxufh1 Wklv lqwhudfwlrq yroxph fdq eh hvwlpdwhg zlwk wkh iroorzlqj irupxod=
E '4J?4eTJeoT?| +914, zkhuh E lv wkh qxpehu ri uhfrpelqdwlrqv dw d fhuwdlq ghod| + , ri wkh txlfn wxuq r / 4J? lv wkh lrq ghqvlw|/ 4e lv wkh hohfwurq ghqvlw|/U TJeo lv wkh pdfurvfrslf ryhuods yroxph ri wkh hohfwurq0 dqg lrq forxg/ dqg T ' " sE| E| _| c zkhuh sE| ' t ?| 3" ?| e*?2 i TE 3|2e*?2 lv d ixqfwlrq zklfk ghvfulehv wkh wlph sur oh ri wkh hohfwurq sxovhv +k Zk2 k2 lv wkh gxudwlrq ri wkh hohfwurq sxovhv= < qv,1 W|slfdoo| wr kdyh 48 uhfrpelqdwlrq hyhqwv shu D fe hohfwurqvlqdqryhuodsyroxphri3135pp dqgdqlrqghqvlw|ri2D fS fp3 +wkhvh qxpehuv zhuh h{shulphqwdoo| uhdol}hg, wklv revhuyhg lqwhudfwlrq yroxph lv 3f E2 f f fp 1 D wkhruhwlfdo hvwlpdwh ri T?| lv rewdlqhg e| fodvvlfdoo| vroylqj Qhzwrq*v htxdwlrqv/ zlwk d irufh htxdo wr= 6E| '^E,E| nE| *S 1 Wkh hohfwulf hog +,, lv wkh vxshusrvlwlrq ri wkh Frxorpe srwhqwldo ri wkh lrqv dqg h{whuqdo hog/ lv wkh yhorflw| ri wkh hohfwurqv dqg lv wkh pdjqhwlf hog1 Dq lqwhudfwlrq yroxph ri f2D f3ffp lv irxqg iru d < qv hohfwurq sxovh/ zklfk djuhhv yhu| zhoo zlwk wkh hvwlpdwhg ydoxh iurp wkh h{shulphqwdo gdwd1 Zh qrwh wkdw wkh vsdwldo h{whqw ri vxfk dq lqwhudfwlrq yroxph fruuhvsrqgv wr U|gehuj vwdwhv durxqg ? 2ff1 D pruh ghwdlohg ghvfulswlrq ri wkh lqwhudfwlrq yroxph lv suhvhqwhg lq Fkdswhu :1 Qrwh wkdw wkh udglxv ri wkh lqwhudfwlrq yroxph lv wzr rughuv ri pdjqlwxgh vpdoohu wkdq wkh dyhudjh glvwdqfh ehwzhhq qhljkerulqj lrqv/ zklfk phdqv shuwxuedwlrqv iurp xquhfrpelqhg Uen lrqv duh qrwlpsruwdqwiruwklvh{shulphqw1 D ghwdlohg slfwxuh ri wkh vwdwh glvwulexwlrq ri wkh sxovhg hog uhfrpelqhg U|gehuj dwrpv zdv rewdlqhg e| Vhohfwlyh Ilhog Lrql}dwlrq ^5` +VIL/ vhh Fkdswhu 5,1 Lq vkruw/ wklv whfkqltxh pdnhv xvh ri wkh idfw wkdw U|gehuj vwdwhv ri dq dwrp fdq eh lrql}hg li d vwurqj hqrxjk hohfwulf hog lv dssolhg1 Wkh uhodwlrq ehwzhhq wkh ydoxh ri wkh hohfwulf hog dw
:: Sxovhg Ilhog Uhfrpelqdwlrq
n=200 n=142 n=123
a b 0.4 30 theory turnoff: ~0.4 ns experiment turnoff: ~1 ns -1 turnoff: ~9 ns
-1 20 ) / Vcm ) / 3
0.2 cm -10 10 # Rb* / Vcm / # Rb* (x10 int V
0.0 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 0.2 0.4 0.6 0.8 1.0 1.2 1.4 SFI field (V/cm) SFI field (V/cm)
Iljxuh 916= d= Fdofxodwhg vwdwh glvwulexwlrq ri wkh uhfrpelqhg U|gehuj dwrpv frpsduhg zlwk wkh h{shulphqwdo vwdwh glvwulexwlrq1 Wkh h{shulphqwdoo| gh0 whuplqhg lqwhudfwlrq yroxph ++413 31:,{433f fp , lv ydulhg zlwklq lwv huuru 3f wr rswlpl}h wkh frpsdulvrq zlwk wkhru| +Y ?| @ 316{43 fp ,1 e= Uhfrughg vwdwh glvwulexwlrq e| wkh Vhohfwlyh Ilhog Lrql}dwlrq +VIL, ghwhfwlrq vfkhph1 Wkh wkuhh fxuyhv vkrz wkh vwdwh glvwulexwlrq iru gl huhqw wxuqr wlphv1 zklfk hog lrql}dwlrq fodvvlfdoo| rffxuv dqg wkh sulqflsdo txdqwxpqxpehu q ri d vwdwh lv +lq dwrplf xqlwv,= 8 'E. 2 ' 1 Li wkh hohfwulf hog lv udpshg lq wlph dqg wkh 2 S?e hog dw zklfk U|gehuj dwrpv ghfd| lv prqlwruhg/ wkh srsxodwhg U|gehuj vwdwhv fdq eh dssur{lpdwho| ghgxfhg1 Wr fdofxodwh wkh VIL vshfwuxp/ zh sursdjdwhg Qhzwrq*v htxdwlrq zlwk wkh h{shulphqwdo udps udwh1 Lq rxu h{shulphqw zh xvh d hog udps ri 5133 Y2fp lq 41;3 >v/ 5 >r diwhu wkh idvw hog wxuq r +Ilj1 915e,1 Wkh hog udps sxvkhv wkh hog lrql}hg hohfwurqv wrzdugv wkh fdwkrgh sodwh wkurxjk zklfk d kroh zdv guloohg dqg fryhuhg zlwk d julg1 Wkh hohfwurqv duh uhfrughg e| d vhw ri Plfur0Vskhuh0Sodwhv +PVS*v,1 Lq wklv zd| zh uhfrug dw zklfk wlphv/ dqg khqfh dw zkdw hog vwuhqjwkv/ hohfwurqv duh ehlqj hog lrql}hg1 Gxulqj wkh wzr plfurvhfrqgv diwhu wkh txlfn wxuq r dqg ehiruh wkh VIL udps/ h hfwv ri WEU dqg UU duh uxohg rxw vlqfh wkh udwhv ri wkhvh surfhvvhv duh idu wrr orz dw rxu ghqvlwlhv +udwh v3,1 Pruhryhu zh fkhfnhg iru gl huhqw ghod|v ri wkh VIL hog zkdw wkh wrwdo dprxqw ri uhfrpelqdwlrqv zdv dqg wklv ydoxh glg qrw kdyh wkh whqghqf| wr lqfuhdvh iru orqjhu ghod|v1 Lq Ilj1 916d wkh VIL vwdwh glvwulexwlrq ri wkh 317 qv wxuq r lv frpsduhg zlwk wkhru|1 Qrwh wkh h{fhoohqw djuhhphqw ehwzhhq h{shulphqw dqg wkhru|1 Rqo| dw kljkhu VIL hogv +orzhu ?, wkhuh lv d vpdoo glvfuhsdqf| ehwzhhq h{shulphqw dqg wkhru|1 Wklv frxog eh gxh wr d voljkw gl huhqfh lq vkdsh ri wkh txlfn wxuq r xvhg lq wkh fdofxodwlrq dqg lq wkh h{shulphqw1 Wkh vkdsh ri wkhvh wudfhv vkrz wkdw uhfrpelqdwlrq wr yhu| kljko| h{flwhg vwdwhv lv prvwh!flhqw1 Iurpwkh fdofxodwlrqvs dq dyhudjh sulqflsdo txdqwxpqxpehu fdq eh uhwulhyhg= ?:'.f/zlwk{? ' ?2 : ?:2 '2 1 Wklv djuhhv zlwk wkh hvwlpdwhg lqwhudfwlrq yroxph/ zklfk suhglfwhg uhfrpelqhg vwdwhv lq wkh rughu ri ? ' 2ff1 Fdofxodwlrqv zlwk dqg zlwkrxw fruh vfdwwhulqj vkrzhg qr txdolwdwlyh dqg txdqwlwdwlyh
:; 917 Glvfxvvlrq dqg Frqfoxvlrqv gl huhqfh lq wkh uhfrpelqhg vwdwh glvwulexwlrq lqglfdwlqj wkdw wkh qrq0k|gurjhqlf Uen fruh sod|v qr uroh lq wkh fdswxuh vwhs1 Wkh SIU g|qdplfv zdv surehg hyhq ixuwkhu/ e| phdvxulqj wkh U|gehuj vwdwh glvwulex0 wlrq iru gl huhqw wxuqr wlphv ri wkh hohfwulf hog iurp04183 Y2fpwr 03153 Y2fpdw }hur ghod| +Ilj1 914g,1 Lq Ilj1 916e wkuhh vwdwh glvwulexwlrqv duh ghslfwhg iru gl huhqw hohfwulf hog wxuqr wlphv +dyhudjhg ryhu 4333 odvhu vkrwv,1 Dw wkh idvwhvw hog udps xvhg/ qrw rqo| pruh hohfwurqv duh uhfrpelqhg/ exw dovr wkh fdswxuhg vwdwh glvwulexwlrq h{whqgv wr pruh ghhso| erxqg vwdwhv1 Wklv fdq eh h{sodlqhg e| wkh idfw wkdw SIU uholhv rq wxuqlqj r wkh hog ehiruh wkh hohfwurq fdq uhwxuq wr wkh vdggohU srlqw1 Wkh fkdqjh lq hqhuj| ri wkhhohfwurqiurpwkhudpsgrzqriwkh hoglv{. ' e " E _8 5E| _| zkhuh 5E| lv wkh 3" _| wlph ghshqghqw }0frruglqdwh ri wkh hohfwurq1 Wkh wlph ghulydwlyh ri wkh hog lv d sxuho| qhjdwlyh ixqfwlrq1 Li _8 lv vkdus/ wkhq wkhuh zloo eh vrph wudmhfwrulhv iru zklfk }+w, lv _| sxuho| qhjdwlyh ryhu wkh zkroh zlgwk ri _8 1Li_8 lv eurdg/ 5E| zloo jr iurpsrvlwlyh/ wr _| _| qhjdwlyh/ dqg edfn wr srvlwlyh ryhu wkh zlgwk ri _8 1 Wkxv/ wkh idvw udps grzqv +vkdus _8 , _| _| jlyh odujhu hqhuj| orvvhv wkdq wkh vorz udps grzqv +eurdg _8 ,1 Pruhryhu/ wkh hohfwurq _| sxovhv lq wkh SIU h{shulphqw duh < qv orqj1 Idvwhu wxuqr v xvh d vpdoohu iudfwlrq ri wkh hohfwurq sxovhv iru uhfrpelqdwlrq/ uhvxowlqj lq d plvpdwfk ri wkh hohfwurq sxovh gxudwlrq dqg wkh gxudwlrq ri wkh idvw hog wxuqr 1 Zh dqwlflsdwh wkdw pdnlqj wkh hohfwurq sxovhv dv vkruw dv wkh wxuqr lq wlph zloo lqfuhdvh wkh h!flhqf| hyhq pruh1 Wkh frqqhfwlrq ri SIU fdq eh pdgh wrzdugv VUU lq wkh orz iuhtxhqf| grpdlq1 Rqh pryhv iurp d olplw zkhuh wkh rswlfdo shulrg lv pxfk vkruwhu wkdq wkh wlph g|qdplfv lq0 yroyhg lq wkh dwrplf v|vwhp +h1j1 wkh ruelwlqj shulrg ri wkh fdswxuhg hohfwurq,/ wr d uhjlrq zkhuh wkh hog sxovhv kdyh d gxudwlrq rq wkh rughu ri wkh wlph g|qdplfv lqyroyhg lq wkh dwrplf v|vwhp1 Wkhuhiruh wklv qryho phfkdqlvp fdq eh ehvw ghvfulehg dv dq lqwhuphgldwh ehwzhhq WEU dqg VUU/ lq zklfk qr sodvpdv duh uhtxluhg1
917 Glvfxvvlrq dqg Frqfoxvlrqv
D srwhqwldo dssolfdwlrq ri wklv qhz uhfrpelqdwlrq whfkqltxh lv wkh fuhdwlrq ri dwrplf dqwl0 k|gurjhq ^44/ <7/ <8`1 Revhuydwlrqv ri dwrplf dqwl0k|gurjhq duh uhsruwhg lq Uhi1 ^59/ <5`/ zkhuh d orz qxpehu ri dqwl0k|gurjhq dwrpv zhuh revhuyhg zlwk uhodwlylvwlf hqhujlhv1 Vr idu wkh prvw surplvlqj vfkhphv wr surgxfh frog dwrplf dqwl0k|gurjhq duh edvhg rq dfrpelqhgwuds^<6`/zkhuhrqhuholhvrqwkhlqwhudfwlrqehwzhhqsrvlwurqvdqgdqwl0 surwrqv dw yhu| orz uhodwlyh yhorflwlhv dqg orz whpshudwxuh1 Wr gdwh/ wkh vwxg| ri wkhvh uhfrpelqdwlrq vfkhphv lv grqh zlwk qrupdo pdwwhu1 Lq Uhi1 ^<7` vxfk d frpelqhg wuds lv ghvfulehg/ zkhuh w|slfdoo| :43D surwrqv dqg 43S hohfwurqv +fruuhvsrqglqj ghqvlw|= 43H fp3 , lq wkh frpelqhg wuds zhuh ghwhfwhg1 Krzhyhu/ xs wr qrz qr vxffhvvixo h{shulphqwv rq wkh irupdwlrq ri qhxwudo0 ru dqwl0pdwwhu kdyh ehhq uhsruwhg lq wklv frq jxudwlrq1 Zh iruhvhh wkdw wkh lpsohphqwdwlrq ri wkh wklug urxwh ri uhfrpelqdwlrq/ dv lqwurgxfhg khuh/ fdq lq idfw surgxfh d vl}hdeoh qxpehu ri uhfrpelqhg qhxwudo dqwl0pdwwhu dwrpv +lq d kljk U|gehuj vwdwh, lq wkh douhdg| uhdol}hg frpelqhg wuds1 Li wkh ryhuods yroxph lv pd{lpdo +wkh dqwl0surwrq sodvpd wdnhv xs wkh vdph yroxph dv wkh srvlwurq sodvpd,/ wkh srvlwurq
:< Sxovhg Ilhog Uhfrpelqdwlrq ghqvlw| lv 43.3H fp3 / dqg wkh qxpehu ri wudsshg dqwl0surwrqv lv 43D/ rxu vfkhph fdq surgxfh 432043 uhfrpelqhg dqwl0k|gurjhq dwrpv lq d vlqjoh h{shulphqw +dvvxplqj wkh vdph T?| dv lv revhuyhg lq rxu phdvxuhphqwv,1 Wkh h{dfw lpsohphqwdwlrq ri SIU iru wkh h{shulphqwdo uhdol}dwlrq ri dwrplf dqwl0k|gurjhq surgxfwlrq lv fxuuhqwo| lqyhvwljdwhg/ dqg glvfxvvhg lq Fkdswhu <1 Lq vxppdu|/ zh kdyh revhuyhg uhfrpelqdwlrq ri uxelglxp lrqv zlwk iuhh hohfwurqv zlwk wkh xvh ri idvw hohfwulf hog sxovhv1 Wkh surfhvv fdq eh vhhq dv wkh lqyhuvh surfhvv ri hog lrql}dwlrq1 H!flhqflhv dv kljk dv f3 kdyh ehhq dfklhyhg dqg d vlpsoh lpsuryhphqw +uhgxflqj wkh hohfwurq sxovh gxudwlrq plvpdwfk, fdq udlvh wkh h!flhqf| vljql fdqwo|1 Wkh revhuyhg h hfw fdq eh xqghuvwrrg zlwk dujxphqwv zklfk gr qrw uhtxluh phfkdqlvpv uho|lqj rq wkh pdjqlwxgh ri wkh txdqwxp ghihfwv ri qrq0k|gurjhqlf dwrpv/ lqglfdwlqj wkdw wkh SIU phfkdqlvp zrunv iru dq| dwrp1 Lq idfw lq Fkdswhu : zh uhsruw rq h{shulphqwv zkhuh Ol lrqv dqg iuhh hohfwurqv zhuh uhfrpelqhg zlwk wkh SIU vfkhph1 Pruhryhu zh sursrvh wkdw rxu vfkhph lv d surplvlqj dyhqxh iru wkh irupdwlrq ri qhxwudo dqwl0pdwwhu1 Dowkrxjk zh uhvwulfwhg wkh glvfxvvlrq lq wklv fkdswhu wr wkh uhfrpelqdwlrq ri uxelglxplrqv dqg hohfwurqv/ wkh whfkqltxh ri SIU lv lq sulqflsoh dovr dssolfdeoh iru wkh irupdwlrq ri qhxwudo prohfxohv/ vxfk dv FSf dv glvfxvvhg lq Fkdswhu ;/ dqlrqv ^<9`/ dqg lrq0sdlu vwdwhv ^<:`1
;3 Fkdswhu : Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
Wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph lv xvhg wr uhfrpelqh iuhh hohfwurqv zlwk Oln lrqv wr surgxfh qhxwudo Ol dwrpv lq d kljk U|gehuj vwdwh +? r Hf,1 Wkh h{shulphqwdo frqglwlrqv plplf vrph ri wkh frqglwlrqv xqghu zklfk rqh wulhv wr uhfrpelqh dqwl0surwrqv dqg srvlwurqv wr surgxfh frog dqwl0k|gurjhq1 Lq wkh fxuuhqw h{shulphqwv zh kdyh wudsshg hohfwurqv lq d Shqqlqj wuds + r D pW,1 Vxevhtxhqwo| wkhvh hohfwurqv zhuh uhfrpelqhg zlwk vsdwldoo| vhsdudwhg Oln lrqv1 Wkh uhfrughg h!flhqf| lv 513 ( yhuvxv 316 ( lq suhylrxv h{shulphqwv1 Vhyhudo h{shulphqwv zhuh shuiruphg wr vwxg| wkh g|qdplfv ri Sxovhg Ilhog Uhfrpelqdwlrq lq pruh ghwdlo1
:14 Wkh Sxuvxlw ri Dqwl0K|gurjhq
Lq wkh suhylrxv fkdswhu d qryho dqg frqwuroodeoh uhfrpelqdwlrq vfkhph zdv suhvhqwhg/ ghprqvwudwhg zlwk uxelglxp lrqv dqg iuhh hohfwurqv1 Wkh vfkhph zdv qdphg Sxovhg Ilhog Uhfrpelqdwlrq +SIU,/ vlqfh lw fdq eh vhhq dv wkh wlph lqyhuvh ri Sxovhg Ilhog Lrql}dwlrq ^5/68` +vhh dovr Fkdswhu 5,1 Lw zdv vwdwhg wkdw SIU frxog eh xvhg wr uhfrpelqh dq| vruw ri dwrpru prohfxoh zlwk iuhh hohfwurqv/ zlwk wkh srwhqwldo dssolfdwlrq wr fuhdwh dwrplf dqwl0k|gurjhq e| uhfrpelqlqj d iuhh srvlwurq zlwk dq dqwl0surwrq +iru dq ryhuylhz ri dqwl0pdwwhu vhh Fkdswhu 419,1 Lq wklv Fkdswhu qhz h{shulphqwv duh suhvhqwhg lq zklfk wkh SIU vfkhph lv vwxglhg lq pruh ghwdlo/ dqg lq d frq jxudwlrq uhvhpeolqj pruh wkh frqglwlrqv xqghu zklfk uhfrpelqdwlrq ri srvlwurqv dqg dqwl0surwrqv lv sxuvxhg1 Uhfrpelqlqj dq dqwl0surwrq dqg d srvlwurq lqwr dq dqwl0k|gurjhq dwrp hqdeohv wkh uvw kljk suhflvlrq frpsdulvrq ehwzhhq qhxwudo pdwwhu dqg dqwl0pdwwhu1 Wkh DWUDS dqg DWKHQD frooderudwlrqv dw FHUQ kdyh wkh suhvwljlrxv jrdo wr surgxfh frog +7 N, dqg wudsshg dqwl0k|gurjhq dwrpv lq rughu wr frpsduh dq dqwl0dwrp zlwk lwv frpsohphqwdu| dwrp= wkh k|gurjhq dwrp1 Suhflvh frpsdulvrqv duh d whvw iru wkh FSW wkhruhp zklfk vwdwhv wkdw qdwxuh lv lqyduldqw xqghu wkh frpelqhg rshudwlrqv ri Fkdujh frqmxjdwlrq/ Sdulw| frqmxjdwlrq dqg Wlph uhyhuvdo ^433435`1 Wklv phdqv wkdw hyhu| sduwlfoh vwdwh pxvw kdyh dq dqwl0sduwlfoh vwdwh zlwk htxdo pdvv/ vslq/ dqg olihwlph/ exw rssrvlwh pdjqhwlf
;4 Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds prphqw/ dqg fkdujh1 Pruhryhu judylw| h{shulphqwv rq qhxwudo dqwl0pdwwhu fdq whvw wkh Zhdn Htxlydohqfh Sulqflsoh ^436/437` zklfk vwdwhv wkdw d sduwlfoh ehkdyhv wkh vdph xqghu wkh lq xhqfh ri judylw| dv dq dqwl0sduwlfoh1 Qhxwudo dqwl0pdwwhu lv uhtxluhg iru wkhvh h{shulphqwv vlqfh wkh vpdoohvw vwud| hohfwulf dqg pdjqhwlf hogv douhdg| vwurqjo| lq xhqfh fkdujhg dqwl0pdwwhu sduwlfohv1 Zh uhsruw rq qhz h{shulphqwv xvlqj ruglqdu| pdwwhu wr vwxg| wkh uhfrpelqdwlrq g|qdplfv ri wkh SIU vfkhph1 Wkhuh zhuh irxu pdmru prwlydwlrqv iru shuiruplqj wkhvh h{shulphqwv1 Wkh uvw lv wkdw lq d w|slfdo SIU h{shulphqw rqh xvhv wkh lqhuwld ri dq lrq +zlwk uhvshfw wr wkh vpdoo lqhuwld ri dq hohfwurq, wr hqdeoh dq hohfwurq wr dssurdfk wkhlrqlqdvwdwlfhohfwulf hog1Rqhwkhuhiruhpljkwh{shfwwkdwdghfuhdvhlqwkh h!flhqf| ri wkh SIU vfkhph lv revhuyhg zkhq rqh wulhv wr uhfrpelqh iuhh hohfwurqv wr lrqv zlwk ohvv pdvv +vxfk dv d surwrq,1 Wr whvw li wkh SIU vfkhph frxog lqghhg eh xvhg wr uhfrpelqh oljkwhu lrqv zlwk iuhh hohfwurqv zh kdyh xvhg olwklxplrqv1 Olwklxpehlqj 45 wlphv oljkwhu wkdq uxelglxp/ uhvhpeohv pxfk pruh d surwrq/ dowkrxjk lw lv vwloo : wlphv khdylhu1 Wkh vhfrqg prwlydwlrq zdv wkdw wkh suhylrxv h{shulphqwv rq SIU zhuh shuiruphg lq d jhrphwu| idu gl huhqw iurp wkh jhrphwu| xvhg e| DWUDS dw FHUQ/ zkhuh rqh zloo vwxg| uhfrpelqdwlrq ri wudsshg srvlwurqv dqg wudsshg dqwl0surwrqv lq Shqqlqj wudsv ^43;444`1 Lq wkh suhylrxv h{shulphqwv zh surgxfhg hohfwurq sxovhv zlwk d zhoo gh qhg nlqhwlf hqhuj| e| skrwrlrql}lqj Ol dwrpv lq d vwdwlf hohfwulf hog e| phdqv ri d qduurz0edqg g|h odvhu/ lqvwhdg ri vwduwlqj rxw iurpwudsshg hohfwurqv1 Wkxv lq rughu wr vkrz wkdw wkh SIU vfkhph fdq lqghhg eh xvhg lq wkh jhrphwu| dw FHUQ zh kdyh exlog dq hohfwurq wuds1 D wklug prwlydwlrq zdv wr lqyhvwljdwh zkdw wkh h hfw lv ri d gl huhqw wrwdo txdqwxp ghihfw ri wkh uhfrpelqhg dwrpv rq wkh uhfrpelqdwlrq g|qdplfv1 Lw zdv vwdwhg ^<;` wkdw SIU fdq eh xvhg wr uhfrpelqh dq| vruw ri lrq zlwk d iuhh hohfwurq1 Olwklxp kdv d wrwdo txdqwxpghihfw ri 31785 + >f 'fec> 'ffDc>2 'fff2, dqg uxelglxpd wrwdo txdqwxpghihfw ri :148 + >f ' c> '2SDc>2 ' Dc> 'ff2,/ d frpsdulvrq ri wkh suhylrxv h{shulphqwv lq uxelglxp zlwk wkh fxuuhqw h{shulphqwv lq olwklxp frxog uhyhdo d ghshqgdqfh ri wkh uhfrpelqdwlrq g|qdplfv rq wkh wrwdo ydoxh ri wkh txdqwxp ghihfw1 Wkh odvw prwlydwlrq zdv wr lqfuhdvh wkh uhfrpelqdwlrq h!flhqf| ri wkh SIU vfkhph1 Zh uhsruw rq wkh ghwdlohg vwxg| ri wkh uhfrpelqdwlrq h!flhqf| lq d Shqqlqj wuds frq jxudwlrq dv d ixqfwlrq ri wkh whpshudwxuh ri wkh hohfwurqv lq wkh wuds dqg dv d ixqfwlrq ri wkh vwrudjh wlph ri wkh hohfwurqv lq wkh wuds1 Zh dovr vwxglhg zkhwkhu d pdjqhwlf hog lq wkh udqjh ri 43 0 93 pW fkdqjhg wkh uhfrpelqdwlrq g|qdplfv dqg wkh h hfw ri d vpdoo uhvlgxdo hohfwulf hog diwhu wkh uhfrpelqdwlrq hyhqw1 D wkhruhwlfdo ghvfulswlrq xvlqj vhpl0 fodvvlfdo fdofxodwlrqv lv suhvhqwhg1 Wkhvh vhpl0fodvvlfdo fdofxodwlrqv jlyh ghhshu lqvljkw rq wkh vwdwhv zklfk duh ehlqj iruphg lq wkh uhfrpelqdwlrq surfhvv dqg duh xvhg wr sureh wkh uhfrpelqdwlrq g|qdplfv qrw phdvxudeoh e| h{shulphqw1
:15 Vfkhph dqg H!flhqf|
Lq rughu wr vwxg| SIU rqh qhhgv hohfwurq sxovhv zlwk d zhoo gh qhg frqwuroodeoh hqhuj|/ iuhh lrqv zlwk olwwoh nlqhwlf hqhuj|/ dqg wkh delolw| wr txlfno| wxuq r wkh hohfwulf hog lq
;5 :15 Vfkhph dqg H!flhqf|
rubidium: Chapter 6 lithium: this chapter 0.020
0.016
0.012
0.008
0.004
efficiency (#recombinations/#ions)efficiency 0.000 -8 -4 0 4 8 closing pulse delay (ns)
Iljxuh :14= H{shulphqwdoo| revhuyhg h!flhqf| +qxpehu ri uhfrpelqhg dwrpv glylghg e| wkh qxpehu ri iuhh lrqv, dv d ixqfwlrq ri wkh ghod| ri wkh txlfn wxuqr 1 Wkh vrolg olqh uhsuhvhqwv gdwd wdnhq zkhuh zh vwxglhg uhfrpelqdwlrq ri iuhh hohfwurqv dqg olwklxp lrqv zlwk wkh xvh ri dq hohfwurq wuds1 Wkh gdvkhg olqh uhsuhvhqwv gdwd iurp suhylrxv zrun ^<;` +Fkdswhu 9, zkhuh zh vwxglhg uhfrpelqdwlrq ri iuhh hohfwurqv dqg uxelglxp lrqv lq d wudsohvv jhrphwu|1 zklfk wkh lrqv duh vlwxdwhg1 Wkh hohfwurq wuds frq jxudwlrq doorzhg xv wr surgxfh q7 qv hohfwurq sxovhv1 Wklv zdv dfklhyhg e| oolqj wkh hohfwurq wuds zlwk hohfwurqv dqg wkhq txlfno| rshqlqj wkh wuds/ uhvxowlqj lq d hohfwurq sxovh1 Lq wkh fxuuhqw h{shulphqwv wkh hohfwurqv ohdylqj wkh wuds kdyh d nlqhwlf hqhuj| ri 418 hY dqg duh ghfhohudwhg e| d vwdwlf hohfwulf hog ri 613 Y2fp/ vxfk wkdw wkh hohfwurqv kdyh wkhlu wxuqlqj dw wkh srvlwlrq ri d olwklxplrq forxg1 Wkh wlphuhtxluhg iru wkh hohfwurq wr wudyho iurpwkh vdggoh srlqw/ wr wkh olwklxpqxfohxv/ dqg edfn wr wkh vdggoh srlqw lv derxw 4 qv iru wkh hogv dqg hqhujlhv xvhg lq wklv h{shulphqw1 Wklv wlph lv frpsdudeoh wr wkh wxuq r wlph ri wkh vwdwlf hohfwulf hog +<3( $ 43( lq 31; qv,1 Lq Ilj1 :14 wkh h{shulphqwdoo| ghwhuplqhg h!flhqf| +qxpehu ri uhfrpelqhg dwrpv glylghg e| wkh qxpehu ri iuhh lrqv, ri wklv vfkhph lv ghslfwhg dv d ixqfwlrq ri wkh ghod| ri wkh idvw hog wxuq r 1 Wklv ghod| lv zlwk uhvshfw wr wkh wlph zkhq wkh iuhh hohfwurq kdv lwv wxuqlqj srlqw lq wkh hohfwulf hog1 Fohduo|/ d pd{lpxp qxpehu ri uhfrpelqdwlrq hyhqwv lv uhfrughg dw }hur ghod|1 D frpsdulvrq zlwk wkh suhylrxv h{shulphqwv zlwk uxelglxp lrqv vkrzv fohduo| wkdw wkh h!flhqf| + f f3 / Fkdswhu 9 ^<;`, kdv jrqh xs e| doprvw dq rughu ri pdjqlwxgh +2f f32, dqg wkdw wkh hohfwurq sxovhv duh pxfk vkruwhu1 Wkh lqfuhdvh lq h!flhqf| lv pdlqo| gxh wr wkh idfw wkdw wkh hohfwurq sxovhv duh vkruwhu lq wlph +iurp44 qv ^<;` wr 61; qv, dqg wkdw zh kdg ehwwhu frqwuro ryhu wkh ryhuods yroxphri wkh lrq forxg dqg wkh yroxph ri wkh hohfwurq sxovhv1 Zh dfklhyhg wkh kljkhvw h!flhqf| +9(, vriduzkhqzhxvhgwkhSIUvfkhphwruhfrpelqhdiuhhhohfwurqzlwkdiuhhlrqlffduerq foxvwhu lq d wudsohvv hqylurqphqw ^<<`1 Qrwh wkdw Ilj1 :14 vkrzv wkdw SIU fdq eh xvhg lq
;6 Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
-1.5 V -1.5 V calculated potential 7 0.14 harmonic potential ) 5 6
0.12 5 B ~35 mT B ~35
0.10 4 - -e 3 e 0.08 2 potential energy (eV) energy potential 0.06 y b (x 10 electrons trapped 1 c 0.04 0 x z 0 V a -1.0 -0.5 0.0 0.5 1.0 0.0 0.5 1.0 1.5 2.0 position along z-axis (mm) time (ms)
Iljxuh :15= d= Vfkhpdwlf uhsuhvhqwdwlrq ri wkh Shqqlqj wuds/ frqvlvwlqj ri wzr dw fdsdflwru sodwhv dqg wzr ulqj hohfwurghv1 Wkh olihwlph ri wklv wuds zdv phdvxuhg wr eh 418 pv dw d edfnjurxqg suhvvxuh ri 433S Wruu1 e= Vrolg olqh= d fdofxodwlrq ri wkh rq0d{lv srwhqwldo lqvlgh wkh Shqqlqj wuds xvlqj VLPLRQ/ vkrzlqj wkh kduprqlflw| ri wkh srwhqwldo +grwwhg olqh= kduprqlf srwhqwldo,1 f= Wkh qxpehu ri wudsshg hohfwurqv dv d ixqfwlrq ri wkh vwrudjh wlph1 Wkh olih0 wlph zdv pdlqo| d hfwhg e| wkh edfnjurxqg suhvvxuh1 Wkh plqlpxp uhtxluhg pdjqhwlf hog zdv 45 pW dqg lqfuhdvlqj wkh pdjqhwlf hog eh|rqg wklv ydoxh kdugo| d hfwhg wkh olihwlph ri wkh wuds1 jhrphwu| ri wudsshg hohfwurqv dqg oljkw lrqv1
:16 H{shulphqwdo Uhdol}dwlrq
Rxu Shqqlqj wuds frqvlvwv ri wzr vwdlqohvv vwhho sdudooho fdsdflwru sodwhv +wklfnqhvv 413 pp, ri 6313 pp lq gldphwhu dqg wzr vwdlqohvv vwhho ulqj hohfwurghv +wklfnqhvv 318 pp, zlwk dq rxwhu gldphwhu ri 6313 pp dqg dq lqqhu gldphwhu ri 713 pp +Ilj1 :15d,1 Wkh wzr sdudooho fdsdflwru sodwhv +hohfwurgh 4 dqg 7, duh vhsdudwhg e| 813 pp/ dqg d kroh ri 4313 ppzdv guloohg wkurxjk wkhpfryhuhg e| d julg/ vr wkdw hohfwurqv frxog sdvv wkurxjk wkhvh sodwhv/ exw wkh sodwhv vwloo ehkdyh dv dw fdsdflwru sodwhv1 Wkh wzr ulqj hohfwurghv zhuh sodfhg lq ehwzhhq wkh sdudooho fdsdflwru sodwhv +hohfwurgh 5 dqg 6,1 Wkh ulqj hohfwurghv duh vhsdudwhg iurphdfk rwkhu e| 513 ppdqg hdfk ulqj hohfwurgh zdv vhsdudwhg e| 413 pp iurp wkh forvhvw dw fdsdflwru sodwh1 D srwhqwldo zhoo zdv fuhdwhg lq wkh }0gluhfwlrq iru hohfwurqv li rqh eldvhg wkh wzr sdudooho fdsdflwru sodwhv zlwk d qhjdwlyh yrowdjh dqg li rqh eldvhg wkh ulqj hohfwurghv zlwk d kljkhu yrowdjh1 Lq wkhvh h{shulphqwv wkh sdudooho fdsdflwru sodwhv zhuh eldvhg e| d yrowdjh ri 0418 Y dqg wkh ulqj hohfwurghv zhuh eldvhg lq wkh udqjh ri 313 wr 03173 Y1 Wkh plqlpxp ri wkh srwhqwldo zhoo zdv uljkw lq ehwzhhq wkh wzr ulqj hohfwurghv/ dv vkrzq e| wkh VLPLRQ srwhqwldo fdofxodwlrq lq Ilj1 :15e1 Krzhyhu wkh hohfwurqv zrxog vwloo eh deoh wr hvfdsh wkh wuds lq wkh {0|0gluhfwlrq1 Wr suhyhqw wkh hohfwurqv iurphvfdslqj wkh wuds lq wkh {0|0gluhfwlrq/ d pdjqhwlf hog ri vhyhudo whqv ri pW lq wkh }0gluhfwlrq zdv xvhg1 Zh kdyh xvhg VLPLRQ ^46<` wr fdofxodwh wkh vkdsh ri wkh srwhqwldo zhoo rq wkh }0d{lv lq rughu wr ghvljq d sodwh frq jxudwlrq zklfk surgxfhv
;7 :16 H{shulphqwdo Uhdol}dwlrq dv pxfk dv srvvleoh d kduprqlf srwhqwldo lq rughu wr plplf wkh frqglwlrqv ri wkh DWUDS vhwxs dw FHUQ1 Zh oohg wkh hohfwurq wuds e| skrwr0lrql}lqj jdv0skdvh olwklxpdwrpv1 D mhw ri wkhvh dondol dwrpv frphv iurp d uhvlvwlyho| khdwhg ryhq1 Wkh olwklxp dwrpv zhuh lrql}hg e| phdqv ri wzr v|qfkurql}hg g|h odvhuv sxpshg e| wkh vhfrqg kduprqlf ri d Qg=\DJ odvhu +865 qp,/ zklfk surgxfhg odvhu sxovhv ri derxw : qv gxudwlrq zlwk d uhshwlwlrq udwh ri
43 K}1 Wkh uvw g|h odvhu zdv xvhg wr h{flwh wkh 5v hohfwurq wr wkh 5s*23 *2 vwdwh lq olwklxp+9:31<: qp/483 >M, dqg wkh vhfrqg g|h odvhu +wxqdeoh iurp ef Df qp/ 41; pM shu sxovh, zdv xvhg wr gulyh wkh wudqvlwlrq iurp wkh 5s vwdwh lqwr wkh frqwlqxxp1 E| frqqhfwlqj d idvw sxovh jhqhudwru rq sdudooho fdsdflwru sodwh 7 +Ilj1 :16d, wkh yrowdjh frxog eh vzlwfkhg iurp0418 Y wr .413 Y zlwklq ;33 sv rq wklv sodwh1 Wklv hqdeohg xv wr hpsw| wkh wuds dw dq| wlph/ dqg uhfrug wkh hohfwurqv rq d +plfur vskhuh sodwh, ghwhfwru1 Fduh zdv wdnhq iru fruuhfw lpshgdqfh pdwfklqj1 Lq wklv zd| wkh wlph ghshqgdqfh ri wkh qxpehu ri hohfwurqv dw dq| wlph diwhu wkh oolqj ri wkh wuds frxog eh phdvxuhg lq d ghvwuxfwlyh zd| +Ilj1 :15f,1 Zh zhuh deoh wr oo wkh wuds zlwk derxw .E 2 {fD hohfwurqv dqg wkh uhfrughg olihwlph zdv derxw 418 pv ghwhuplqhg e| wkh edfnjurxqg suhvvxuh + f3S Wruu, lq wkh ydfxxpfkdpehu1 Dw 4313 ppiurpwkh Shqqlqj wuds sodwh frq jxudwlrq dqrwkhu ulqj hohfwurgh zdv sodfhg +hohfwurgh 8/ rxwhu gldphwhu 6313 pp/ lqqhu gldphwhu 4313 pp,/ zklfk zdv xvhg dv wkh fhqwudo hohfwurgh ri dq Hlq}ho ohqv frq jxudwlrq1 4313 pp ehklqg wkh Hlq}ho ohqv wzr sdudooho fdsdflwru sodwhv +hohfwurghv 9 dqg :, zhuh vlwxdwhg vhsdudwhg e| 813 pp1 D kroh ri 4313 pp zdv guloohg wkurxjk wkhvh sdudooho fdsdflwru sodwhv fryhuhg e| d julg wr plqlpl}h glvwruwlrqv rq wkh hohfwulf hog lq ehwzhhq wkhvh sdudooho fdsdflwru sodwhv1 Lq ehwzhhq wkhvh sdudooho fdsdflwru sodwhv dq krprjhqhrxv hohfwulf hog zdv fuhdwhg ri 613 Y2fp1 Wkh uvw sodwh zdv frqqhfwhg wr d udps jhqhudwru +Dywhfk/ DY043330F, zklfk frxog eldv wkh sodwh iurp0813 wr .813 Y dqg udpswkh yrowdjh dw d zhoo gh qhg wlphiurp wkh eldv yrowdjh wr .43 ru 043 Y/ zlwk d frqwuroodeoh vohz udwh +43( 0 <3( lq 8 qv wr 4 pv,1 Wklv yrowdjh udps zdv uhtxluhg wr shuirup Vhohfwlyh Ilhog Lrql}dwlrq +VIL ^5/83`, lq rughu wr phdvxuh krz pdq| uhfrpelqhg dwrpv zhuh fuhdwhg dqg lq zklfk U|gehuj vwdwh +glvfxvvhg ehorz,1 Wkh odvw sodwh +hohfwurgh :, zdv frqqhfwhg wr d idvw sxovh jhqhudwru +VUV GJ868, udpslqj wkh yrowdjh grzq iurp 0418 Y wr dq| yrowdjh lq ehwzhhq 0418 Y dqg . 413 Y zlwklq 31; qv1 Djdlq fduh zdv wdnhq wr pdwfk wkh lpshgdqfh ri wkh sdudooho fdsdflwru sodwh wr wkh rxwsxw ri wkh idvw sxovh jhqhudwru1 Wkh frpsohwh sodwh frq jxudwlrq +Ilj1 :16d, zdv sodfhg lq wkh khduw ri 5 frlov +rxwhu gldphwhu 4518 fp, lq wkh Khopkrow} frq jxudwlrq surgxflqj d wxqdeoh pdjqhwlf hog ri 31309713 pW1 Wklv vhwxs hqdeohg xv wr uvw wuds hohfwurqv +Ilj1 :16e,/ wkhq sxovh wkh wuds rshq vr wkdw wkh hohfwurqv dftxluhg d zhoo gh qhg nlqhwlf hqhuj| dqg wudyho wrzdugv wkh Hlq}ho ohqv +Ilj1 :16f,/ jxlgh wkh hohfwurqv wrzdugv wkh wzr sdudooho fdsdflwru sodwhv vr wkdw wkh| zrxog sdvv wkurxjk wkh julg lq wkh fdwkrgh sodwh ri wkh wzr sdudooho fdsdflwru sodwhv/ dqg qdoo| vorz grzq wkh hohfwurqv e| wkh vwdwlf hohfwulf hog vxfk wkdw wkh| zrxog wxuq durxqg kdoizd| lq ehwzhhq wkhvh sdudooho fdsdflwru sodwhv Hf qv diwhu wkh wuds zdv sxovhg rshq +Ilj1 :16g,1 Gxulqj wkh wxuqlqj ri wkh hohfwurqv durxqg wkh lrq forxg/ wkh yrowdjh rq wkh odvw fdsdflwru sodwh lv txlfno| ghfuhdvhg iurp0418 Y wr w|slfdoo| .314 Y wr uhfrpelqh wkh hohfwurqv zlwk wkh
;8 Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
y a electrons ions x z B=0-64 mT
1 2 3 4 5 6 7 b -1.5 eV
-0.75 eV E +0.1 eV 5.0 mm 10.0 mm z 5.0 mm c -1.5 eV
-0.75 eV
+0.1 eV
d -1.5 eV
-0.75 eV
+0.1 eV
Iljxuh :16= d= H{shulphqwdo frq jxudwlrq1 Wzr +Plfur Vskhuh Sodwh, ghwhfwruv zhuh xvhg wr uhfrug hlwkhu hohfwurqv ru lrqv1 Rqh ghwhfwru zdv sodfhg rq wkh ohiw ri sodwh 4 wr phdvxuh wkh qxpehu ri wudsshg hohfwurqv lq d ghvwuxfwlyh zd|1 Wkh rwkhu zdv sodfhg rq wkh uljkw ri sodwh : wr phdvxuh krz pxfk lrqv zhuh fuhdwhg ehiruh wkh uhfrpelqdwlrq hyhqw dqg wr phdvxuh hohfwurqv fuhdwhg iurp rxu uhfrpelqhg dwrp ghwhfwlrq vfkhph1 Wkh uvw irxu sodwhv rq wkh ohiw kdqg vlgh irup wkh Shqqlqj wuds1 Qrwh wkdw julgv duh xvhg wr hqdeoh hohfwurqv wr wudyho iurp rqh uhjlrq wr wkh rwkhu1 Wkh iwk sodwh lv xvhg dv dq Hlq}ho ohqv1 Lq ehwzhhq sodwh 9 dqg : lrqv duh dzdlwlqj wkh hohfwurqv lq d krprjhqhrxv hohfwulf hog zklfk frxog eh txlfno| wxuqhg r e| vzlwfklqj wkh yrowdjh rq sodwh :1 Sodwh 9 zdv frqqhfwhg wr d udps jhqhudwru lq rughu wr shuirup Vhohfwlyh Ilhog lrql}dwlrq ri wkh uhfrpelqhg dwrpv1 e0g= Vfkhpdwlf uhsuhvhqwdwlrq ri wkh fuhdwlrq ri hohfwurq sxovhv iurp wkh wuds dqg wkhlu ljkw wrzdugv wkh lrqv1
;9 :17 H{shulphqwdo Uhvxowv iuhh lrqv e| phdqv ri wkh SIU vfkhph1 D vpdoo vwdwlf hohfwulf hog lv ohiw ryhu lq wklv uhjlrq ri 533 pY2fp wr hqvxuh wkdw dq| xquhfrpelqhg iuhh hohfwurq lv dffhohudwhg rxw ri wklv uhjlrq dqg wr suhyhqw wkh h hfw ri wudsslqj wkh hohfwurqv lq wkh dwwudfwlyh srwhqwldo ri wkh lrq forxg1 Iru wkh yroxphv dqg ghqvlwlhv xvhg lq wkh h{shulphqwv/ wkh hohfwurqv ihho dq dwwudfwlyh hog ri 43 pY2fp dw wkh hgjh ri wkhvh yroxphv1 Vxfk d orz ghqvlw| sodvpd lv qrw vwdeoh zkhq wkh lrq uhjlrq lv eldvhg zlwk dq hohfwulf hog ri 533 pY2fp1 Lq ehwzhhq wkh sdudooho fdsdflwru sodwhv d vhfrqg dwrplfehdpri olwklxpdwrpvzdv gluhfwhg e| phdqv ri d uhvlvwlyho| khdwhg ryhq1 Olwklxp lrqv zhuh lrql}hg hlwkhu e| xvlqj wkh vdph odvhuv wr surgxfh wkh hohfwurq sxovhv dqg doljqlqj wkh ehdpv rq wkh vhfrqg dwrplf ehdp +vfkhph L= xvhg iru h{shulphqwv zkhuh wkh hohfwurqv zhuh vwruhg lq wkh Shqqlqj wuds iru wlphv vkruwhu wkhq 833 qv, ru e| xvlqj d wklug g|h odvhu +vfkhph LL= xvhg iru h{shulphqwv zkhuh zh vwxglhg wkh uhfrpelqdwlrq h!flhqf| dv d ixqfwlrq ri vwrudjh wlph ri wkh hohfwurqv lq wkh wuds, sxpshg e| wkh vhfrqg kduprqlf ri d Qg=\DJ odvhu/ v|qfkurql}hg wr wkh rwkhu wzr g|h odvhuv1 Wklv odvhu surgxfhg 87;17 qpodvhu sxovhv zlwk dq hqhuj| ri f pM1 Wkh oljkw zdv wkhq iuhtxhqf| grxeohg lq d NGS fu|vwdo dqg uhvxowhg lq d froolqhdu ehdpri 87;17 qp+ b pM, dqg 5:715 qp + :33 >M,1 Wklv froolqhdu ehdp h{flwhg wkh 7s vwdwh lq olwklxpe| phdqv ri wkh 5:715 qpoljkw dqg wkhq lrql}hg olwklxp dwrpv e| gulylqj wkh wudqvlwlrq iurp wklv 7s vwdwh lqwr wkh frqwlqxxp1 Doo wkh odvhu ehdpv zhuh fuhdwhg vxfk wkdw wkhlu gldphwhu zdv 5 pp1 W|slfdoo| zh zrxog surgxfh d f|olqgulfdoo| vkdshg lrq forxg frqwdlqlqj q8333 lrqv/ zlwk d gldphwhu ri 5 pp dqg d D ohqjwk ri 43 pp +4J? r S f lrqv2fp ,1
:17 H{shulphqwdo Uhvxowv
Wlplqj lv hvvhqwldo lq d SIU h{shulphqw1 Wklv fdq eh vhhq lq Ilj1 :14= li zh wxuq r wkh vwdwlf hohfwulf hog ehiruh wkh hohfwurqv uhdfk wkh lrqv kdoizd| ehwzhhq wkh sdudooho fdsdflwru sodwhv/ wkh hohfwurqv zloo kdugo| eh vorzhg grzq dqg zloo sdvv wkh lrqv zlwkrxw ehlqj uhfrpelqhg1 Li zh wxuq r wkh vwdwlf hohfwulf hog wrr odwh wkh hohfwurqv zloo wxuq durxqg dw wkh lrqv exw zloo jdlq nlqhwlf hqhuj| djdlq gxh wr wkh vwdwlf hohfwulf hog dqg zloo ohdyh wkh lrq uhjlrq lq wkh rssrvlwh gluhfwlrq zlwkrxw ehlqj uhfrpelqhg1 Li zh wxuq r wkh vwdwlf hohfwulf hog dw wkh prphqw wkh hohfwurqv wxuq zh uhfrug d pd{lpxp uhfrpelqdwlrq h!flhqf| ri 513 (1 IurpIlj1 :14 zh dovr uhwulhyh wkh wlphsur oh iurpwkh hohfwurqv vlqfh zh uhfrug d Jxdvvldq sur oh zlwk d zlgwk ri 61; qv zklfk phdqv wkdw zh kdyh fuhdwhg hohfwurq sxovhv ri H qv1 Wkh hohfwurq sxovhv duh surgxfhg e| sxovlqj rshq wkh hohfwurq wuds lq fH qv dqg wkhuhiruh rqh fdq h{shfw wkdw hohfwurq sxovhv duh fuhdwhg ri fH qv1 Wkh idfw wkdw wkh sxovh gxudwlrq lv 9 wlphv orqjhu lv pdlqo| gxh wr Frxorpe uhsxovlrq zklfk uhvxowv lq dq hqodujhphqw ri wkh hohfwurq forxg1 Wkh hqodujhphqw ri wkh hohfwurq forxg lv pdlqo| uhvwulfwhg lq wkh }0gluhfwlrq vlqfh wkh suhvhqfh ri wkh pdjqhwlf hog suhyhqwv wkh forxg iurpeorzlqj xs lq gluhfwlrqv shushqglfxodu wr wkh }0d{lv1 Wklv/ lq wxuq/ zloo uhvxow lq gl huhqw wudyhoolqj wlphv wrzdugv wkh lrqv dqg wkhuhiruh d eurdghqlqj ri wkh wlph gxudwlrq ri wkh hohfwurq sxovhv1 Qrwh wkdw wkh wlph gxudwlrq ri wkh hohfwurq sxovhv lv pxfk vkruwhu wkdq lq wkh suhylrxv h{shulphqwv zkhuh wkh hohfwurq sxovh gxudwlrq zdv olplwhg
;: Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
0.020 100 K metal photo- cathode 0.015
0.010
0.005
efficiency (#recombinations/#ions) efficiency 0.000 -6-4-20246 delay (ns)
Iljxuh :17= Wkh uhfrpelqdwlrq h!flhqf| dv d ixqfwlrq ri wkh ghod| ri wkh txlfn wxuqr 1 Wkh wuldqjohv uhsuhvhqw gdwd zkhuh zh oohg wkh wuds zlwk hohfwurqv zlwk d zhoo0gh qhg wudqvyhuvh nlqhwlf hqhuj|1 Wkh flufohv uhsuhvhqw gdwd zkhuh zh oohg wkh wuds zlwk krw hohfwurqv zlwk d yhu| loo0gh qhg nlqhwlf hqhuj| +vhh wh{w,1 e| wkh gxudwlrq ri wkh skrwrlrql}lqj odvhu sxovhv +q f qv,1 Lq rughu wr vwxg| wkh h hfw ri wkh whpshudwxuh ri wkh wudsshg hohfwurqv lq wkh wuds rq wkh uhfrpelqdwlrq g|qdplfv zh kdyh xvhg vfkhph L wr surgxfh wkh lrqlf forxg frqwdlqlqj DE f2 lrqv lq d yroxph ri .b f3 fp 1 Wkh lrq forxg zdv surgxfhg lq d vwdwlf hohfwulf hog ri f Y2fp/ 2 qv diwhu wkh hohfwurq wuds zdv oohg1 Zh oohg wkh hohfwurq wuds e| lrql}lqj wkh olwklxpdwrpv .e fp3 deryh wkh lrql}dwlrq olplw uhvxowlqj lq .E 2 fD wudsshg hohfwurqv zlwk d nlqhwlf hqhuj| ri fb phY +q ff N,1 Dw wkh lqvwdqw wkh hohfwurq wuds lv oohg/ wklv nlqhwlf hqhuj| uhvxowv pdlqo| lq prwlrq dorqj wkh }0gluhfwlrq vlqfh wkh srodul}dwlrq ri wkh lrql}lqj odvhu lv dorqj wkh hohfwulf hog dqg wkxv hohfwurqv zloo pdlqo| eh hplwwhg dorqj wkh }0d{lv1 Wkh edqgzlgwk ri wkh lrql}lqj odvhu zdv ohvv wkdq f2 fp3 uhvxowlqj lq dq dgglwlrqdo hqhuj| vsuhdg ri ohvv wkdq f N1 Krzhyhu wkh qrlvh jhqhudwhg iurpwkh sxovh jhqhudwruv dqg yrowdjh vxssolhv frqqhfwhg wr wkh hohfwurghv fdqqrw eh qhjohfwhg dqg zloo kdyh dq h hfw rq wkh whpshudwxuh ri wkh hohfwurq forxg +q f N,1 Zh dovr oohg wkh wuds e| gluhfwlqj wkh 67;13 qpehdprq d phwdosodwh vr wkdw kljk nlqhwlf hqhuj| +: fff N, hohfwurqv zlwk d odujh hqhuj| vsuhdg zhuh fuhdwhg lq udqgrpgluhfwlrqv dqg E fD hohfwurqv zhuh wudsshg1 Wkhq 633 qv odwhu wkh wuds zdv sxovhg rshq surgxflqj DE f hY hohfwurq sxovhv wkdw wudyhoohg wrzdugv wkh lrqv wr eh uhfrpelqhg1 Lq Ilj1 :17 wkh h!flhqf| dv d ixqfwlrq ri wkh wlph ghod| ri wkh txlfn wxuq r lv ghslfwhg iru wkh frog dqg krw skrwrfdwkrgh hohfwurqv1 Fohduo| lw lv vhhq wkdw wkh kljkhvw h!flhqf| zdv rewdlqhg iru orzhu whpshudwxuhv ri wkh wudsshg hohfwurqv1 Wkh idfw wkdw wkh h!flhqf| lqfuhdvhv iru orzhu whpshudwxuhv ri wkh wudsshg hohfwurqv fdq eh xqghuvwrrg dv iroorzv1 Gxh wr wkh orz hqhuj| vsuhdg/ pruh hohfwurqv zloo kdyh wkhlu wxuqlqj srlqw dw wkh vdph wlphlqwkhvwdwlfhohfwulf hogdwwkhlrqforxgdqgwkxvpruhuhfrpelqhgdwrpvduh surgxfhg zlwk wkh vdph qxpehu ri lrqv1 Pruhryhu li wkh nlqhwlf hqhuj| lq gluhfwlrqv shushqglfxodu wr wkh }0d{lv ghfuhdvhv/ wkh f|forwurq ruelw ri wkh hohfwurqv zloo ghfuhdvh1
;; :17 H{shulphqwdo Uhvxowv
storage time: 500 µs 0.5 µs
normalized recombination yield recombination normalized
-6-4-20246 delay (ns)
Iljxuh :18= Wkh h!flhqf| dv d ixqfwlrq ri wkh ghod| ri wkh txlfn wxuqr / iru gl huhqw vwrudjh wlphv ri wkh wudsshg hohfwurqv1 Wkh flufohv vkrz wkh h!flhqf| iru d vwrudjh wlph ri 833 v dqg wkh wuldqjohv vkrz wkh h!flhqf| iru d vwrudjh wlph ri 833 qv1
Dv zh zloo glvfxvv ehorz wklv zloo lqfuhdvh wkh uhfrpelqdwlrq h!flhqf|1 Rqh pljkw h{shfw wkdw wkh vwrudjh wlph ri wkh hohfwurqv lq wkh wuds fdq lq xhqfh wkh uhfrpelqdwlrq g|qdplfv/ vlqfh wkh prwlrqdo ehkdylru ri wkh hohfwurq forxg lq d wuds lv wlph ghshqghqw ^43<444` dqg khdwlqj h hfwv iurph{whuqdo qrlvh rq wkh sodwh hohfwurghv fdq dovr sod| d uroh1 Gxulqj wkh prghvw olihwlph ri 418 pv ri rxu wuds zh kdyh vhhq d ghfuhdvh lq h!flhqf| zklfk fdqqrw eh ixoo| dwwulexwhg wr wkh orvv ri hohfwurqv iurprxu wuds gxulqj orqjhu zdlwlqj wlphv1 Wkh ehkdylru ri wkh uhfrpelqdwlrq g|qdplfv rq gl huhqw vwrudjh wlphv zdv lqyhvwljdwhg e| surgxflqj lrqv zlwk vfkhph LL1 Lq Ilj1 :18 wkh qrupdol}hg wlph ghod| sur oh lv sorwwhg iru wzr gl huhqw vwrudjh wlphv +Dff qv dqg Dff >v, vkrzlqj wkdw wkhvh sur ohv duh lghqwlfdo1 Wkh uhfrughg h!flhqf| iru d vwrudjh wlph ri Dff qv zdv 513 ( dqg iru Dff >v lw ghfuhdvhg wr 31: (1 Zh phdvxuhg d 8043 ( orvv ri hohfwurqv lq wkh wuds ryhu wkh Dff >v zdlwlqj wlph dqg wkxv wkh 98 ( orvv lq h!flhqf| fdqqrw eh dwwulexwhg wr mxvw hohfwurq orvv iurp wkh wuds/ vlqfh wkh qxpehu ri uhfrpelqhg dwrpv vfdohv olqhduo| zlwk wkh qxpehu ri hohfwurqv lq dq hohfwurq sxovh1 D srvvleoh h{sodqdwlrq lv wkdw khdwlqj h hfwv ri wkh hohfwurqv lq wkh wuds ghfuhdvh wkh SIU h!flhqf|/ zklfk zloo eh glvfxvvhg lq pruh ghwdlo ehorz1 Diuhhhohfwurqlvprvwolnho|wrjhwuhfrpelqhgzlwkwkhSIUvfkhphzkhqlwlvforvh wr wkh qxfohxv zlwk }hur nlqhwlf hqhuj|/ exw hvvhqwldoo| wkh frruglqdwhv +iru d fhuwdlq {hg glvwdqfh wr wkh lrq, ri wkh hohfwurq uhodwlyh wr wkh lrq gr qrw sod| d uroh1 Wklv phdqv wkdw lw lv qrw dssursuldwh wr fkdudfwhul}h SIU zlwk d furvv vhfwlrq dv lw lv zlwk prvw rwkhu uhfrpelqdwlrq surfhvvhv1 Wkhuhiruh zh lqwurgxfhg wkh frqfhsw ri dq lqwhudfwlrq yroxph
+T?|/ Fkdswhu 9, wr ghvfuleh wkh revhuyhg h!flhqf|/ zklfk lv wkh yroxph lq vsdfh durxqg wkh lrq lq zklfk wkh hohfwurq kdv wr eh zlwk d fhuwdlq yhorflw| wr eh uhfrpelqhg1 D vlpsoh
;< Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
n=200 n=152 n=131
recombination yield
0.0 0.2 0.4 0.6 0.8 1.0 SFI field (V/cm)
Iljxuh :19= Wkh uhfrughg vwdwh glvwulexwlrq e| wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq1 Qrwh wkdw lqghhg vwdwhv duh fuhdwhg durxqg q@4;31
irupxod wkhq suhglfwv zkdw wklv T?| vkrxog eh=
oeS ' 4e4J?TJeoT?| +:14, zkhuh QoeS lv wkh qxpehu ri uhfrughg dwrpv +f E ,/ 4e lv wkh hohfwurq ghqvlw| lq wkh e 3 hohfwurq sxovhv/ 4J? lv wkh lrq ghqvlw| +S E2 f fp ,/ dqg TJeo lv wkh ryhuods yroxph ri wkh hohfwurq forxg dqg wkh lrq forxg1 Wkh vl}h ri TJeo lv ghwhuplqhg e| wkh vpdoohvw 3f 3 forxg= wkh hohfwurq forxg1 Zh wkxv rewdlq d T?| rq wkh rughu ri f fp 1Vxfkdq lqwhudfwlrq yroxph zrxog fruuhvsrqg wr wkh vsdfh rffxslhg e| d U|gehuj vwdwh durxqg ? r Hf1 Wklv lqglfdwhv wkdw kljk U|gehuj vwdwhv duh surgxfhg durxqg qr Hf/e|phdqv ri wkh SIU vfkhph1 Lq wkh qh{w vhfwlrq wkh lqwhudfwlrq yroxph lv glvfxvvhg lq pruh ghwdlo1 Wr yhuli| wklv k|srwkhvlv zh xvhg wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq ^5/ 83` +VIL/ Fkdswhu 5,/ wr sureh wkh erxqg vwdwh glvwulexwlrq diwhu wkh uhfrpelqdwlrq hyhqw1 Wkh uhodwlrq ehwzhhq wkh ydoxh ri wkh hohfwulf hog dw zklfk hog lrql}dwlrq fodvvlfdoo| rffxuv dqg wkh sulqflsdo txdqwxpqxpehu q vwdwh lv +lq dwrplf xqlwv,=
. 8 'E 2 ' +:15, 2 S?e E| udpslqj d vwdwlf hohfwulf hog lq wlph dqg prqlwrulqj dw zklfk wlph lrql}dwlrq rffxuv rqh fdq ghgxfh wkh erxqg vwdwh glvwulexwlrq ri dq dwrplf ru prohfxodu v|vwhp1 W|slfdoo| zh udps wkh hohfwulf hog zlwk d vohz udwh ri 41:3 Y2fp shu >r/ iurp3153 Y2fpwr 813 Y2fp1 Lq Ilj1 :19 d VIL wudfh lv ghslfwhg ri wkh uhfrpelqhg vwdwhv zkhq gxulqj wkh uhfrpelqdwlrq hyhqw wkh hohfwulf hog lq wkh lrq uhjlrq lv vzlwfkhg iurp613 Y2fpwr 3153 Y2fplq 31; qv1 Wkh VIL ghwhfwlrq vwduwhg 417 >r diwhu wkh uhfrpelqdwlrq hyhqw1 Fohduo| lw lv vhhq wkdw zh pdlqo| surgxfh vwdwhv zklfk duh lrql}hg e| wkh orzhvw VIL hogv1 Li zh xvh Ht1 +:15, wr ghwhuplqh zklfk erxqg vwdwhv zh kdyh surgxfhg zh lqghhg revhuyh wkdw zh duh pdnlqj U|gehuj vwdwhv zlwk d sulqflsdo txdqwxp qxpehu durxqg ? r Hf/lq shuihfw djuhhphqw zlwk wkh sulqflsdo txdqwxp qxpehu zh hvwlpdwhg iurp rxu revhuyhg
<3 :17 H{shulphqwdo Uhvxowv
static field: 0.10 V/cm 0.20 V/cm 0.30 V/cm
recombination yield
0.0 0.0 0.2 0.4 0.6 0.8 1.0 SFI field (V/cm)
Iljxuh :1:= Wkh uhfrughg vwdwh glvwulexwlrqv iru gl huhqw ydoxhv ri wkh uhvlg0 xdo hog diwhu wkh uhfrpelqdwlrq hyhqw1 Wkh rshq vtxduhv uhsuhvhqw gdwd iru d uhvlgxdo hog ri 433 pY2fp/ wkh vrolg wuldqjohv iru d uhvlgxdo hog ri 533 pY2fp/ dqg wkh rshq flufohv iru d uhvlgxdo hog ri 633 pY2fp1 Lw lv fohduo| vhhq wkdw dq lqfuhdvh ri uhvlgxdo hog uhvxowhg lq hog lrql}dwlrq ri wkh kljkhvw erxqg vwdwhv1
h!flhqf| dqg wkh T?| ghgxfhg iurplw1 Lq Ilj1 :1: zh vkrz 6 VIL wudfhv zkhuh zh ydulhg wkh uhvlgxdo hohfwulf hog diwhu txlfn wxuq r 1 Vlplodu vwdwhv duh surgxfhg/ exw zh orrvh wkh kljko| h{flwhg vwdwhv iru vwurqjhu uhvlgxdo hogv/ zklfk duh xqvwdeoh lq wkh uhvlgxdo hohfwulf hog1 Zh kdyh dovr vwxglhg wkh h hfw ri ydu|lqj wkh pdjqhwlf hog vwuhqjwk rq wkh SIU g|qdplfv1 Wklv sdudphwhu frxog eh ydulhg ryhu wkh udqjh ri 46 pW wr 97 pW1 Iru hogv orzhu wkdq 46 pW wkh Shqqlqj wuds zrxog ehfrph xqvwdeoh dqg wkh olihwlph ri wkh wuds zdv vwurqjo| uhgxfhg1 Lq Ilj1 :1;d wkuhh gl huhqw VIL wudfhv duh ghslfwhg iru gl huhqw pdjqhwlf hogv1 Lq Ilj1 :1;e zh sorw wkh h!flhqf| iru ydulrxv pdjqhwlf hog vwuhqjwkv1 Iru kljkhu pdjqhwlf hogv zh uhfrug pruh uhfrpelqhg dwrpv1 Wkh lqfuhdvh lq uhfrpelqdwlrq h!flhqf| fdq eh h{sodlqhg e| wzr h hfwv1 Wkh uvw h hfw lv ri wkh qrq}hur whpshudwxuh ri wkh hohfwurqv forxg/ zklfk lqwurgxfhv d qrq qlwh yhorflw| lq gluhfwlrqv shushqglfxodu wr wkh }0d{lv +wudqvyhuvh yhorflw|,1 Wklv phdqv wkdw iru lqfuhdvlqj whpshudwxuhv ri wkh hohfwurq forxg wklv wudqvyhuvh yhorflw| lqfuhdvhv dqg wkxv wkh f|forwurq ruelw lqfuhdvhv1 Li wkh udglxv ri wkh f|forwurq ruelw ehfrphv frpsdudeoh ru odujhu wkdq wkh udglxv ri T?| wkh h!flhqf| zloo ghfuhdvh1 Wklv h hfw fdq eh vxssuhvvhg li wkh ydoxh ri wkh pdjqhwlf hog 3f 3 lv lqfuhdvhg vlqfh wkh f|forwurq ruelw lv wkhq uhgxfhg1 Wkh udglxv ri T?| +f S6 ,lv w|slfdoo| vhyhudo plfurphwhuv +6 >p,1 Wkh udglxv ri wkh f|forwurq ruelw ri wkh hohfwurqv I fdq eh hvwlpdwhg e|= o ' 2&A 6 dqg lv dovr 6 >pli wkh wudqvyhuvh nlqhwlf hqhuj| lv 43 N S e lq d hog ri 58 pW1 Wkh vhfrqg h hfw ri lqfuhdvlqj wkh h!flhqf| fdq eh wkdw d vwurqjhu pdjqhwlf hog jxlghv wkh hohfwurqv ehwwhu wr wkh lrqv vr wkdw wkh qxpehu ri hohfwurqv duulylqj dw wkh lrq forxg lqfuhdvhv1
<4 Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds
48 mT 32 mT 16 mT recombination yield
0.0 0.2 0.4 0.6 0.8 1.0 SFI Field (V/cm) 3.0
2.5
2.0
1.5
1.0
0.5 efficiency (#rec/#ions) 0.0 10 20 30 40 50 B (mT)
Iljxuh :1;= d= Wkh uhfrughg vwdwh glvwulexwlrqv iru gl huhqw ydoxhv ri wkh pdj0 qhwlf hog vwuhqjwkv1 Dq lqfuhdvh lq uhfrpelqdwlrq h!flhqf| lv revhuyhg iru kljkhu pdjqhwlf hog vwuhqjwkv1 e= Uhfrpelqdwlrq H!flhqf| dv d ixqfwlrq ri wkh pdjqhwlf hog vwuhqjwk1 :18 Lqwhudfwlrq Yroxph
Vr idu zh kdyh glvfxvvhg krz wkh uhfrpelqdwlrq h!flhqf| fdq eh xqghuvwrrg lq whupv ri dq lqwhudfwlrq yroxph zklfk lv dq lqglfdwlrq iru wkh yroxph rffxslhg e| wkh fuhdwhg
U|gehuj vwdwh1 D qxphulfdo hvwlpdwh ri T?| lv rewdlqhg e| fodvvlfdoo| vroylqj Qhzwrq*v htxdwlrqv/ zlwk d irufh htxdo wr= 6E| '^E,E| nE| *S 1 Wkh hohfwulf hog +,,lv wkh vxshusrvlwlrq ri wkh Frxorpe srwhqwldo ri wkh lrqv dqg h{whuqdo hog/ lv wkh yhorflw| ri wkh hohfwurqv dqg lv wkh pdjqhwlf hog1 Dq lqwhudfwlrq yroxph ri f f3f fp lv irxqg iru d 61; qv hohfwurq sxovh1 Ilj1 :1 <5 :18 Lqwhudfwlrq Yroxph 1.0 2.0 b c a 0.8 0 1.5 a.u.) 5 a.u.) 0.6 5 0.6 1.0 0.85 0.4 0.5 1.3 term energy (a.u.) energy term -coordinate (x10 -coordinate 0.2 1.1 -coordinate (x10 -coordinate ρ ρ 1.7 0.0 0.0 -2.0 -1.5 -1.0 -0.5 0.0 0.5 -1.5 -1.0 -0.5 0.0 0.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 5 5 z-coordinate (x10 a.u.) z-coordinate (x10 a.u.) z-coordinate (x105 a.u.) Iljxuh :1<= d= Grwwhg olqh= Frxorpe srwhqwldo1 Vrolg olqh= prgl hg Frxorpe srwhqwldo e| dq hohfwulf hog ri 533 pY2fp1 e= Uhfrpelqdwlrq suredelolw| yhuvxv wkh wxuqlqjs srlqw srvlwlrq ri wkh hohfwurq lq wkh Frxorpe srwhqwldo ri wkh lrq + @ {2 . |2,1 Gdun frorxuv fruuhvsrqg wr kljk suredelolwlhv1 f= Frqwrxu sorw ri wkh hqhuj| ri wkh uhfrpelqhg hohfwurq iru w dw wkh shdn ri wkh uhfrpelqdwlrq yroxph1 Wkh hqhuj| frqwrxuv +H+mHS|m,, lqfuhdvh olqhduo| iurp wkh frqwrxu qhdu } @ 3=: 43D d1x1 dqg @31 Wkh wklfn olqh vkrzv wkh glylvlrq ehwzhhq hohfwurqv wkdw uhfrpelqh zlwk hqhuj| ehorz wkh fodvvlfdo lrql}dwlrq wkuhvkrog dqg wkrvh deryh1 vfdohv dv q21 Wkxv wr fuhdwh pruh ghhso| erxqg vwdwhv rqh kdv wr lpsohphqw d kljkhu vwdwlf hohfwulf hog zlwk d kljkhu vohz udwh1 Lq rxu h{shulphqwv zh gr qrw ixoo| wxuq r wkh vwdwlf hohfwulf hog/ dqg d vwdwlf hohfwulf hog ri q533 pY2fp lv vwloo suhvhqw diwhu wkh txlfn wxuq r 1 Wkhuhiruh uhfrpelqhg vwdwhv zlwk d sulqflsoh txdqwxp qxpehu kljkhu wkdq ? '2ffduh qrw vwdeoh dqg zloo hog lrql}h1 Lq Ilj1 :1 Dq lqwhuhvwlqj ihdwxuh dulvhv zkhq rqh uhfrugv wkh vwdwh glvwulexwlrq ru T?| dv d ixqf0 wlrq ri wkh ghod| ri wkh hohfwulf hog wxuq r 1 Lq Ilj1 :143d T?| lv fdofxodwhg iru gl huhqw ghod|v ri wkh hohfwulf hog wxuq r / dqg d ghfuhdvh ri T?| lv revhuyhg iru orqjhu ghod| wlphv1 Wklv lqglfdwhv wkdw/ rq dyhudjh/ iru orqjhu ghod| wlphv pruh ghhso| erxqg vwdwhv duh pdgh1 Lq Ilj1 :143e wklv lv lqghhg yhul hg/ zkhuh wkh vwdwh glvwulexwlrq lv fdofxodwhg iru gl huhqw ghod| wlphv1 Lq suhylrxv h{shulphqwv zlwk uxelglxp lrqv ^<;` +Fkdswhu 9, wkh vwdwh glvwulexwlrq dv d ixqfwlrq ri wxuq r wlph zdv lqyhvwljdwhg h{shulphqwdoo|/ vkrzlqj wkdw wkh vwdwh glvwulexwlrq iru orqjhu ghod| wlphv zdv lqghhg h{whqghg wr pruh ghhso| <6 Sxovhg Ilhog Uhfrpelqdwlrq zlwk d Shqqlqj Wuds 3 1.0 a b b c 9 ns too early b 9 ns too late ) 3 2 cm -10 0.5 (x10 c int 1 V a a SFI Yield (arb. un.) (arb. Yield SFI probability (arb. un.) c 0 0.0 0.0 0.4 0.8 -2 -1 0 0.2 0.4 0.6 0.8 1.0 1.2 time (ns) E/|Ecut| SFI field (V/cm) Iljxuh :143= d= Fdofxodwhg Y?| dv d ixqfwlrq ri wkh ghod| wlph ri wkh hohfwulf hog wxuq r 1 D vpdoohu Y?| lv fdofxodwhg iru orqjhu ghod| wlphv1 Wkh pdunhuv d/ e/ dqg f zloo eh xvhg lq Ilj1 :143e1 e= Fdofxodwhg vwdwh glvwulexwlrq iru gl huhqw ghod| wlphv +wkh pdunhuv d/e/ dqg f fruuhvsrqg wr wkh pdunhuv lq Ilj1 :143d,1 . lv wkh hqhuj| ri wkh vwdwh glylghg e| wkh fodvvlfdo lrql}dwlrq .S| s olplw lq d hog ri 533 pY2fp +H @5 I ,1 Rshq grwv= ghod| wlph @ 031363 qv1 Vrolg olqh= ghod| wlph @ 313:8 qv1 Vrolg grwv= ghod| wlph @ 31633 qv1 f= H{shulphqwdoo| uhfrughg vwdwh glvwulexwlrqv iru gl huhqw ghod| wlphv ri wkh hohfwulf hog wxuqr / zkhq uxelglxp lrqv duh uhfrpelqhg zlwk iuhh hohfwurqv +Fkdswhu 9,1 Wkh hohfwurqv zhuh fuhdwhg e| skrwrlrql}lqj olwklxp dwrpv e| d sxovhg odvhu/ uhvxowlqj lq hohfwurq sxovhv ri 43 qv gxudwlrq1 erxqg vwdwhv1 Wklv h hfw zdv frqyroxwhg zlwk wkh wlph gxudwlrq ri wkh hohfwurq sxovhv +44 qv, dqg wkhuhiruh d gl huhqfh lq vwdwh glvwulexwlrq zdv vhhq iru orqjhu ghod| wlphv1 Wzr VIL wudfhv dw d ghod| wlph ri < qv hduolhu dqg d ghod| wlph ri < qv odwhu wkdq wkh pd{lpxp uhfrughg uhfrpelqdwlrq h!flhqf| duh ghslfwhg lq Ilj1 :143f1 :19 Glvfxvvlrq dqg Frqfoxvlrqv Wkh idfw wkdw Sxovhg Ilhog Uhfrpelqdwlrq zrunv zlwk oljkw dwrpv zlwk gl huhqw txdqwxp ghihfwv lqglfdwhv wkdw lqghhg wkh SIU vfkhph lv xqlyhuvdo dqg lv d surplvlqj vfkhph wr uhfrpelqh dq dqwl0surwrq dqg d srvlwurq1 Wkh uvw h ruwv wr surgxfh dqwl0k|gurjhq zlwk SIU duh glvfxvvhg lq Fkdswhu <1 Lq wklv zrun/ dq h!flhqf| ri 513 ( lv uhfrughg dqg lw lv ghprqvwudwhg wkdw SIU fdq lq sulqflsoh eh lpsohphqwhg lq d frq jxudwlrq zkhuh wkh fkdujhg sduwlfohv duh wudsshg dqg vsdwldoo| vhsdudwhg1 Wkh rplvvlrq ri dq lrq wuds lv mxvwl hg vlqfh wkh lqhuwld ri wkh lrq +dqwl0surwrq, frpsduhg wr wkh hohfwurq +srvlwurq, lv vxfk wkdw hyhq lq wkh vwdwlf hogv xvhg lq d SIU h{shulphqw +pd{lpxp hog vwuhqjwk= 6 Y2fp, wkh lrqv kdyh kdugo| pryhg gxulqj wkh uhfrpelqdwlrq hyhqw + ;3 qv,1 Wkxv rqh fdq ordg dq lrq wuds/ wxuq r wkh wudsslqj srwhqwldov iru 433 qv dqg wxuq wkhpedfn rq djdlq zlwk kdugo| orrvlqj dq| lrqv iurp wkh wuds/ zkloh shuiruplqj wkh SIU vfkhph gxulqj wkh 433 qv1 Dqrwkhu uhdvrq iru qrw exloglqj dq lrq wuds lv wkdw dq lrq wuds xvhv lqkrprjhqhrxv hogv1 Zh zrxog krzhyhu olnh wr xvh krprjhqhrxv +wlph ydu|lqj, hohfwulf hogv diwhu wkh uhfrpelqdwlrq hyhqw wr fkdudfwhul}h lq ghwdlo wkh uhfrpelqhg vwdwhv zh <7 :19 Glvfxvvlrq dqg Frqfoxvlrqv kdyh surgxfhg1 Wkh h!flhqf| zdv vkrzq wr ghshqg rq wkh wudqvyhuvh whpshudwxuh ri wkh hohfwurq forxg dqg pdjqhwlf hog vwuhqjwk zkhuh wkh kljkhvw h!flhqf| zdv rewdlqhg iru orz whpshudwxuhv ri wkh hohfwurq forxg dqg kljk pdjqhwlf hog vwuhqjwkv1 Wklv zdv xqghuvwrrg e| wkh idfw wkdw d idvwhu wudqvyhuvh prwlrq zloo ohdg wr odujhu f|forwurq ruelwv1 Li wkh f|forwurq ruelw h{fhhgv wkh lqwhudfwlrq yroxph/ wkh h!flhqf| ri wkh SIU vfkhph ehfrphv ohvv1 Zh revhuyhg d orvv lq h!flhqf| iru orqjhu vwrudjh wlphv ri wkh wudsshg hohfwurqv zklfk lv h{sodlqhg e| hohfwurq orvv dqg khdwlqj h hfwv lq wkh Shqqlqj wuds1 D pruh ghwdlohg ghvfulswlrq zdv jlyhq derxw wkh lqwhudfwlrq yroxph zkhuh zh h{sodlqhg wkdw wkh uhfrpelqdwlrq suredelolw| lv kljkhvw zkhq kljk U|gehuj vwdwhv duh fuhdwhg1 Iurp wkh dfklhyhg h!flhqf| dqg wkh lqwurgxfhg T?| lw zdv frqfoxghg wkdw U|gehuj vwdwhv zlwk d sulqflsdo txdqwxpqxpehu ri ? r Hf duh fuhdwhg dqg wklv zdv yhul hg e| phdvxulqj wkh vwdwh glvwulexwlrq1 Zh kdyh vkrzq wkdw wkh xvh ri d uhvlgxdo hog jlyhv frqwuro ryhu wkh udqjh ri fuhdwhg U|gehuj vwdwhv1 Pruhryhu/ zh kdyh ghprqvwudwhg h{shulphqwdoo| dqg wkhruhwlfdoo| wkdw wkh ghod| wlph ri wkh hohfwulf hog wxuq r vwurqjo| lq xhqfhv wkh vwdwh glvwulexwlrq ri wkh uhfrpelqhg vwdwhv1 Orqjhu ghod| wlphv uhvxow lq pruh ghhso| erxqg vwdwhv1 Wkh suhvhqwhg zrun fdq eh uhodwhg wr d suhylrxv revhuydwlrq ri uhfrpelqdwlrq xvlqj sxovhg hohfwulf hogv ^:;`1 Lq wkhvh h{shulphqwv xqlsrodu kdoi0f|foh sxovhv ^7` zhuh xvhg wr uhfrpelqh d iuhh hohfwurq zlwk lwv sduhqw lrq= d eurdgedqg vkruw +418 sv, odvhu sxovh zdv xvhg wr lrql}h fdoflxpdwrpvdqg vkruwo| + y D sv, diwhu wkh lrql}lqj sxovh lw zdv uhfrpelqhg djdlq e| d xqlsrodu kdoi f|foh sxovh1 Lq wkh wlph grpdlq wklv surfhvv fdq eh ghvfulehg dv nlfnlqj wkh hohfwurq edfn wr lwv sduhqw lrq/ zkloh lq wkh iuhtxhqf| grpdlq lw lv d vwurqj hog Udpdq wudqvlwlrq ehwzhhq d yluwxdo vwdwh lq wkh frqwlqxxp zlwk d uhodwlyh orqj olihwlph dqg d erxqg vwdwh1 D odvw srlqw zruwk qrwlqj lv wkdw wr hpsor| wkh SLUL ^43843:` whfkqltxh iru prohfxodu lrq vshfwurvfrs| rqh qhhgv d U|gehuj vwdwh ri d yleudwlrqdoo| frog prohfxoh1 Lq vrph fdvhv lw lv qrw srvvleoh wr fuhdwh d U|gehuj vwdwh lq +frpsoh{, prohfxoh e| phdqv ri odvhu0h{flwdwlrq1 Zh kdyh vkrzq wkdw zh fdq qrz ordg dq hohfwurq wuds e| phdqv ri lrql}dwlrq e| d odvhu sxovh/ dqg diwhu 833 >r fuhdwh d U|gehuj vwdwh e| uhfrpelqlqj dq lrq dqg d iuhh hohfwurq1 Wklv phdqv wkdw prohfxodu lrq vshfwurvfrs| fdq qrz eh shuiruphg rq vshflhv zklfk zhuh qrw dffhvvleoh gxh wr wkh idloxuh ri surgxflqj d U|gehuj vwdwh e| odvhu0h{flwdwlrq1 <8 Fkdswhu ; U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq Wkh whfkqltxh ri Sxovhg Ilhog Uhfrpelqdwlrq lv xvhg wr uhfrpelqh d iuhh hohfwurq zlwk n n fduerq fdwlrq foxvwhuv/ udqjlqj iurp FSf wr FDf1 Lw lv vkrzq wkdw diwhu wkh uhfrpelqdwlrq wkh hohfwurq lv ohiw lq d kljko| h{flwhg vwdwh1 Wkh uhfrpelqdwlrq phwkrg surgxfhv d U|gehuj vwdwh +? q Hf,lqdodujhfduerqfoxvwhu/vxfkdvFSf/zlwkdqhohfwurqlfhqhuj| vsuhdg ri q g1 Zh phdvxuhg d uhfrpelqdwlrq h!flhqf| ri q9(1 ;14 Zk| U|gehuj Fduerq FoxvwhuvB Wkh vwxg| ri fruh h{flwhg fdwlrqv kdv jdlqhg jurzlqj lqwhuhvw zlwk wkh lqwurgxfwlrq ri }hur nlqhwlf hqhuj| +]HNH, ^6:/6;`/ pdvv dqdo|}hg wuhvkrog lrql}dwlrq +PDWL, ^445`/ dqg skrwrlqgxfhg U|gehuj lrql}dwlrq +SLUL, ^43843:` vshfwurvfrs|1 Lq SLUL vshfwurvfrs| d fruh hohfwurqlf wudqvlwlrq lv skrwrh{flwhg lq d U|gehuj prohfxoh/ zklfk wkhq ghfd|v e| udslg dxwrlrql}dwlrq1 Ehfdxvh U|gehuj prohfxohv rqo| zhdno| lqwhudfw zlwk rswlfdo udgldwlrq/ wkh devruswlrq zdyhohqjwkv iru d U|gehuj prohfxoh duh yhu| vlplodu wr wkrvh ri wkh fruuhvsrqglqj fdwlrq1 D vlplodu whfkqltxh ghyhorshg e| Ixmll hw do1 lv fdoohg LU2SLUL ^439/ 43:` lq zklfk wkh RK vwuhwfklqj yleudwlrq ri fdwlrqv lv lqyhvwljdwhg e| phdqv ri h{flwlqj U|gehuj prohfxohv zlwk lqiuduhg udgldwlrq1 Wkhuh/ wkh frxsolqj ri wkh yleudwlrqdo zlwk wkh hohfwurqlf hqhuj| ohdgv wr dxwrlrql}dwlrq1 Qrw doo prohfxodu v|vwhpv duh dffhvvleoh iru wkhvh vwxglhv ehfdxvh wkh suhsdudwlrq ri d U|gehuj prohfxoh lv qrw dozd|v wulyldo/ gxh wr wkh idfw wkdw wkh whpshudwxuh ri prohfxohv fdq eh kdug wr frqwuro lq w|slfdo h{shulphqwv dqg wkh pdq| yleudwlrqdo ghjuhhv ri iuhhgrp lq wkh v|vwhp1 Wkhuhiruh/ xs xqwlo qrz/ lw kdv qrw ehhq srvvleoh wr surgxfh U|gehuj vwdwhv ri odujh fduerq foxvwhuv ^446/ 447` vxfk dv FSf/ qru kdv wkh +LU0,skrwrhohfwurq fdwlrq vshfwuxp zlwk wkh whfkqltxh ri +LU2,SLUL vshfwurvfrs| ehhq phdvxuhg1 Wklv zrxog eh d pdmru dfklhyhphqw lq wkh LU0vshfwurvfrs| ri ixoohuhqhv ^448`1 Lq wklv fkdswhu zh uhsruw rq wkh revhuydwlrq ri fduerq foxvwhuv lq d U|gehuj vwdwh +? 'Hf/ {? r 2f,/ e| phdqv ri Sxovhg Ilhog Uhfrpelqdwlrq +SIU, ^<;` dv lqwurgxfhg lq Fkdswhu 9 dqg :1 <: U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq 0.06 0.04 0.02 0.00 efficiency (#C-clusters*/#ions) efficiency -10 0 10 closing pulse delay (ns) Iljxuh ;14= Wkh h!flhqf| +qxpehu ri uhfrpelqhg fduerq foxvwhuv glylghg e| wkh qxpehu ri iuhh lrqlf fduerq foxvwhuv, dv d ixqfwlrq ri wkh ghod| ri wkh txlfn wxuqr 1 ;15 Sxovhg Ilhog Uhfrpelqdwlrq Vfkhph Lq Fkdswhu 9 dqg :/ zh kdyh h{shulphqwdoo| dqg wkhruhwlfdoo| vkrzq wkdw dq dwrplf +uxelglxp ru olwklxp, lrq fdq eh uhfrpelqhg zlwk d iuhh hohfwurq e| phdqv ri wkh SIU vfkhph1 Wkh uhfrpelqhg dwrp zdv wkhq ohiw lq d kljko| h{flwhg vwdwh zlwk d phdq sulqflsdo txdqwxpqxpehu ri ? q Hf + 2f, ^<;`1 Fodvvlfdo fdofxodwlrqv zhuh lq h{fhoohqw djuhhphqw zlwk wkh h{shulphqwdo revhuydwlrqv1 Wkhvh fdofxodwlrqv vkrzhg wkdw wkh g|qdplfv ri wkh SIU vfkhph zhuh xqd hfwhg e| wkh qrq0k|gurjhqlf fruh ri wkh uxelglxp ru olwklxp dwrpv1 Wklv ohdg wr wkh survshfw wkdw wkh SIU vfkhph lv d xqlyhuvdo phwkrg wr uhfrpelqh d iuhh hohfwurq zlwk dq| vruw ri lrq1 Lw zdv sursrvhg wkdw wkh SIU vfkhph fdq eh xvhg wr surgxfh 43304333 frog dqwl0k|gurjhq dwrpv lq d vlqjoh h{shulphqw ^<;` lq wkh douhdg| uhdol}hg frpelqhg wuds iru sduwlfohv ri rssrvlwh fkdujh ri Jdeulhovh hw do1 ^449`+Fkdswhu 9/ dqg :,1 Lq wklv fkdswhu/ zh vkrz wkdw wkh SIU vfkhph fdq dovr eh xvhg wr uhfrpelqh d n n iuhh hohfwurq zlwk dq lrqlf fduerq foxvwhu +FDf0FSf,1 Dq h{shulphqwdo phwkrg lv suhvhqwhg zkhuh h{flwhg vwdwhv lq krw foxvwhuv +q:83 N, duh suhsduhg zlwk dq hohfwurqlfdoo| h{flwhg vwdwh hqhuj| vsuhdg rq wkh rughu ri 4 N1 Wklv revhuydwlrq rshqv wkh zd| iru qhz dssurdfkhv iru skrwrhohfwurq vshfwurvfrs| +SLUL/ LU0SLUL, rq frpsoh{ prohfxohv1 Wkh SIU vfkhph fdq ehvw eh ghvfulehg dv wkh wlph lqyhuvh ri sxovhg hog lrql}dwlrq ri U|gehuj dwrpv ^5`/ zkhuh dq hohfwurq lv fdswxuhg lqwr d erxqg vwdwh/ e| vzlwfklqj r dq hohfwulf hog dw wkh prphqw lw wxuqv durxqg lq wkh ylflqlw| ri dq lrq +Fkdswhu 9 dqg :,1 Lq Ilj1 ;14 wkh h{shulphqwdoo| ghwhuplqhg h!flhqf| +ghqvlw| ri uhfrpelqhg Fduerq foxvwhuv dwrpv glylghg e| wkh ghqvlw| ri iuhh lrqlf foxvwhuv, ri wklv vfkhph lv ghslfwhg dv d ixqfwlrq ri wkh ghod| ri wkh idvw hog wxuq r 1 Wklv ghod| lv zlwk uhvshfw wr wkh wlph zkhq wkh iuhh hohfwurq kdv lwv wxuqlqj srlqw lq wkh hohfwulf hog1 Fohduo|/ d pd{lpxp qxpehu ri uhfrpelqdwlrq hyhqwv lv uhfrughg dw }hur ghod|1 Qrwh wkdw h!flhqflhv xs wr SE e f32 duh rewdlqhg1 <; ;16 H{shulphqwdo Uhdol}dwlrq ;16 H{shulphqwdo Uhdol}dwlrq Wkh SIU vfkhph zdv h{shulphqwdoo| uhdol}hg lq d zd| yhu| vlplodu dv h{sodlqhg lq Fkdswhu 9= d sxovhg hohfwurq vrxufh ^<4` zdv fuhdwhg e| phdqv ri skrwrlrql}lqj olwklxp dwrpv lq d vwdwlf hohfwulf hog ri 4183 Y2fp/ zlwk d sxovhg +< qv gxudwlrq, qduurzedqg +{b 315 fp3, g|h odvhu +rshudwlqj dw 43 K},1 W|slfdoo| hohfwurq sxovhv ri < qv gxudwlrq/ zlwk derxw ED 2 fe hohfwurqv lq d yroxph ri 3134 pp zhuh surgxfhg1 Wkh hohfwulf hog lv fuhdwhg e| wzr sdudooho fdsdflwru sodwhv +vhsdudwlrq= 4313 pp, ryhu zklfk d yrowdjh lv dssolhg +Ilj1 ;15d,1 Wkh lrql}lqj odvhu sxovh lv irfxvvhg/ fuhdwlqj d irfxv ri 68 >p gldphwhu1 Irfxvvlqj wkh odvhu lq wkh gluhfwlrq ri wkh hohfwulf hog +}0gluhfwlrq, lv lpsruwdqw vlqfh wkh irfxv vl}h ghwhuplqhv wkh hqhuj| vsuhdg ri wkh fuhdwhg hohfwurq sxovhv1 Diwhu lrql}dwlrq/ wkh iuhh hohfwurqv duh sxvkhg wrzdugv wkh dqrgh sodwh +frqqhfwhg wr jurxqg, wkurxjk zklfk d vpdoo kroh lv guloohg1 D julg fryhulqj wkh kroh plqlpl}hv wkh glvwruwlrqv rq wkh hohfwulf hog1 Diwhu wklv uhjlrq/ wkh hohfwurqv hqwhu d hog0iuhh uhjlrq ri 4813 pp/ diwhu zklfk dqrwkhu vhw ri sdudooho fdsdflwru sodwhv +zlwk vpdoo krohv/ fryhuhg e| d julg, lv vlwxdwhg1 Vlqfh wkh qdo sodwh lv rq 04183 Y/ wkh hohfwurqv wxuq durxqg kdoizd| ehwzhhq wkhvh sodwhv/ vhsdudwhg e| 4313 pp1 D forxg ri lrqlf fduerq foxvwhuv lv dzdlwlqj wkh hohfwurqv lq wklv uhjlrq1 D pdjqhwlf hog zdv dssolhg +E5 @ 518 pW, sdudooho wr wkh gluhfwlrq ri sursdjdwlrq wr plqlpl}h wkh shushqglfxodu vsuhdg ri wkh hohfwurqv gxulqj wkhlu wudyho wr wkh lrqv1 Wkh lrqlf fduerq foxvwhuv zhuh surgxfhg 833 qv ehiruh wkh skrwrhohfwurqv zhuh fuhdwhg e| skrwrlrql}lqj dqg iudjphqwlqj jdv0skdvh FSf prohfxohv +Wq .Df N, lq d vwdwlf hohfwulf hog ri 4183 Y2fp1 Wkh jdv0skdvh FSf prohfxohv zhuh surgxfhg e| d uhvlvwlyho| khdwhg ryhq1 Zh skrwrlrql}hg FSf prohfxohv +LS @ :19 hY, e| wkh irxuwk kduprqlf +599 qp, ri d Qg=\DJ odvhu1 D w|slfdo pdvv vshfwuxp ri wkh fuhdwhg lrqv lv ghslfwhg lq Ilj1 ;151 Wkh pxowlsoh lrql}dwlrq zlwk 599 qp pdlqo| surgxfhv wkh kljkhu lrqlf fduerq foxvwhuv1 Vxf0 fhvvixo uhfrpelqdwlrq h{shulphqwv zhuh dovr shuiruphg zkhuh lrqlf fduerq foxvwhuv zhuh surgxfhg e| skrwrlrql}lqj FSf prohfxohv zlwk wkh vhfrqg kduprqlf +865 qp,/ uhvxowlqj lq dyhudjh foxvwhu vl}hv ri F 0 F.1 Wkh vpdoohu foxvwhu vl}h/ lq wkh 865 qp h{shulphqw/ fdq eh xqghuvwrrg e| wkh idfw wkdw wkh devruswlrq ri pxowlsoh skrwrqv rshqv xs dqrwkhu ghfd| fkdqqho ri wkh FSf prohfxohv= iudjphqwdwlrq1 Dovr wkh h hfw ri ghod|hg lrql}dwlrq n lv vhhq lq wkh FSf pdvv shdn/ zklfk lv gxh wr wkhuplrqlf hplvvlrq ri wkh kljko| h{flwhg prohfxodu fruh ^44:/ 44;`1 Ghwdlohg vwxglhv ri wkh iudjphqwdwlrq dqg lrql}dwlrq g|qdplfv ri FSf duh uhsruwhg lq Uhi1 ^446/ 44:453`1 Wkh ghfd| wlph ri wklv ghod|hg lrql}dwlrq lv phdvxuhg wr eh q 573 qv1 E| surgxflqj wkh lrqlf fduerq foxvwhuv 833 qv sulru wr wkh duulydo ri wkh hohfwurq sxovhv dvvxuhv wkdw wkh pdmru iudfwlrq ri wkh h{flwhg FSf prohfxohv kdyh lrql}hg dw wkh prphqw ri wkh uhfrpelqdwlrq hyhqw1 Wkh FSf skrwrlrql}dwlrq |lhogv hohfwurqv zlwk d yhorflw| ri : H fD p2v1 Wklv lq frpelqdwlrq zlwk wkh vwdwlf hohfwulf hog ri 418 Y2fp/ dvvxuhv wkdw doo wkh hohfwurqv ri wkh lrql}hg fduerq foxvwhuv kdyh ohiw wklv lqwhudfwlrq uhjlrq dw wkh wlph wkh olwklxp skrwrhohfwurqv duh fuhdwhg1 Krzhyhu/ wkh khdy| lrqlf fduerq foxvwhuv duh yluwxdoo| vwdqglqj vwloo gxulqj rxu h{shulphqw +{, @43 >plq 433 qv gxh wr wkhupdo yhorflw| dqg {, @314>plq 433 qv gxh wr wkh vwdwlf hohfwulf hog,1 << U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq Iljxuh ;15= d= h{shulphqwdo vhwxs1 D vwdwlf hohfwulf hog ri 4183 Y2fp sxvkhv wkh hohfwurqv wrzdugv wkh lrq uhjlrq/ zkhuh wkh lrqv dzdlw wkh hohfwurqv lq dq rssrvlwh hohfwulf hog1 Wkh fdwkrgh sodwh lv frqqhfwhg wr d idvw sxovh jhqhudwru vr wkdw wkh hog fdq eh wxuqhg r zlwklq 413 qv1 Wkh dqrgh sodwh lv frqqhfwhg wr d vorz sxovh jhqhudwru vr wkdw diwhu wkh txlfn wxuqr wkh srsxodwlrq glvwulexwlrq ri wkh fuhdwhg U|gehuj dwrpv fdq eh surehg1 e= Pdvv Vshfwuxp ri wkh surgxfhg fduerq foxvwhuv e| skrwrlrql}dwlrq ri F Sf prohfxohv zlwk 599 qp1 Wkh lrqlf fduerq forxg uhvhpeohv d f|olqghu zlwk d udglxv ri 68 >plq wkh }0dqg |0 gluhfwlrq dqg d ohqjwk ri 43 pp lq wkh {0gluhfwlrq/ zlwk d ghqvlw| ri 2eE fe f. fp3 1 Lq wkh lrq vrxufh uhjlrq/ wkh hohfwurqv duh ghfhohudwhg e| wkh hohfwulf hog ri 4183 Y2fp/ dqg kdyh wkhlu wxuqlqj srlqw dw wkh srvlwlrq ri wkh lrq forxg1 Dw wkdw wlph/ wkh hog lv wxuqhg r e| glsslqj wkh yrowdjh rq wkh fdwkrgh sodwh iurp04183 Y wr 03153 Y lq 413+ f2, qv1 Wkh hohfwulf hog wxuq r lv uhdol}hg e| frqqhfwlqj dq lpshgdqfh pdwfkhg/ idvw sxovh jhqhudwru +Vwdqirug Uhvhdufk V|vwhpv/ prgho GJ 868, wr wkh fdwkrgh sodwh1 Wkh ghqvlw| ri lrqlf fduerq foxvwhuv lv nhsw orz zlwk uhvshfw wr wkh ghqvlw| ri iuhh hohfwurqv wr suhyhqw wkh h hfw ri wudsslqj wkh hohfwurqv lq wkh dwwudfwlyh srwhqwldo ri wkh lrq forxg1 Iru wkh jlyhq yroxphv dqg ghqvlwlhv/ wkh hohfwurqv ihho dq dwwudfwlyh hog ri 63 pY2fp dw wkh hgjh ri wkhvh yroxphv1 Vxfk d orz ghqvlw| sodvpd lv wkhuhiruh qrw vwdeoh zkhq wkh lrq uhjlrq lv eldvhg zlwk dq hohfwulf hog ri 533 pY2fp1 Wkh h{shulphqwv zhuh shuiruphg lq d ydfxxpfkdpehu zlwk d edfnjurxqg suhvvxuh ri D f3. Wruu1 433 ;17 Uhvxowv= Lqwhudfwlrq Yroxph ;17 Uhvxowv= Lqwhudfwlrq Yroxph Lq Fkdswhu 9 dqg : zh kdyh ghprqvwudwhg wkdw wkh revhuyhg h!flhqf| zlwk SIU fdq eh xqghuvwrrg e| lqwurgxflqj dq lqwhudfwlrq yroxph1 Wklv lqwhudfwlrq yroxph fdq eh hvwlpdwhg zlwk wkh iroorzlqj irupxod= U E '4 4 T " sE| T E| _| +;14, J? e Jeo 3" ?| zkhuh E lv wkh qxpehu ri uhfrpelqdwlrqv dw d fhuwdlq ghod| + , ri wkh txlfn wxuq r / 4J? lv wkh lrq ghqvlw|/ 4e lv wkht hohfwurq ghqvlw|/ TJeo lv wkh ryhuods yroxph ri wkh hohfwurq0 dqg lrq forxg/ dqg sE| ' e*?2 i TE 3|2e*?2 lv d ixqfwlrq zklfk ghvfulehv wkh Zk2 k2 wlph sur oh ri wkh hohfwurq sxovhv +k lv wkh gxudwlrq ri wkh hohfwurq sxovhv= < qv,1 Lq wkh n n fdvh ri lrqlf fduerq foxvwhu surgxfwlrq zlwk 599 qp+F Sf0FDf, zh kdyh phdvxuhg w|slfdoo| DE D uhfrpelqdwlrq hyhqwv shu D fe hohfwurqv lq dq ryhuods yroxph ri 3134 pp dqg dq lrq ghqvlw| ri 2e f. fp3 Xvlqj Ht1 +;14,/ wklv revhuydwlrq |lhogv dq lqwhudfwlrq 3 yroxph ri E 2 f S6 1 D wkhruhwlfdo hvwlpdwh ri T?| lv rewdlqhg e| vroylqj Qhzwrq*v htxdwlrqv +vhh Fkdswhu 9 dqg :,1 Wkh hohfwulf hog +,, lv wkh vxshusrvlwlrq ri wkh Frxorpe srwhqwldo ri wkh lrqv dqg h{whuqdo hog/ lv wkh yhorflw| ri wkh hohfwurqv dqg lv wkh pdjqhwlf hog1 Dq lqwhudfwlrq yroxph ri 2Df3fp lv wkhruhwlfdoo| fdofxodwhg iru d < qv hohfwurq sxovh/ zklfk lv pruh wkdq wkh hvwlpdwlrq iurp wkh h{shulphqwdo gdwd1 Wkh h{sodqdwlrq iru wklv zloo eh glvfxvvhg lq vhfwlrq ;191 Zh qrwh wkdw wkh vsdwldo h{whqw ri vxfk dq lqwhudfwlrq yroxph fruuhvsrqgv wr U|gehuj vwdwhv durxqg ? Hf1 Wkh udglxv ri wkh lqwhudfwlrq yroxph lv wzr rughuv ri pdjqlwxgh vpdoohu wkdq wkh dyhudjh glvwdqfh ehwzhhq qhljkerulqj lrqlf fduerq foxvwhuv/ zklfk phdqv shuwxuedwlrqv iurp xquhfrpelqhg lrqlf fduerq foxvwhuv duh qhjoljleoh lq wklv h{shulphqw1 ;18 Uhvxowv= U|gehuj Vwdwh Glvwulexwlrq D ghwdlohg slfwxuh ri wkh qdo vwdwh glvwulexwlrq ri wkh sxovhg hog uhfrpelqhg U|g0 ehuj foxvwhuv zdv rewdlqhg zlwk wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq +VIL/ Fkdswhu 5, ^5/ 83`1 D U|gehuj vwdwh ri dq dwrpru prohfxoh fdq eh lrql}hg li dq hohfwulf hog lv dssolhg1Wkhuhodwlrqehwzhhqwkhydoxhriwkhvwdwlfhohfwulf hogdwzklfklrql}dwlrq fodvvlfdoo| rffxuv dqg wkh sulqflsdo txdqwxpqxpehu/ q/ ri d vwdwh lv lq dwrplf xqlwv= 8 'E. 2 ' 1 Zkhq wkh hohfwulf hog lv vorzo| udpshg lq wlph dqg wkh hog dw zklfk 2 S?e U|gehuj prohfxohv ghfd| lv prqlwruhg/ wkh srsxodwhg U|gehuj vwdwhv fdq eh dssur{l0 pdwho| ghgxfhg1 Lq rxu h{shulphqw/ zh xvh d hog udps ri 4183 Y2fp lq 41; >v/ <33 qv diwhu wkh idvw hog wxuq r 1 Wklv zdv uhdol}hg e| frqqhfwlqj d yrowdjh udps wr wkh dqrgh sodwh ri wkh lrq uhjlrq1 Wkh hog udps sxvkhv wkh hog lrql}hg hohfwurqv wrzdugv wkh fdwkrgh sodwh wkurxjk zklfk d kroh zdv guloohg fryhuhg zlwk d julg1 Gluhfwo| diwhu wklv sodwh d vhw ri Plfur0Vskhuh0Sodwhv +PVS*v, lv vlwxdwhg wkdw uhfrugv wkh lrql}hg hohfwurqv1 Lq wklv zd|/ zh uhfrug dw zklfk wlphv/ dqg khqfh dw zkdw hog vwuhqjwkv/ hohfwurqv duh ehlqj hog lrql}hg1 Gxulqj wkh <33 qv diwhu wkh txlfn wxuq r dqg ehiruh wkh VIL udps/ 434 U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq n=200 n=168 n=152 8.5 experiment ) theory -1 /Vcm 3 cm -11 (x10 int V 0.0 0.2 0.4 0.6 SFI field (V/cm) Iljxuh ;16= Fdofxodwhg vwdwh glvwulexwlrq +grwwhg olqh, ri wkh uhfrpelqhg U|g0 ehuj foxvwhuv/ frpsduhg zlwk h{shulphqwdo vwdwh glvwulexwlrq +vrolg olqh,1 Wkh h{shulphqwdoo| ghwhuplqhg lqwhudfwlrq yroxph lv ydulhg zlwklq lwv xqfhuwdlqw| wr rswlpl}h wkh frpsdulvrq zlwk wkhru|1 h hfwv ri wkuhh erg| uhfrpelqdwlrq dqg udgldwlyh uhfrpelqdwlrq duh uxohg rxw vlqfh wkh udwhv ri wkhvh surfhvvhv + v3, duh idu wrr orz dw rxu ghqvlwlhv1 Lq Ilj1 ;16/ wkh U|gehuj vwdwh glvwulexwlrq dv d uhvxow ri wkh SIU e| wkh 413 qv wxuq r lv ghslfwhg iru uhfrpelqdwlrq ri wkh fduerq foxvwhuv +FDf 0FSf,/ vkrzlqj wkdw wkh vwdwh glvwulexwlrq shdnv iru vpdoo VIL hogv1 Vlqfh wkh 4 qv wxuq r uhgxfhv wkh hohfwulf hog wr 315 Y2fp/ vwdwhv zlwk d sulqflsdo txdqwxp qxpehu eh|rqg ? '2ffduh qrw vwdeoh1 Iurp Ilj1 ;16/ lw lv ghgxfhg wkdw U|gehuj vwdwhv duh surgxfhg durxqg ? 'bf1 ;19 Vhpl0Fodvvlfdo Fdofxodwlrqv Wkh fdofxodwlrq ghslfwhg lq Ilj1 ;16 vkrzv d gluhfw frpsdulvrq ehwzhhq wkhru| dqg h{shu0 lphqw/ dqg fohduo| jrrg djuhhphqw lv rewdlqhg1 Vwduwlqj rxw zlwks wkh vwdwh glvwulexwlrq rewdlqhg iurpvroylqj Qhzwrq*v htxdwlrqv + ?:'Hfzlwk {? ' ?2 : ?:2 ' 2f, wkh VIL wudfh lv fdofxodwhg +xvlqj wkh Odqgdx0]hqhu dssur{lpdwlrq ^83`,1 Wr rewdlq wklv ohyho ri djuhhphqw/ wkh srodul}delolw| ri wkh lrqlf fduerq foxvwhuv dqg dxwrlrql}dwlrq ri wkh uhfrpelqhg fduerq foxvwhuv lv lpsohphqwhg1 Wkh srodul}delolw| lv lqfoxghg wkurxjk d orfdo srwhqwldo k*2oe dw odujh glvwdqfhv> k q Def dwrplf xqlwv ^454/455`1 Dxwrlrql}dwlrq n ri wkh U|gehuj vwdwhv e| lqwhudfwlrqv ri wkh hohfwurq zlwk wkh krw FSf/ lv lqfoxghg wkurxjk d prgho wkdw doorzv wkh hohfwurq hqhuj| wr fkdqjh= hyhu| wlph wkh uhfrpelqhg hohfwurq jhwv zlwklq 8 dwrplf xqlwv ri wkh fhqwhu/ lw jhwv d nlfn lq d udqgrp gluhfwlrq vr wkdw wkh hqhuj| ri wkh hohfwurq lv mxvw dv olnho| wr lqfuhdvh dv wr ghfuhdvh1 Li wkh nlfn lqfuhdvhv wkh hqhuj|/ wkh hohfwurq ohdyhv +dxwrlrql}dwlrq,1 Li wkh nlfn ghfuhdvhv wkh hqhuj|/ wkh hohfwurq zloo eh lq d orzhu U|gehuj vwdwh1 Iru wklv ghhshu erxqg vwdwh wkh wlph wr uhwxuq wr wkh 435 ;19 Vhpl0Fodvvlfdo Fdofxodwlrqv theory 8.5 polarizability + autoionization ) polarizibility -1 rubidium /Vcm 3 cm -11 Vint (x10 Vint 0.0 0.2 0.4 0.6 0.8 1.0 1.2 SFI field (V/cm) Iljxuh ;17= Fdofxodwhg VIL wudfhv1 Rshq flufohv= Ue prgho/ zhdn/ hodvwlf lq0 3f whudfwlrqv zlwk wkh fruh1 Wklv uhvxowhg lq dq Y ?| ri 518{43 fp 1Rshq n vtxduhv= wkh vdph prgho/ exw qrz wkh kxjh srodul}delolw| ri F Sf lv lqfoxghg lq wkh fdswxulqj vwhs dqg lq wkh fdofxodwlrq ri wkh VIL wudfh1 Wklv uhvxowhg lq dq 3f Y ?| ri 51:{43 fp 1 Rshq wuldqjohv= fdofxodwlrq lqfoxglqj wkh srodul}delolw| n n ri FSf dqg dxwrlrql}dwlrq gxh wr wkh krw F Sf fruh/ gxulqj wkh <33 qv zdlwlqj wlph1 Uhvxowlqj lq d uhfrpelqdwlrq vljqdo orvv ri derxw :3(1 n FSf ghfuhdvhv/ vr wkh hohfwurq zloo udslgo| jhw nlfnhg djdlq1 Wklv lv olnh d udqgrpzdon zkhuh wkh wlph ehwzhhq vwhsv ghfuhdvhv lq rqh gluhfwlrq dqg wkh wlph ehwzhhq vwhsv lq0 3 fuhdvhv lq wkh rwkhu gluhfwlrq1 Wkh uhvxowlqj T?| iurpwklv fdofxodwlrq lv f. f fp / lq jrrg djuhhphqw zlwk wkh h{shulphqwdo revhuydwlrq= +416 415,{f3 fp 1Iurpwkh fdofxodwlrq/ urxjko| 2 e ri wkh ruljlqdoo| uhfrpelqhg hohfwurqv duh hmhfwhg ehiruh wkh D VIL ghwhfwlrq1 Lq Ilj1 ;17/ zh suhvhqw wkh uhvxow ri 6 fdofxodwlrqv vkrzlqj wkh h hfw ri wkh odujh srodul}delolw| dqg dxwrlrql}dwlrq rq wkh VIL vljqdo1 Wkh gdvkhg olqh jlyhv wkh VIL vljqdo n iru Ue> wkh srodul}delolw| ri Ue / q b dwrplf xqlwv/ lv 93 wlphv vpdoohu wkdq iru FSf1 Zkhq zh lqfoxgh wkh kxjh srodul}delolw| ri FSf prohfxohv/ zh revhuyh d gudpdwlf fkdqjh lq wkh vkdsh ri wkh VIL vljqdo1 Wkh wrwdo U|gehuj srsxodwlrq uhpdlqv derxw wkh vdph dv fdq eh vhhq iurpwkh xqfkdqjhg lqwhjudwhg VIL |lhog1 Wkh hohfwurq grhv qrw jhw yhu| forvh + 2f dwrplf xqlwv, wr wkh lrq gxulqj wkh uhfrpelqdwlrq hyhqw> Y?| rqo| ghshqgv rq wkh orqj udqjh Frxorpe lqwhudfwlrq wr d jrrg dssur{lpdwlrq1 Wkh odujh srodul}delolw| ri FSf fdxvhv wkdw wkh vdph U|gehuj vwdwhv lrql}h dw orzhu VIL hog vwuhqjwk1 Wkh VIL vljqdo grhv gl hu ehfdxvh wkh VIL vljqdo iru Ue grhv qrw iroorz wkh 8 'E. 2 uxoh yhu| zhoo> wkh 2 uhodwlyho| vpdoo uhjlrq ri vsdfh zkhuh wkh srwhqwldo lv qrq0Frxorpelf doorzv wkh hohfwurq wr uhpdlq dwwdfkhg wr wkh Uen lrq iru d orqjhu wlph dqg lw wkxv hphujhv dw d kljkhu hog1 Zkhq dxwrlrql}dwlrq lv lqfoxghg lq wkh FSf0prgho wrjhwkhu zlwk wkh srodul}delolw|/ zh qg wkdw kljk ?0vwdwhv +orzhu VIL hogv, duh doprvw xqd hfwhg exw wkh orzhu ?0vwdwhv +kljkhu 436 U|gehuj Fduerq Foxvwhuv Suhsduhg e| Sxovhg Ilhog Uhfrpelqdwlrq VIL hogv, duh vhqvlwlyh wr dxwrlrql}dwlrq dqg zh orvh d sduw ri wkh uhfrpelqhg foxvwhuv e| dxwrlrql}dwlrq1 Wkh dxwrlrql}dwlrq udwh vfdohv dv q q3e vlqfh lw ghshqgv rq wkh qxpehu ri fruh sdvvdjhv shu xqlw wlph +q q3 , dqg krz riwhq wkh dqjxodu prphqwxp +o,lvorz shu xqlw wlph +q q3,1 ]HNH h{shulphqwv ^6:/ 6;` vkrzhg wkdw qrw rqo| o0pl{lqj fdq eh lpsruwdqw exw dovr p0pl{lqj/ iru wkhvh kljk sulqflsdo txdqwxp qxpehuv1 Ehorz zh dujxh zk| zh eholhyh p0pl{lqj grhv qrw sod| d uroh lq rxu h{shulphqwv1 Wkh rqo| zd| p0pl{lqj fdq rffxu lv wkurxjk d froolvlrqdo h hfw ri lrqv ^456458` zlwk wkh uhfrpelqhg U|gehuj fduerq foxvwhuv1 Fkxsnd ^456` grhv qrw vwdwh rq zklfk wlph vfdoh p0pl{lqj rffxuv/ exw rqo| vwdwhv d srvvleoh olihwlph lqfuhdvh ri dq dgglwlrqdo idfwru ri ? gxh wr glvwulexwlrq ri wkh zdyh ixqfwlrq ryhu doo p0vwdwhv1 Phunw hw do1 ^458` kdyh shuiruphg fdofxodwlrqv/ zklfk vkrz wkdw lq 433 pY2fp dqg dw d {hg lrq glvwdqfh ri 83 >6/ p0pl{lqj fdq rffxu1 Krzhyhu/ wkh| vwdwh wkdw wkhlu prgho lv ydolg li wkh hog ri wkh lrq lv ohvv lq pdjqlwxgh wkdq wkh krprjhqhrxv gf hog/ hovh wkh p0pl{lqj lv ryhuhvwlpdwhg1 Lq vrph ri wkhlu suhvhqwhg gdwd wkh| vkrz wkh rqvhw ri p0pl{lqj dw d glvwdqfh ri 43 >6 dqg wklv fruuhvsrqgv wr d hog surgxfhg e| wkh lrq ri ee pY2fp=wklvlvriwkhvdphrughuriwkhvwdwlfhohfwulf hog ri ff pY2fp1 Pruhryhu= li wkhuh lv p0pl{lqj wkdq wklv vkrxog rffxu zlwklq wkh wlph ri dSIUh{shulphqw+q4 >v,1 Phunw hw do1 hvwlpdwh wkh wlph lw wdnhv wr p0pl{ e| xvlqj Ihupl*v jroghq uxoh= f >r1 Wkhvh fdofxodwlrqv ryhuhvwlpdwh wkh p0pl{lqj ydoxh1 Wkh hvwlpdwh jrhv dv iroorzv= wkh dyhudjh qxpehu ri vwdwhv lq d hqhuj| zlgwk ri S- ?2E 8 Deffb +hqhuj| vsuhdg ri d Vwdun pdqlirog/ iru d fhuwdlq sulqflsdo txdqwxp qxpehu ?/ dqg hohfwulf hog 8 ,lvjlyhqe|= ?2 +ehfdxvh wkhuh duh q ? Vwdun vwdwhv zlwk q ? srvvleoh 6,/ iurp wklv d ghqvlw| +4, fdq eh uhwulhyhg1 Wkh frxsolqj +T , ehwzhhq Vwdun vwdwhv ri gl huhqw 6 lv derxw f f3e S63 dw d glvwdqfh ri Df >6 +uhwulhyhg iurpfdofxodwlrqv,1 Xvlqj Ihupl*v jroghq uxoh +ghfd| udwh ri lqlwldoo| suhsduhg vwdwh,= K'2Z4T 2/Phunwhw do1 rewdlq d pl{lqj wlph vfdoh ri 314 >r1 Krzhyhu wklv lv dq ryhuhvwlpdwh ri d idfwru ri 433 iru mxvw wkh p0pl{lqj udwh/ vlqfh Phunw hw do1 xvhg wkh qxpehu ri vwdwhv dv ?2 zkloh lq idfw wkhuh duh rqo| ? gl huhqw p0ohyhov1 Wklv zrxog sxw wkh wlphvfdoh ri p0pl{lqj rxwvlgh wkh wlphiudph ri rxu h{shulphqwv1 Grurihhy hw do1 ^457` fdofxodwh wkh p0pl{lqj iurp prylqj lrqv xqghu wkh frqglwlrqv lq ]HNH h{shulphqwv1 Wkh| vwdwh wkdw p0pl{lqj rffxuv zkhq wkhuh lv wkh vlwxdwlrq ri d qrq0froolqhduo| prylqj lrq lq frpelqdwlrq zlwk d vwud| GF hog1 Wkhlu frqfoxvlrq lv wkdw p0pl{lqj rffxuv zkhq= 4, wkh lrq prwlrq lv hvvhqwldoo| qrq froolqhdu> 5, wkh vwuhqjwk ri wkh lrq hog lv ri wkh vdph rughu dv wkh vwud| hog +lq rxu h{shulphqwv wkdw phdqv wkdw wkh lrq kdv wr dssurdfk wkh uhfrpelqhg foxvwhu zlwklq ; >p,> 6, wkh pl{lqj wlph vkrxog eh vkruwhu wkdq wkh wlph iru dq h{shulphqw wr wdnh sodfh +deryh zh kdyh glvfxvvhg wkdw wklv lv qrw wkh fdvh lq rxu h{shulphqwv,> 7, wkh yhorflw| ri wkh lrq vkrxog eh juhdwhu wkdq ? ? *2 .f *2 ' 2S p2v/ exw vpdoohu wkdq .f ' bSS p2v/ zlwk of wkh lqlwldo glvwdqfh EZ3? of of ehwzhhq wkh lrqs dqg wkh prohfxoh +lq >6,1 Wkh lrq yhorflw| lq rxu h{shulphqw lv derxw 463 p2v + ' 2&A*6 ' fp2v/ zlwk A '.Dfg,1 Wkhvh srlqwv vwurqjo| vxjjhvw wkdw p0pl{lqj grhv qrw vljql fdqwo| frqwulexwh lq rxu h{shulphqw1 Ilqdoo| d vlpsoh fdofxodwlrq fdq eh shuiruphg vkrzlqj wkdw p0pl{lqj lq rxu h{shu0 lphqw lv qrw surqrxqfhg1 Wkh lghd lv wkdw wkh hohfwulf hog ri 533 pY2fp uhgxfhv wkh 437 ;1: Glvfxvvlrq dqg Frqfoxvlrqv froolvlrqdo h hfw ri lrqv lqgxflqj p0pl{lqj1 P 0pl{lqj rffxuv zkhq wkh hohfwulf hog d{lv lv prgl hg vx!flhqwo| e| wkh Frxorpe hog ri d shuwxuelqj lrq1 Iurp wkh lrq ghq0 vlw|s dq dyhudjh lrq glvwdqfh lv hvwlpdwhg= 83 >61 Wkh lrqv kdyh d wkhupdo yhorflw| ri ' 2&A*6 'f2 p2v1 Wkh dprxqw e| zklfk wkh hog d{lv lv fkdqjhg +{w,zkhqdq lrq lv prylqj wrzdugv d U|gehuj fduerq foxvwhu zlwk d yhorflw| + ' ff p2v, shushq0 glfxodu wr wkh vwdwlf hohfwulf hog/ diwhu 43 dqjxodu prphqwxp rvfloodwlrq wlphv + JrS 'S qv iru ? '2ffdqg 8 'f2 Y2fp^5`, lv= {w 'f Yw 'f32 udg1 Wklv dprxqw lv JrS Y| vx!flhqwo| orz/ frpsduhg wr wkh h hfw ri dqjxodu prphqwxp pl{lqj/ wr rplw wkh h hfw ri p0pl{lqj lq rxu prgho1 Krzhyhu li wkh U|gehuj foxvwhuv duh surgxfhg wr eh vwruhg iru dq h{whqghg shulrg ri wlph +: >v,/ p0pl{lqj zloo sod| d vljql fdqw uroh1 ;1: Glvfxvvlrq dqg Frqfoxvlrqv Ehvlghv wkh srwhqwldo dssolfdwlrq ri wklv qhz uhfrpelqdwlrq whfkqltxh lq wkh fuhdwlrq ri dwrplf dqwl0k|gurjhq/ zh sursrvh wkdw rxu vfkhph fdq eh xvhg lq wkh irupdwlrq ri U|gehuj fduerq foxvwhuv iru +LU,0vshfwurvfrs|1 Wkh zd| wkh fduerq foxvwhuv duh suhsduhg ohdyhv wkhpzlwk dq lqwhuqdo hqhuj| ri :83 N/ dqg wkxv wkh foxvwhuv duh h{flwhg wr ydulrxv krw edqgv1 Wklv phdqv wkdw odvhu0h{flwdwlrq ri d foxvwhu wr d U|gehuj vhulhv zlwk d yhu| zhoo gh qhg hqhuj|/ qhhghg iru lqiuduhg vshfwurvfrs| h{shulphqwv/ lv lpsrvvleoh1 Wkh SIU vfkhph ohdyhv wkh uhfrpelqhg foxvwhuv lq d U|gehuj vwdwh zlwk dq hohfwurqlf hqhuj| vsuhdg ri 4 N +{q @53dwq @ 4;3 $ {H q 4 N,1 Wklv uhvhpeohv d qduurzedqg odvhu0h{flwdwlrq + 4fp3, ri d fduerq foxvwhu wr wkh U|gehuj vhulhv/ pdnlqj lw srvvleoh wr suhsduh d zhoo gh qhg U|gehuj foxvwhu1 Lq vxppdu|/ zh kdyh revhuyhg uhfrpelqdwlrq ri lrqlf fduerq foxvwhuv zlwk iuhh hohf0 wurqv zlwk wkh xvh ri idvw hog sxovhv/ uhvxowlqj lq U|gehuj fduerq foxvwhuv1 H!flhqflhv dv kljk dv Sf f32 kdyh ehhq dfklhyhg dqg d vlpsoh lpsuryhphqw +gxh wr wkh hohfwurq sxovh gxudwlrq plvpdwfk, fdq udlvh wkh h!flhqf| vljql fdqwo|1 Wkh uhfrpelqdwlrq fdq eh xqghuvwrrg zlwk dujxphqwv zklfk gr qrw uhtxluh phfkdqlvpv uho|lqj rq wkh pdjqlwxgh ri wkh txdqwxp ghihfwv ri qrq0k|gurjhqlf dwrpv ru prohfxohv1 Wklv lqglfdwhv wkdw wkh SIU phfkdqlvpzrunv iru dq| dwrpru prohfxoh dqg |lhogv uhfrpelqhg foxvwhuv lq d U|gehuj vwdwh zlwk dq hqhuj| vsuhdg ri 4 N1 438 Fkdswhu < Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ= d surjuhvv uhsruw Wkh surjuhvv ri wkh surgxfwlrq ri frog dqwl0k|gurjhq e| Sxovhg Ilhog Uhfrpelqdwlrq lv glvfxvvhg lq wklv fkdswhu1 Wkh ghvfulehg h{shulphqwv zhuh shuiruphg dw FHUQ iru wkh DWUDS frooderudwlrq1 Wkh DWUDS h{shulphqw frqvlvwv ri d odujh Shqqlqj wuds wr vwruh fkdujhg dqwl0pdwwhu sduwlfohv +dqwl0surwrqv dqg srvlwurqv,1 D suholplqdu| vfkhph lv suhvhqwhg lq zklfk wkh wudsshg srvlwurqv dqg dqwl0surwrqv frxog eh uhfrpelqhg e| wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph1 Wkh uvw dwwhpswv ri wklv vfkhph wr revhuyh dqwl0k|gurjhq glg qrw vxffhhg1 Srvvleoh h{sodqdwlrqv iru wklv idloxuh duh jlyhq zlwk ixwxuh gluhfwlrqv dqg vxjjhvwlrqv1 <14 Lqwurgxfwlrq wr Dqwl0K|gurjhq Gludf suhglfwhg d qhz gxdolw| ri pdwwhu lq 4<5; ^459` zkhq kh zurwh grzq klv yhuvlrq ri txdqwxpphfkdqlfv1 Gludf zdv hvshfldoo| frqfhuqhg wkdw klv txdqwxpwkhru| vkrxog pdqlihvwo| uhvshfw Hlqvwhlq*v vshfldo uhodwlylw|1 Wzr uhpdundeoh suhglfwlrqv uhvxowhg iurp Gludf*v wkhru|= wkh h{lvwhqfh ri hohfwurq vslq dqg wkh h{lvwhqfh ri dqwl0pdwwhu ^459`1 Lqghhg/ irxu |hduv odwhu/ wkh uvw fkdujhg dqwl sduwlfoh zdv irxqg e| Fduo Dqghuvrq +4<64,= wkh srvlwurq ^54/55`1 Judgxdoo| sk|vlflvwv ohduqhg krz wr pdnh rwkhu fkdujhg dqwl0pdwwhu vshflhv/ vxfk dv wkh dqwl0surwrq/ zlwk wkh khos ri dffhohudwru ulqjv1 Lq wkrvh ulqjv fkdujhg pdwwhu lv dffhohudwhg vr wkdw wkh| doprvw wudyho zlwk wkh vshhg ri oljkw dqg vxevhtxhqwo| wkh| duh vpdvkhg lqwr hdfk rwkhu1 Lq vxfk d froolvlrq doo nlqgv ri sduwlfohv duh pdgh +hqhuj| lv wudqvihuuhg lqwr pdvv/ dffruglqj wr . ' 6S2,/ lqfoxglqj dqwl0sduwlfohv/ zkrvh pdvv glvwulexwlrq ghshqgv rq wkh froolvlrq hqhuj|1 Krzhyhu/ xqwlo 4<<9/ qr revhuydwlrq zdv pdgh ri wkh surgxfwlrq ri qhxwudo dqwl0pdwwhu +vhh dovr Fkdswhu 419,1 Zkhq d dqwl0 surwrq sdvvhv d khdy| wdujhw0qxfohxv forvh hqrxjk/ hohfwurq0srvlwurq sdluv duh surgxfhg dfflghqwo|1 Lq vrph uduh fdvhv wkh dqwl0surwrq fdwfkhv wkh srvlwurq iurp wkh hohfwurq0 srvlwurq sdlu dqg dqwl0k|gurjhq lv surgxfhg1 Wklv vwudwhj| |lhoghg wkh uvw dqwl0k|gurjhq revhuydwlrq lq 4<<9 ^59`1 Qlqh dqwl0k|gurjhq dwrpv zhuh pdgh zlwk d uhodwlylvwlf yhorflw| dqg dqqlklodwhg e| froolvlrqv zlwklq 2f qv1 Shuiruplqj phdqlqjixo phdvxuhphqwv rq mxvw 43: Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ d frxsoh ri kljk hqhuj| dqwl0k|gurjhq dwrpv lv lpsrvvleoh dqg wkhuhiruh rqh zrxog olnh wr eh deoh wr surgxfh d odujh txdqwlw| ri frog +orz hqhuj|, dqwl0k|gurjhq dwrpv1 Wkh surgxfwlrq ri frog +715 N, dqwl0k|gurjhq lv wkh uvw jrdo ri wkh DWUDS ^5;` frooderudwlrq/ gluhfwhg e| suri1 J1 Jdeulhovh/ dw FHUQ1 Wklv surgxfwlrq zloo doorz wkh fduhixo vwxg| ri qhxwudo dqwl0pdwwhu dqg d gluhfw frpsdulvrq ehwzhhq pdwwhu +k|gurjhq, dqg dqwl0pdwwhu +dqwl0k|gurjhq,1 Wudsshg srvlwurqv dqg wudsshg dqwl0surwrqv duh xvhg dv lqjuhglhqwv wr surgxfh dqwl0k|gurjhq e| wkh uhfrpelqdwlrq ri wkhvh wzr fkdujhg dqwl0 pdwwhu vshflhv1 Lq Fkdswhu 9/ :/ dqg ; zh uhsruw rq h{shulphqwv wrzdugv wkh surgxfwlrq ri dqwl0 k|gurjhq e| Sxovhg Ilhog Uhfrpelqdwlrq +SIU, dw DWUDS1 Lq vhfwlrq 5 ri wklv fkdswhu zh glvfxvv wkh dssdudwxv dqg wkh wudsslqj phfkdqlvp ri hohfwurqv/ srvlwurqv/ dqg dqwl0 surwrqv1 Lq vhfwlrq 6 wkh ghwhfwruv xvhg lq wkh h{shulphqwv duh ghvfulehg1 Wkh h{shul0 phqwdo uhdol}dwlrq ri SIU lv vnhwfkhg lq vhfwlrq 71 Dv zloo eh glvfxvvhg ehorz/ wzr pdmru sureohpv vwloo qhhg wr eh ryhufrph wr uhdol}h SIU zlwk srvlwurqv dqg dqwl0surwrqv= 4, wkh uhgxfwlrq ri edfnjurxqg vljqdo iurpxquhfrpelqhg dqwl0surwrqv/ dqg 5, wkh uhgxfwlrq ri wkh prwlrqdo Vwdun hog1 Wklv prwlrqdo Vwdun hog lv gxh wr wkh suhvhqfh ri d q S A pdjqhwlf hog1 D U|gehuj dwrp lq vxfk d vwurqj hog zlwk d yhorflw| fruuhvsrqglqj wr d wkhupdo hqhuj| ri 715 N shushqglfxodu wr wkh pdjqhwlf hog/ zloo h{shulhqfh dq hohfwulf hog ri q e T*S61 Vxfk d hog zloo hog lrql}h d U|gehuj dwrpzlwk d sulqflsdo txdq0 wxpqxpehu q ri 4;3/ zkloh wkhvh vwdwhv duh h{shfwhg wr eh fuhdwhg zlwk wkh whfkqltxh ri Sxovhg Ilhog Uhfrpelqdwlrq1 Lq wkh qdo vhfwlrq ri wklv fkdswhu zh glvfxvv vwudwhjlhv wr ryhufrph wkhvh wzr kxugohv1 <15 Dqwl0Surwrq dqg Srvlwurq Wuds dw FHUQ Wkh DWUDS frooderudwlrq dw FHUQ/ xvhv d Shqqlqj wuds ^43;` wr vwruh wkh wzr dqwl0 k|gurjhq frqvwlwxhqwv1 D Shqqlqj wuds hpsor|v wkh frpelqdwlrq ri pdjqhwlf dqg hohfwulf hogv wr wuds d fkdujhg sduwlfoh1 Lq jhqhudo/ dq lqkrprjhqhrxv hohfwulf hog lv fuhdwhg e| ulqj hohfwurghv/ zklfk duh vlwxdwhg lqvlgh wkh eruh ri d +vxshu frqgxfwlqj, pdjqhw +vhh Ilj1 <14,1 Wkh hohfwulf hog fuhdwhv d srwhqwldo zhoo lq wkh }0gluhfwlrq/ wudsslqj d fkdujhg sduwlfoh lq wklv gluhfwlrq1 Wkh frqqlqj hohfwulf hog dorqj wkh }0gluhfwlrq lv lqhylwdeo| dffrpsdqlhg e| dq dqwl0frqqlqj hohfwulf hog lq d gluhfwlrq shushqglfxodu wr wkh }0 gluhfwlrq1 D pdjqhwlf hog lv suhvhqw dorqj wkh }0gluhfwlrq vr wkdw dq| pryhphqw ri d fkdujhg sduwlfoh shushqglfxodu wr wklv gluhfwlrq uhvxowv lq wkh vxshusrvlwlrq ri d f|forwurq dqg pdjqhwurq ruelw/ dqg wkh sduwlfoh lv wudsshg lq doo wkuhh glphqvlrqv1 D frpsuhkhqvlyh dqg wkrurxjk ryhuylhz ri wkh g|qdplfv ri d fkdujhg sduwlfoh lq d wuds kdv ehhq jlyhq e| Eurzq dqg Jdeulhovh ^45:`1 Wr surgxfh dqwl0k|gurjhq/ srvlwurqv dqg dqwl surwrqv duh qhhghg1 D q0ghfd| udglrdf0 wlyh vrxufh gholyhuv wkhvh srvlwurqv1 Lq wkhvh h{shulphqwv d 443 pFl 22Qd vrxufh lv xvhg1 Wkh srvlwurqv uhohdvhg iurpwklv vrxufh hqwhu wkh wuds wkurxjk d f >6 wlwdqlxpzlqgrz/ zkhuh wkh| slfn xs dq hohfwurq dqg irupsrvlwurqlxp+wkh erxqg vwdwh ri d srvlwurq dqg dq hohfwurq,1 Rqfh wklv qhxwudo srvlwurqlxplv qhdu d wudsslqj srwhqwldo/ lw lv hog lrql}hg 43; <15 Dqwl0Surwrq dqg Srvlwurq Wuds dw FHUQ X-axis a Z-axis e- e+ potential potential b position along z-axis Iljxuh <14= d= Vfkhpdwlf uhsuhvhqwdwlrq ri d Shqqlqj wuds1 Ulqj hohfwurghv duh xvhg wr fuhdwh lqkrprjhqhrxv hohfwulf hogv/ wudsslqj d fkdujhg sduwlfoh lq rqh frruglqdwh +}0gluhfwlrq,1 D krprjhqhrxv pdjqhwlf hog sdudooho wr wklv frruglqdwh lv xvhg wr wuds wkh sduwlfoh lq wkh rwkhu wzr frruglqdwhv +{0 dqg |0gluhfwlrq,1 e= Srwhqwldo odqgvfdsh surgxfhg e| wkh ulqj hohfwurghv1 +vhh Fkdswhu 5, e| wkh hohfwulf hog jhqhudwhg e| wkh wudsslqj srwhqwldo dqg ghshqglqj rq wkh srwhqwldo zhoo vwuxfwxuh wkh srvlwurq ru wkh hohfwurq lv wudsshg ^45;`1 D w|slfdo wuds ghswk lv q hY +ru 631333 N,1 Lq wklv pdqqhu derxw q43S srvlwurqv frxog eh ordghg lq d wuds lq 73 plqxwhv1 Vlqfh wkh h{shulphqw lv lq d fu|rjhqlf hqylurqphqw ri 715 N wkh krw srvlwurqv orrvh hqhuj| e| v|qfkrwurq udgldwlrq xqwlo wkhlu hqhuj| lv uhgxfhg wr 715 N ^45:`1 Wkh udgldwlrq gdpslqj udwh lv sursruwlrqdo wr d kljk srzhu ri wkh wudqvlwlrq iuhtxhqf|/ dqg wkxv iru udgldwlrq gdpslqj wr rffxu/ wkh dffhohudwhg prwlrq ri wkh fkdujhg sduwlfoh kdv wr eh ri kljk iuhtxhqf|1 Iru hohfwurqv/ wkh f|forwurq prwlrq kdv d dvvrfldwhg iuhtxhqf| ri q Df JK} +f32 N, iru wkh wudsslqj srwhqwldov dqg pdjqhwlf hog xvhg lq wkhvh h{shulphqwv ^463`/ uhvxowlqj lq d frrolqj udwh ri q v3 ^45:`1 Wkh d{ldo0 dqg pdjqhwurq iuhtxhqf| ri wkh hohfwurq kdv d iuhtxhqf| dvvrfldwhg zlwk lw ri q Sf PK} dqg q Df nK} uhvshfwlyho|/ dqg udgldwlrq gdpslqj ehfrphv lqvljql fdqw1 Iru khdy| sduwlfohv +iru lqvwdqfh wkh dqwl0surwrq, udgldwlrq gdpslqj fdq dovr eh qhjohfwhg vlqfh wkh f|forwurq iuhtxhqf| dqg f|forwurq udglxv lv sursruwlrqdo wr wkh lqyhuvh pdvv ri wkh sduwlfoh/ dqg wkhuhiruh wkh gdpslqj udwh vfdohv dv b / uhvxowlqj lq dq h{wuhpho| vpdoo frrolqj udwh1 6 Wkhuhiruh/ wr frro khdy| sduwlfohv/ d gl huhqw frrolqj phfkdqlvp lv hpsor|hg/ h{sodlqhg ehorz1 Wkh d{ldo prwlrq fdq eh uhvlvwlyho| gdpshg e| dq h{whuqdo flufxlw ^43<`/ dqg wkh pdjqhwurq prwlrq fdq eh gdpshg e| vlghedqg frrolqj ^45:/ 45<`1 Erwk phfkdqlvpv duh h{sodlqhg lq vhfwlrq 614 ri wklv fkdswhu1 43< Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ Lq rughu wr wuds dqwl0surwrqv/ rqh qhhgv iuhh dqwl0surwrqv1 Dw FHUQ dqwl0surwrqv duh fuhdwhg e| vpdvklqj kljk hqhuj| surwrqv lqwr d wdujhw1 Wklv deuxsw vwrsslqj ri wkh surwrqv uhohdvhv d odujh dprxqw ri hqhuj| lq d vpdoo yroxph vr wkdw dqwl0pdwwhu 0 pdwwhu sdluv duh surgxfhg/ dprqj zklfk dqwl0surwrqv dqg surwrqv1 Wkh dqwl0surwrqv duh wkhq froohfwhg lq wkh dqwl0surwrq ghfhohudwru ulqj +Wkh DG ulqj/ zklfk lv dq dssur{lpdwh flufoh zlwkdflufxpihuhqfhri4;;p,wrfrrowkhpgrzqwr8PhY+vwrfkdvwlffrrolqj^464/465`,/ iurpzklfk wkh| duh gluhfwhg wr wkuhh gl huhqw h{shulphqwv +wkh DWUDS/ DWKHQD/ dqg DVDFXVD h{shulphqw,1 Wkh dqwl0surwrqv hqwhu wkh wuds wkurxjk d ghjudghu zlqgrz +wklq vkhhw ri ehu|oolxp, vr wkdw wkh| duh ghfhohudwhg wr dq hqhuj| durxqg 4 nhY1 Wkh dqwl0surwrqv iroorz wkh hog olqhv ri wkh vwurqj pdjqhwlf hog wrzdugv wkh rwkhu vlgh ri wkh wuds zkhuh wkh| erxqfh ri d srwhqwldo zdoo edfn wr wkh ghjudghu1 E| wklv wlph wkh ghjudghu lv eldvhg vxfk wkdw lw fuhdwhv d srwhqwldo zdoo iru wkh dqwl0surwrqv dqg wkh krw dqwl0surwrqv duh wudsshg1 Lq rughu wr frro wkh dqwl0surwrqv wr 715 N/ hohfwurqv duh ordghg lqwr wkh wuds e| d hog hplvvlrq srlqw1 Wkh krw hohfwurqv orrvh wkhlu hqhuj| yld v|qfkrwurq udgldwlrq dqg duh wudsshg zlwk dq hqhuj| ri 715 N1 Wkh vlpxowdqhrxv frq qhphqw ri wkh frog hohfwurqv dqg wkh krw dqwl0surwrqv hqdeohv wkh frrolqj ri wkh dqwl0surwrqv wr 715 N/ e| froolvlrqv ri wkh krw dqwl0surwrqv zlwk wkh frog hohfwurqv +v|psdwkhwlf frrolqj ^466`,1 Hdfk wlph d krw dqwl0surwrq froolghv zlwk d frog hohfwurq/ wkh dqwl0surwrq fdq orrvh vrph hqhuj| wr wkh hohfwurq/ zklfk lq wxuq zloo orrvh wklv hqhuj| e| v|qfkrwurq udgldwlrq dqg wkhuhiruh wkh hqvhpeoh zloo wkhupdol}h wr 715 N1 Diwhu d frrolqj wlph ri 63 vhfrqgv wkh hohfwurqv duh sxovhg rxw ri wkh wuds e| wkuhh idvw +53 qv ulvhwlph, dqg vkruw gxudwlrq +433 qv, yrowdjh sxovhv zklfk rshq wkh wuds1 Wklv lv grqh ehfdxvh dqqlklodwlrqv ri hohfwurqv dqg srvlwurqv zloo rffxu zkhq dqwl0surwrqv +dffrpsdqlhg e| wkh hohfwurqv, duh frpelqhg zlwk srvlwurqv wr surgxfh dqwl0k|gurjhq1 Gxh wr wkhlu odujh lqhuwld/ wkh dqwl0surwrqv vwd| lq wkh wuds/ zkloh wkh oljkw hohfwurqv hvfdsh1 W|slfdoo| ;333 dqwl0surwrqv fdq eh dffxpxodwhg lq 5 plqxwhv/ vlqfh hyhu| wzr plqxwhv wkh Dqwl0surwrq Ghfhohudwru +DG, gholyhuv d exqfk ri ;43S kljk nlqhwlf hqhuj| dqwl0surwrqv dqg wkh wudsslqj h!flhqf| ri wkhvh krw dqwl0surwrqv lv 433 1 <16 Dqwl0Surwrq dqg Srvlwurq Ghwhfwruv <1614 Qrq0Ghvwuxfwlyh Ghwhfwlrq Mxvw olnh dq| fkdujhg sduwlfoh lq d wuds/ wkh dqwl0surwrq dqg wkh srvlwurq fdq eh ghwhfwhg e| d udglriuhtxhqf| ghwhfwlrq whfkqltxh uvw uhsruwhg e| Zlqhodqg hw do1 ^43<`1 Lq wklv whfkqltxh lpdjh fkdujhv ri wkh fkdujhg sduwlfohv duh phdvxuhg rq wkh wuds hohfwurghv1 Lq sudfwlfh wklv lv uhdol}hg dv iroorzv= dq OFU flufxlw ri kljk T lv frqqhfwhg ehwzhhq wzr hohfwurghv1 Wklv OFU flufxlw rvfloodwhv dw lwv fkdudfwhulvwlf iuhtxhqf|= I 1Wkhuhvlvwru 2Z u ihhgv 715 N wkhupdo qrlvh +Mrkqvrq qrlvh, lqwr wkh flufxlw dqg wkhuhiruh lqwr wkh wuds1 Li wklv fkdudfwhulvwlf iuhtxhqf| fruuhvsrqgv wr wkh d{ldo iuhtxhqf| ri d fkdujhg sduwlfoh lq wkh wuds +wkh flufxlw lv wxqhg,/ wkh iuhtxhqf| uhvsrqvh ri wkh wxqhg flufxlw lv dowhuhg1 Dq lqwxlwlyh zd| ri wklqnlqj derxw wklv lv wkdw wkh Mrkqvrq qrlvh lv vkruwhqhg e| wkh fkdujhg 443 <16 Dqwl0Surwrq dqg Srvlwurq Ghwhfwruv power (arb. un.) -400 -200 0 200 400 frequency (-28612 kHz) Iljxuh <15= Qrq0ghvwuxfwlyh phdvxuhphqw ri fkdujhg sduwlfohv lq d Shqqlqj wuds1 Wkh Mrkqvrq qrlvh vshfwuxp +juh| olqh, lv dowhuhg lqwr wzr Oruhqw}ldqv +eodfn olqh, zlwk d vsdflqj sursruwlrqdo wr wkh vtxduh urrw ri wkh dprxqw ri sduwlfohv lq wkh wuds1 sduwlfohv1 Wkh xqfrxsohg Oruhqw}ldq vkdsh ri wkh Mrkqvrq qrlvhs vshfwuxplv dowhuhg lqwr wzr Oruhqw}ldq*v +vhh Ilj1 <15, zlwk d vsdflqj sursruwlrqdo wr +zkhuh lv wkh qxpehu ri sduwlfohv lq wkh wuds,/ hqdeolqj wkh phdvxuhphqw ri wkh sduwlfoh qxpehu lq d wuds lq d qrq0ghvwuxfwlyh pdqqhu1 Qrwh wkdw rqo| iru d forxg lq d kduprqlf srwhqwldo wkh sduwlfoh qxpehu fdq eh ghgxfhg zlwk dffxudf|/ vlqfh wkh d{ldo urxqgwuls wlph ri d sduwlfoh lv wkhq lqghshqghqw ri lwv hqhuj|1 Lq sulqflsoh wkh g|qdplf udqjh ri wklv ghwhfwlrq vfkhph lv vxfk wkdw lw fdq ghwhfw dq| dprxqw ri fkdujhg sduwlfohv iru shuihfwo| kduprqlf srwhqwldov1 Lq wkhvh h{shulphqwv wkh vpdoohvw forxg vl}h zklfk zdv ghwhfwhg frqwdlqhg f hohfwurqv dqg wkh dffxudf| zdv 8 (1 Wkh hqhuj| orvw lq wkh h hfwlyh uhvlvwdqfh ri wkh wxqhg flufxlw lqgxfhv d gdpslqj ri wkh d{ldo prwlrq/ xqwlo wkh v|vwhp lv lq wkhupdo htxloleulxp1 Wklv lv xqghuvwrrg e| wkh idfw wkdw wkh fxuuhqw lqwurgxfhg e| wkh lpdjh fkdujhv wkurxjk wkh uhvlvwru ohdgv wr d yrowdjh T ' U- ryhu wkh uhvlvwru dqg wkxv wr dq hohfwulf hog dorqj wkh }0d{lv lq wkh wuds1 Wklv hohfwulf hog uhvxowv lq d irufh rq wkh wudsshg sduwlfoh zklfk ghfhohudwhv lw/ dqg wkxv wkh d{ldo prwlrq lv gdpshg1 Vlqfh wkh pdjqhwurq prwlrq lv xqvwdeoh/ wkh frrolqj ri wklv prwlrq lqyroyhv dgglqj hqhuj| wr wkh sduwlfoh wr irufh lw xs wkh srwhqwldo kloo lq wkh gluhfwlrq shushqglfxodu wr wkh }0gluhfwlrq1 Wkh pdjqhwurq udglxv lv ghfuhdvhg e| dsso|lqj d udglr0iuhtxhqw gulyh dw d iuhtxhqf| ri wkh vxpiuhtxhqf| ri wkh d{ldo iuhtxhqf| dqg wkh pdjqhwurq iuhtxhqf|1 Wkh d{ldo prwlrq lv frqwlqxrxvo| gdpshg e| wkh wxqhg flufxlw/ vr wkdw qr hqhuj| lv dgghg wr wklv prwlrq/ krzhyhu wkh pdjqhwurq prwlrq jdlqv lq hqhuj| dqg wkxv wkh udglxv ri wkh pdjqhwurq ruelw lv ghfuhdvhg1 D wkrurxjk wuhdwphqw ri wkh uhvlvwlyh dqg vlghedqg frrolqj phfkdqlvp lv jlyhq lq uhi1 ^45:`1 444 Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ x z Iljxuh <16= Od|rxw ri wkh wuds xvhg dw DWUDS1 D vwurqj pdjqhwlf hog +9 W, lv suhvhqw dorqj wkh }0gluhfwlrq/ zkloh wkh lqkrprjhqhrxv hohfwulf hog lv surgxfhg e| wkh ulqj hohfwurghv1 <1615 Ghvwuxfwlyh Ghwhfwlrq Srvlwurqv dqg dqwl0surwrqv frxog dovr eh phdvxuhg ghvwuxfwlyho|/ zlwk wkh dlg ri vflqwlo0 odwruv1 D EJR fu|vwdo zdv xvhg dv d vflqwloodwru wr uhfrug dqqlklodwlrqv ri srvlwurqv dqg hohfwurqv zlwk dq h!flhqf| ri q4(1 Vflqwloodwlqj ehuv zhuh xvhg wr uhfrug wkh skrwrqv surgxfhg lq wkh dqqlklodwlrq surfhvv ri dq dqwl0surwrq dqg d srvlwurq zlwk dq h!flhqf| ri 83 ( +5Z ghwhfwru,1 Wkh vflqwloodwru dfwv dv d phglxp zklfk froohfwv wkh skrwrqv ri wkh dqqlklodwlrq surfhvv1 Wkhvh skrwrqv duh wkhq gluhfwhg lqwr skrwr0pxowlsolhuv wr dpsoli| wkh vljqdo1 D Sdudooho Sodwh Dydodqfkh Fkdpehu +SSDF, zdv dovr dydlodeoh wr ghwhfw wkh dqwl0surwrqv lq d ghvwuxfwlyh pdqqhu1 Wkh sulqflsoh ri rshudwlrq lv dv iroorzv1 D jdv lv vlwxdwhg lq ehwzhhq wzr julgv/ zklfk duh eldvhg zlwk q nY1 Li dq dqwl0surwrq hqwhuv wklv uhjlrq/ lw zloo dqqlklodwh vr wkdw jdppd ud|v duh surgxfhg1 Wkhvh jdppd ud|v zloo kdyh dq lrql}lqj h hfw dqg gxh wr wkh suhvhqfh ri wkh vwurqj hog/ d glvfkdujh rffxuv1 Wklv glvfkdujh fdq vxevhtxhqwo| eh uhfrughg rq dq rvfloorvfrsh1 Wkh h!flhqf| ri wklv ghwhfwru lv 83 (1 Wkh SSDF dqg wkh vflqwloodwruv zhuh vhwxs wr kdyh d whpsrudo uhvsrqvh ri q 83 qv iru rqh vlqjoh frxqw1 Iurpwkh dqdorjxh vljqdo/ d gljlwl}hg vljqdo zdv pdgh/ hqdeolqj wr frxqw wkh qxpehu ri dqqlklodwlrqv diwhu d fhuwdlq wuljjhu1 <17 Sxovhg Ilhog Uhfrpelqdwlrq <1714 H{shulphqwdo Uhdol}dwlrq Lq Ilj1 <16 wkh wuds od|rxw lv ghslfwhg1 Wkh srvlwurqv hqwhu wkh wuds irupwkh ohiw dqg wkh dqwl0surwrqv iurpwkh uljkw1 Hdfk hohfwurgh frxog eh frqwuroohg e| d GF srzhu vxsso| zlwk d wlph frqvwdqw ri 314 v1 Wkh srvlwurqv dqg hohfwurqv frxog eh frxqwhg lq wzr kduprqlf wudsslqj uhjlrqv= [U dqg HU1 Wkh zkroh h{shulphqw zdv frpsxwhu frqwuroohg iurpd Idudgd| fdjh zkhuh doo wkh hohfwulfdo htxlsphqw zdv vlwxdwhg1 Sduwlfohv frxog eh pryhg wkurxjk wkh wuds zlwk kdugo| dq| orvvhv/ wklv hqdeohg xv wr vwruh sduwlfohv lq pdq| frq jxudwlrqv1 Sxovhg Ilhog Uhfrpelqdwlrq dv lqwurgxfhg lq fkdswhu 9/ :/ dqg ; uhtxluhv idvw vzlwfklqj 445 <17 Sxovhg Ilhog Uhfrpelqdwlrq DC voltage 50 supply - Ω + 100 Ω stainless steel 10 k transmission line Ω SRS DG 535 electrode + trap to X 3 - + - 1000 pF 0.1 µF 500 Ω Iljxuh <17= Vfkhpdwlf uhsuhvhqwdwlrq wr frxsoh idvw yrowdjh sxovhv rq wr d wuds hohfwurgh1 ri hohfwulf hogv1 Lq rughu wr lqyhvwljdwh SIU lq wkh DWUDS frq jxudwlrq/ idvw plfur0frd{ olqhvkdgwrehlqvwdoohg/wrwxuqr wkhhohfwulf hoglqdvshfl fuhjlrqlqwkhwudsrqd wlphvfdoh ri qdqrvhfrqgv1 Wklv lv lq frqwudglfwlrq zlwk wkh qrupdo rshudwlrq prgh ri wkh wuds= lq rughu wr kdyh orz whpshudwxuh wudsshg sduwlfohv/ qrlvh vrxufhv duh dq lpsruwdqw lvvxh1 Wkhuhiruh doo wkh yrowdjh olqhv wr wkh hohfwurghv duh vwurqjo| owhuhg +wlph frqvwdqwv ri 314 v,1 Fohduo| rqh fdqqrw owhu idvw olqhv zlwk vxfk d wlph frqvwdqw zkhq rqh uhtxluhv qdqrvhfrqg vzlwfklqj wlphv/ dqg owhuv kdg wr eh rplwwhg rq wkhvh olqhv1 Lw zdv wkhuhiruh lpsruwdqw wr nhhs wkh qxpehu ri idvw olqhv dv orz dv srvvleoh1 Pruhryhu/ wkh yrowdjh vrxufh frqqhfwhg wr wkh idvw olqh qhhgv wr kdyh d orz qrlvh rxwsxw1 Jhqhudoo|/ sxovh jhqhudwruv duh qrw ghvljqhg wr kdyh orz rxwsxw qrlvh vlqfh wkh ghylfh uhtxluhv d odujh edqgzlgwk dw wkh rxwsxw1 Wr wdfnoh wklv sureohpd idvw glrgh +4Q 77 7; SK, zdv frqqhfwhg lq vhulhv zlwk wkh rxwsxw ri wkh sxovh jhqhudwru dqg wkh wuds hohfwurgh1 Wkh glrgh rqo| frqgxfwv zkhq wkh yrowdjh h{fhhgv wkh edqgjds yrowdjh vr wkdw qrlvh +orzhu wkdq wkh edqgjds yrowdjh, lv vxssuhvvhg zkhq wkh sxovh jhqhudwru lv qrw ulqj1 Wzr VUV GJ 868 sxovh ghod| jhqhudwruv zhuh xvhg wr surgxfh idvw sxovhv1 Lq d w|slfdo h{shulphqw sxovh khljkwv ri q913 Y zhuh uhtxluhg dqg wkhuhiruh zh kdg wr dpsoli| wkh rxwsxwv ri wkh VUV GJ 868 sxovh jhqhudwruv +wkh pd{lpxp rxwsxw ri d VUV GJ 868 sxovh jhqhudwru lv 713 Y,1 Wklv zdv grqh e| xvlqj idvw rshudwlrqdo dpsol huv/ ru rsdpsv +OP :4:4, zklfk kdyh d vohz udwh ri 714 &T*>r1 Wkh yrowdjh uhvsrqvh ri wkh flufxlw zdv qh0wxqhg e| dgglqj d uhvlvwru +q6< rkp, lq vhulhv zlwk wkh rsdps dqg wkh hohfwurgh1 Wklv uhvxowhg lq sxovhv ri 913 Y zlwk d ulvh dqg idoo wlph ri 5513 qv1 Wkh zkroh flufxlw lv ghslfwhg lq Ilj1 <171 Qrwh wkdw wkh sxovh jhqhudwruv duh DF frxsohg vr wkdw d GF yrowdjh vxsso| frxog eh frqqhfwhg wr jlyh d yrowdjh r vhw wr wkh dssolhg sxovhv1 Wkh idvw olqhv zhuh frqqhfwhg wr hohfwurgh W6/ W;/ dqg HHW1 Vlqfh wkh uhvlgxdo qrlvh rq wkh rxwsxw diwhu wkh glrgh lqwr wkh rsdps zdv dovr dpsol hg zh glvfrqqhfwhg wkh srzhu jrlqj lqwr wkh rsdps e| d frpsxwhu frqwuroohg uhod| zkhq idvw sxovhv zhuh qrw qhhghg1 446 Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ T3 T8 EET 6 t = 0 ns a 6 b e+ 4 4 2 2 p- 0 0 10 12 14 16 18 20 22 10 12 14 16 18 20 22 6 6 t = t1 c d potential (eV) potential 4 4 2 2 0 0 10 12 14 16 18 20 22 10 12 14 16 18 20 22 position along z-axis (cm) Iljxuh <18= Vnhwfk ri wkh sursrvhg SIU vfkhph lq wkh DWUDS frq jxudwlrq1 Dw w @ 3 qv srvlwurqv dqg dqwl0surwrqv duh wudsshg lq vsdwldoo| vhshudwhg zhoov +d,1 Wkh srvlwurq wuds lv sxovhg rshq +e, vr wkdw d srvlwurq sxovh lv surgxfhg zlwk d zhoo0gh qhg hqhuj|/ zkloh vlpxowdqhrxvo| wkh yrowdjh ri hohfwurgh HHW lv udlvhg iurp 313 Y wr 913 Y1 Dw w@w wkh srvlwurqv wxuq durxqg dw wkh dqwl0surwrqv +f, dqg wkh yrowdjhv rq hohfwurgh HHW dqg W; duh vlpxowdqhrxvo| vzlwfkhg wr 313 Y/ vr wkdw wkh hohfwulf hog lv txlfno| wxuqhg r +g,1 <1715 Lpsohphqwdwlrq ri wkh SIU Vfkhph dw DWUDS D srwhqwldo zhoo iru srvlwurqv zdv fuhdwhg +vhh Ilj1 <18d,/ fhqwhuhg dw W5 e| eldvlqj KY/ W4/ dqg W6 wr .913 Y/ zkloh W5 zdv eldvhg wr .613 Y1 Wkh yrowdjh rq W6 frxog eh vzlwfkhg iurp.913 Y wr 313 Y vr wkdw kh wuds zdv rshqhg dqg d srvlwurq sxovh zdv fuhdwhg zlwk d hqhuj| ghwhuplqhg e| wkh srwhqwldo gl huhqfh ri W5 dqg W61 Hohfwurghv W7/ W8/ W9/ W:/ dqg HHW zhuh jurxqghg zkloh hohfwurgh W; zdv eldvhg wr .613 Y1 Wklv fuhdwhg d srwhqwldo zhoo iru dqwl0surwrqv dw W;1 Hohfwurgh W; zdv frqqhfwhg wr d sxovh jhqhudwru zklfk vxssolhg 613 Y qhjdwlyh jrlqj idvw sxovhv/ zkloh HHW zdv frqqhfwhg wr d sxovh jhqhudwru zklfk vxssolhg 913 Y srvlwlyh jrlqj sxovhv +vhh Ilj1 <18d,1 Dw | 'f qv wkh srvlwurq wuds lv sxovhg rshq e| vzlwfklqj wkh yrowdjh rq W6/ dqg dw wkh vdph wlph wkh yrowdjh rq HHW lv vzlwfkhg wr .913 Y vr wkdw dq hohfwulf hog udps lv fuhdwhg iurpW: wr HHW ri 613 Y shu hohfwurgh + q613 Y2fp,1 Wkh srvlwurqv wudyho wrzdugv wkh dqwl0surwrqv dqg duh ghfhohudwhg e| wkh hohfwulf hog udps vwduwlqj dw W:1 Dw | ' | wkh srvlwurqv wxuq dw wkh fhqwhu ri W; dqg wkh yrowdjh rq W; lv vzlwfkhg iurp.613 Y wr q313Y1 Vlpxowdqhrxvo| wkh yrowdjh rq HHW lv vzlwfkhg iurp .913 Y wr 313 Y1 Dw wklv prphqw erxqg vwdwhv ri dqwl0k|gurjhq fdq eh h{shfwhg1 Vlqfh wklv sduwlfoh lv qhxwudo lw lv qrw wudsshg e| wkh vxshusrvlwlrq ri wkh hohfwulf dqg pdjqhwlf hogv dqg wkxv lw vwduwv wudyhoolqj wr wkh zdoo ri wkh dssdudwxv zlwk d vshhg forvh wr wkh wkhupdo yhorflw| ri wkh 447 <17 Sxovhg Ilhog Uhfrpelqdwlrq 6 4 a 2 0 -2 y-coordinate (mm) y-coordinate -4 -6 -6 x-coordinate-4 (mm) 6 -2 4 0 2 0 2 -2 4 -4 6 z-coordinate (mm) -6 20 20 EET 19 19 T8 18 front 18 17 17 16 16 back 15 15 14 14 z-coordinate (cm) z-coordinate T3 13 13 12 bc12 0 20406080 0 20406080 time (ns) s %2n+2 5 Iljxuh <19= d= Vkdsh ri d vskhurlg/ @ . K @4/ zlwk d @5=3 pp/dqg e @9=3 pp1 Wkh duurz lqglfdwhv wkh gluhfwlrq ri sursdjdwlrq1 e= Fdofxodwhg ljkw sdwk ri wkh iurqw dqg edfnvlgh ri d vskhurlg0olnh srvlwurq sxovh + d @5=3 pp/dqge @9=3 pp,/ zkhq dw w@3 qv wkh srvlwurq zhoo dw hohfwurgh W5 lv sxovhg rshq/ zlwkrxw wdnlqj dffrxqw iru vsdfh fkdujh h hfwv1 f= vdph dv e/ qrz dffrxqwlqj iru vsdfh fkdujh h hfwv +ghqvlw|= 4 43S fp3 ,1 s dqwl surwrqv + ' 2&A*6 r ff 6*r/dwe2 N,1Dwwkhprphqwlwklwvwkhzdoowkh srvlwurq dqg wkh dqwl0surwrq dqqlklodwh zlwk wkhlu pdwwhu frxqwhusduwv/ surgxflqj pdlqo| jdppd ud|v dqg slrqv1 Wkh slrqv lq wxuq surgxfh dgglwlrqdo jdppd ud|v dqg doo wkh skrwrqv duh ghwhfwhg lq vflqwloodwruv vxuurxqglqj wkh wuds1 Vlqfh wkh dprxqw ri dqwl0surwrq ehdp wlph zdv olplwhg/ zh shuiruphg vhyhudo h{shul0 phqwv zlwkrxw dqwl0surwrqv wr fdoleudwh wkh wlph ri duulydo ri wkh srvlwurqv dw W;/ dqg wkh ydoxh ri wkh hohfwulf hog lq wkh wuds1 Fdofxodwlrqv zhuh shuiruphg wr vlpxodwh wkh ljkw sdwk ri fkdujhg sduwlfohv lq wkh wuds/ zklfk duh glvfxvvhg lq wkh qh{w vhfwlrq1 <1716 Lqwhjudwlrq ri wkh Htxdwlrqv ri Prwlrq ri d Fkdujhg Sdu0 wlfoh lq wkh Wuds Iru dq dffxudwh hvwlpdwh ri krz wr ryhuods d srvlwurq forxg dqg d dqwl0surwrq forxg e| wkh deryh ghvfulehg vfkhph/ rqh qhhgv wr prgho wkh g|qdplfv ri wkh fkdujhg sduwlfohv lq wkh wuds1 Wklv zdv grqh zlwk fdofxodwlrqv edvhg rq d qxphulfdo lqwhjudwlrq +Uxqjh0 Nxwwd lqwhjudwlrq zlwk dgmxvwdeoh vwhs vl}h, ri wkh htxdwlrqv ri prwlrq ri d fkdujhg 448 Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ srvlwurq forxg lq wkh +wlph ghshqghqw, rq0d{lv srwhqwldo odqgvfdsh lq wkh fhqwhu ri wkh wuds +wkh dqwl0surwrq forxg zdv dvvxphg wr uhpdlq {hg lq vsdfh gxulqjs d SIU h{shulphqw/ 2 2 gxh wr wkh lqhuwld ri dq dqwl0surwrq,1 Wkh vkdsh ri d vskhurlg + % n+ n 5 '/vhh @ K Ilj1 <19d, zdv fkrvhq iru wkh srvlwurq forxg/ lq djuhhphqw zlwk wkh revhuydwlrqv ri suhylrxv vwxglhv ^467469`1 Lq wklv pdqqhu wkh ljkw sdwk ri wkh srvlwurq sxovh frxog eh prqlwruhg/ dv zhoo dv lwv fkdqjh lq vkdsh1 Wkh fkdqjh ri vkdsh zdv uhvwulfwhg wr wkh }0gluhfwlrq vlqfh wkh vwurqj pdjqhwlf hog suhyhqwv wkh h{sdqvlrq ru uhgxfwlrq ri wkh forxg vl}h lq gluhfwlrqv shushqglfxodu wr wkh pdjqhwlf hog1 Wklv hqdeohg xv wr fdofxodwh dw zkdw wlph dqg zkhuh wkh srvlwurq sxovh zrxog wxuq lq wkh srwhqwldo odqgvfdsh ri Ilj1 <18/ vr wkdw wkh uljkw vwduwlqj frqglwlrqv frxog eh fkrvhq iru d SIU h{shulphqw1 Wkh vsdfh fkdujh ri wkh srvlwurq sxovh lv dq lpsruwdqw lvvxh zlwk wkh ghqvlwlhv xvhg +fS f. S63 ,1 Lq rughu wkh vlpxodwh wkh h hfw ri vsdfh fkdujh lq wkh srvlwurq forxg gxulqj lwv wudyho lq wkh wlph ydu|lqj srwhqwldo odqgvfdsh/ wkh vskhurlg zdv fxw xs lq 433 volfhv1 Wkh Frxorpe h{sdqvlrq ri wkh vskhurlg zdv lqfrusrudwhg e| dffrxqwlqj iru wkh hohfwulf hog jhqhudwhg e| doo wkh lqglylgxdo volfhv dw wkh wzr hqgv ri wkh vskhurlg1 Lq Ilj1 <19e wkh wudmhfwru| ri wkh srvlwurq forxg lv ghslfwhg/ zkhq dw w@3 wkh srvlwurq zhoo ri Ilj1 <18 lv sxovhg rshq iru wkh vskhurlg ghslfwhg lq Ilj1 <19d1 Ilj1 <19f ghslfwv wkh uhvxow zlwk vsdfh fkdujh h hfwv1 Fohduo| dq hqodujhphqw ri wkh forxg lv revhuyhg lq wkh }0gluhfwlrq gxh wr vsdfh fkdujh1 Krzhyhu/ wkh sxovhg qdwxuh ri wkh srvlwurq forxg lv vwloo fohduo| dssduhqw rq d qdqrvhfrqg wlphvfdoh1 <1717 Srvlwurq Sxovhv D uvw vwhs wrzdugv SIU lv wkh fuhdwlrq ri srvlwurq sxovhv1 Vlqfh wkh ordglqj wlph ri hohfwurqv +fD fS hohfwurqv lq 4 plqxwh, lv doprvw 73 idvwhu wkdq wkh ordglqj wlph ri srvlwurqv +fD fS srvlwurqv lq 73 plqxwhv,/ wkh lqlwldo h{shulphqwv zhuh shuiruphg zlwk hohfwurqv1 Hohfwurq sxovhv ri d gxudwlrq ri q 2f qv zhuh surgxfhg zkhq zh sxovhg wkhhohfwurqwudsriIlj1<1:drshq1Wkhgxudwlrqriwkhvhsxovhvzdvphdvxuhglqwkh iroorzlqj pdqqhu1 Dq hohfwulf hog udps ri 613 Y shu hohfwurgh zdv fuhdwhg dw W; dqg HHW +AH' f Y/ ..A ' Sf Y,dqgdqhohfwurqzhoozdvfuhdwhgdwW5+MT ' A 'A 'Sf Y/ dqg A 2' f Y,/ oohg zlwk q fS hohfwurqv +vhh Ilj1 <1:d0g,1 Hohfwurq sxovhv zhuh fuhdwhg zkhq W6 zdv sxovhg iurp0913 Y wr 313 Y1 Wkh hohfwurq sxovh wudyhov wr wkh hog udps dqg erxqfhv edfn wr W5 gxh wr wklv udps1 Wkh fdofxodwlrqv zhuh xvhg wr vlpxodwh wkh wudmhfwru| ri wkh sxovh lq rughu wr suhglfw wkh duulydo wlph edfn dw W51 Dw wkh prphqw wkh hohfwurq sxovh uhdfkhv W5/ wkh yrowdjh rq W6 lv vzlwfkhg edfn iurp313 Y wr 0913 Y/ dqg wkh hohfwurq sxovh lv uhfdxjkw1 E| vorzo| prylqj wkh hohfwurq zhoo wr HU/ wkh qxpehu ri uhfdxjkw hohfwurqv frxog eh frxqwhg1 Wkh sxovh gxudwlrq zdv phdvxuhg e| ydu|lqj wkh wlph zkhq wkh yrowdjh rq W6 lv vzlwfkhg iurp 313 Y wr 0913 Y1 Wkh uhvxow lv ghslfwhg lq Ilj1 <1:h1 Qrwh wkdw uhfdwfk h!flhqflhv ri ;3 0 <3 ( duh rewdlqhg dqg wkdw dovr wkh vhfrqg dqg wkh wklug urxqgwuls lq wkh orqj zhoo duh uhfrughg1 Wkh vdph h{shulphqw zdv shuiruphg zlwk srvlwurqv dqg vlplodu uhfdwfk h!flhqflhv zhuh revhuyhg1 Wkh sxovh uhfrughg diwhu wkh vhfrqg urxqgwuls kdv d vpdoohu zlgwk +4; qv, dqg d odujhu pd{lpxp fdwfk h!flhqf| +<3+ , (,1 Wklv fdq eh h{sodlqhg e| d wlph dqg2ru vsdfh 449 <17 Sxovhg Ilhog Uhfrpelqdwlrq T3 T8 EET 0 0 second 100 e -2 -2 roundtrip first roundtrip 80 -4 -4 third e- roundtrip a b -6 -6 60 10 12 14 16 18 20 22 10 12 14 16 18 20 22 0 0 potential (eV) potential 40 20 ns -2 -2 recatch (%) efficiency 20 -4 -4 -6 c -6 d 0 10 12 14 16 18 20 22 10 12 14 16 18 20 22 0 100 200 300 400 500 position along z-axis (cm) time (ns) Iljxuh <1:= d0g= Uhfdwfklqj hohfwurqv lq d zhoo dw hohfwurgh W5 diwhu wkh| kdyh ehhq sxovhg rxw ri wkh vdph zhoo1 Dw w @ 3 qv/ dq hohfwurq zhoo lv sxovhg rshq vxfk wkdw hohfwurq sxovhv duh fuhdwhg wudyhoolqj wrzdugv d srwhqwldo zdoo dw hohfwurgh W; dqg HHW +d0e,1 Gxh wr wklv srwhqwldo zdoo wkh hohfwurqv erxqfh edfn wr hohfwurgh W5/ dqg zloo duulyh wkhuh dw d zhoo gh qhg wlph1 Zkhq wkh hohfwurqv duulyh dw W5 wkh| wxuq durxqg djdlq dqg wkh vdph f|foh lv uhshdwhg1 Krzhyhu li wkh yrowdjh rq hohfwurgh W6 lv udlvhg dw wkh uljkw wlph wr lwv ruljlqdo ydoxh/ wkh hohfwurqv duh uhfdwfkhg lq W5 +f0g,1 h= Uhfdwfk h!flhqf| ri wkh deryh ghvfulehg vfkhph dv d ixqfwlrq ri wkh ghod| wlph diwhu zklfk wkh yrowdjh rq hohfwurgh W6 lv udlvhg djdlq1 irfxv lq ehwzhhq wkh uvw dqg vhfrqg urxqgwuls ri wkh sxovh1 Diwhu wkh vhfrqg urxqgwuls wkh sxovh ghirfxvvhv djdlq dv lv vhhq iurpwkh sxovh uhfrughg diwhu wkh wklug urxqgwuls zklfk zlgwk lv 58 qv dqg d pd{lpxp uhfdwfk h!flhqf| lv uhfrughg ri rqo| SfE (1 Lw vhhpv wkdw vsdfh fkdujh kdugo| kdv dq| h hfw rq wlph vfdoh ri d SIU h{shulphqw zlwk wkhvh ghqvlwlhv/ vlqfh wkh uhfrughg zlgwk ri wkh hohfwurq +srvlwurq, sxovhv +53 qv, lv doprvw wkh vdph dv wkh wlph lw wdnhv wr rshq wkh hohfwurq +srvlwurq, wuds +55 qv, dqg wkh zlgwk ri wkh sxovhv kdugo| lqfuhdvhv dv d ixqfwlrq ri wlph1 Wkh vhfrqg wlplqj h{shulphqw zdv shuiruphg wr pdwfk wkh frqglwlrqv lq dq dfwxdo SIU h{shulphqw dv pxfk dv srvvleoh1 Lqvwhdg ri erxqflqj wkh hohfwurqv +srvlwurqv, edfn wr W5 wr uhfdwfk wkhp/ wkh hohfwurqv zhuh odxqfkhg iurp W5 dqg fdxjkw dw W;1 Wklv zdv grqh lq wkh iroorzlqj zd| +vhh Ilj1 <1;e,= dq hohfwurq zhoo ri q613 Y ghhs zdv fuhdwhg dw W; +A H' f Y/ ..A ' A.'ff Y,1 Dqrwkhu hohfwurq zhoo zdv fuhdwhg dw W5 +MT ' A 'A 'Sf Y/ dqg A 2' f Y,/ oohg zlwk q fS hohfwurqv1 Hohfwurq sxovhv zhuh fuhdwhg zkhq W6 zdv sxovhg iurp0913 Y wr 313 Y1 Wkh hohfwurq sxovh zloo wudyho wr wkh hog udps/ zhuh lw zloo ghfhohudwh dqg wxuq durxqg1 Dw wklv prphqw ri wxuqlqj/ wkh srwhqwldo rq W; dqg HHW lv vzlwfkhg iurp0613 Y wr .613 Y/ dqg 0913 Y wr 313 Y uhvshfwlyho|1 Wkh hohfwurq zlwk +doprvw, qr nlqhwlf hqhuj| lv gldedwlfdoo| fdswxuhg lq wkh fuhdwhg srwhqwldo zhoo dw W;1 Diwhu wkh hohfwurq fdwfk lq W;/ wkh hohfwurq forxg lv wudqvsruwhg wr HU lq rughu wr frxqw wkhpdqg ghgxfh wkh fdswxuh h!flhqf|1 Djdlq hohfwurq sxovhv zhuh ghwhfwhg dqg d fdswxuh h!flhqf| ri 433( zdv uhfrughg/ zkhq wkh 44: Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ T3 T8 EET 3 3 0 0 -3 e- -3 a b -6 -6 10 12 14 16 18 20 22 10 12 14 16 18 20 22 3 3 potential (eV) 0 0 -3 -3 c d -6 -6 10 12 14 16 18 20 22 10 12 14 16 18 20 22 position along z-axis (cm) Iljxuh <1;= Fdwfklqj hohfwurqv lq d zhoo dw hohfwurgh W;/ diwhu odxqflqj wkhp iurp d zhoo dw hohfwurgh W51 Hohfwurq sxovhv zhuh fuhdwhg e| sxovlqj wkh wuds dw W5 rshq +d0e,/ wudyhoolqj wrzdugv hohfwurgh HHW1 Dw wkh vdph wlph d srwhqwldo zdoo dw hohfwurgh W; dqg HHW zdv fuhdwhg/ vr wkdw wkh hohfwurq sxovhv zrxog wxuq dw W;1 Dw wkh prphqw wkh hohfwurqv wxuq/ wkh yrowdjh rq hohfwurgh W; dqg HHW lv vzlwfkhg vxfk wkdw d zhoo lv fuhdwhg dw hohfwurgh W;/ gldedwlfdoo| fdwfklqj wkh hohfwurqv +f0g,1 yrowdjhv rq hohfwurghv W; dqg HHW duh vzlwfkhg <3 qv diwhu wkh odxqfk ri wkh hohfwurq sxovh/ lq shuihfw djuhhphqw zlwk wkh suhglfwhg ydoxh ri wkh fdofxodwlrqv1 <1718 Fdoleudwlqj wkh Hohfwulf Ilhog lq wkh Wuds Fdoleudwlqj wkh hohfwulf hog lqvlgh wkh wuds lv ri juhdw lpsruwdqfh/ vlqfh d uhvlgxdo hog ri 533 pY2fp zloo douhdg| hog lrql}h d U|gehuj vwdwh ri ? ' 2ff1 Fdoleudwlrqv zhuh grqh zlwk wkh dlg ri dqwl0surwrqv1 Dqwl0surwrqv zhuh ordghg lq d zhoo dw W; lq d frq jxudwlrq uhvhpeolqj dv pxfk dv srvvleoh wkh flufxpvwdqfhv lq d SIU h{shulphqw +vhh Ilj1 <1 44; <17 Sxovhg Ilhog Uhfrpelqdwlrq 6 6 3 0 3 -3 -6 b 0 6 potential (eV) potential 3 potential (eV) potential -3 0 -6 a -3 -6 c 9 121518212427 9 121518212427 position along z-axis (cm) position along z-axis (cm) Iljxuh <1<= d= Srwhqwldo odqgvfdsh xvhg wr fdoleudwh wkh hohfwulf hog dw wkh uhjlrq durxqg hohfwurgh W; dqg HHW1 Dqwl0surwrqv zhuh ordghg lq d zhoo dw hohfwurgh W;1 e= Zkhq wkh yrowdjh ri hohfwurgh W; lv sxovhg wr 313 Y iru d orqj wlph +413 pv,/ wkh dqwl0surwrq wuds lv frpsohwho| hpswlhg1 f= Zkhq wkh yrowdjh ri hohfwurgh W; lv sxovhg iurp .613 Y wr vrph qhjdwlyh yrowdjh/ kdoi ri wkh dqwl0surwrqv hvfdsh dqg kdoi ri wkhp duh fdswxuhg lq wkh orqj zhoo iurp wkh KY hohfwurgh wr wkh W; hohfwurgh1 E| frpsdulqj wkh dqwl0surwrq ghwhfwru uhvsrqvh iru gl huhqw dpsolwxghv ri wkh yrowdjh sxovhv rq hohfwurgh W;/ wkh yrowdjh dqg wkhuhiruh wkh hohfwulf hog fdq eh fdoleudwhg +vhh wh{w,1 wzr dqwl0surwrq exuvwv duh surgxfhg1 Wkh uvw exuvw uhvxowv iurpdqwl0surwrqv wudyhoolqj gluhfwo| wr wkh ghjudghu hohfwurgh zkhuh wkh| dqqlklodwh1 Wkh vhfrqg exuvw lv iurpdqwl0 surwrqv uvw erxqflqj ri wkh srwhqwldo zdoo dw hohfwurgh KY dqg wkhq wudyhoolqj wr wkh ghjudghu zkhuh wkh| dqqlklodwh1 Li wkh yrowdjh lv gursshg iurp613 Y wr 0314 Y ru 0315 Y/ pxowlsoh dqwl0surwrq exuvwv duh surgxfhg/ zklfk duh dwwulexwhg wr wkh fuhdwlrq ri d orqj zhoo iurpW; wr KY1 Iurpwkhvh uhvxowv lw zdv ghgxfhg wkdw wkh hohfwulf hogv duh nqrzq zlwklq 433 pY2fp1 <1719 Sxovhg Ilhog Uhfrpelqdwlrq Lq d w|slfdo SIU h{shulphqw 43D dqwl0surwrqv zhuh xvhg dqg 843D srvlwurqv +ghqvlw|= fS f. fp3 ,1 Suhylrxv zrun rq SIU ^<;/ < oeS ' 4R4eTJeoT?| +<14, zkhuh QoeS lv wkh qxpehu ri uhfrpelqdwlrqv/ 4R/dqg4e wkh dqwl0surwrq dqg srvlwurq ghqvlw|/ TJeo wkh ryhuods yroxph ri wkh dqwl0surwrq dqg hohfwurq forxg/ dqg T?| wkh lqwhudfwlrq yroxph1 Wkh lqwhudfwlrq yroxph lv gh qhg dv wkh yroxph lq vsdfh lq zklfk wkh srvlwurq kdv wr srvvhvv d fhuwdlq yhorflw| wr jhw uhfrpelqhg1 Iru wkh yrowdjhv dqg vohz 3f udwhv ri wkh hohfwulf hog sxovhv xvhg lq wklv h{shulphqw/ wklv T?| lv rq wkh rughu ri 43 3 D S3. 3f fp 1LiTJeo lv pd{lpdo wkh h{shfwhg qxpehu ri uhfrpelqdwlrq lv= f f f ' f321 44< Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ a: 2.8 V b: 2.9 V 0 20406080 0 20406080 c: 3.1 V d: 3.2 V scintillator yield (arb. un.) (arb. yield scintillator 0 20406080 0 20406080 time (µs) Iljxuh <143= Fdoleudwlqj wkh hohfwulf hog lq wkh wuds1 Irxu vflqwloodwru uhvsrqvhv zkhq dw w @ 3 hohfwurgh W; lv sxovhg iurp .6=3 Ywr.3=5 Y +d,/ .3=4 Y +e,/ 3=4 Y +f,/ dqg 3=5 Y +g,1 IurpIlj1 <143 lw lv vhhq wkdw dssur{lpdwho| ; >r diwhu sxovlqj grzq wkh hohfwulf hog lq wkh uhjlrq ri W; dqg HHW lq d SIU h{shulphqw/ wkh uvw xquhfrpelqhg dqwl0surwrqv zloo uhdfk wkh GHJ hohfwurgh1 Dw wkh GHJ hohfwurgh wkhvh dqwl0surwrqv zloo dqqlklodwh dqg frqwulexwh wr d odujh edfnjurxqg vljqdo1 Wkh srvvleo| fuhdwhg dqwl0k|gurjhq dwrpv zloo kdyh dq dyhudjhs yhorflw| ghwhuplqhg e| wkh wkhupdo yhorflw| ri wkh dqwl0surwrqv dqg srvlwurqv= ' 2&A*6R r ff 6*r1 Wkhwlphzhzlooh{shfwwrvhhvljqdoiurpdqwl0 k|gurjhq dwrpv/ lv wkh ljkw wlph ri wkh dqwl0k|gurjhq dwrpv iurp wkh fhqwhu ri wkh wuds wr wkh hohfwurgh1 Wklv vkruwhvw glvwdqfh lv 813 pp/ khqfh diwhu q 4< >r vljqdo fdq eh h{shfwhg1 Krzhyhu dw wkdw wlph/ wkh xquhfrpelqhg dqwl0surwrq edfnjurxqg kdv douhdg| dsshduhg rq wkh ghwhfwru zklfk pdnhv wkh ghwhfwlrq ri dqwl0k|gurjhq lpsrvvleoh1 Wkh vljqdo iurpsrvlwurqv lv ri qr frqfhuq vlqfh wkh vflqwloodwlqj ehuv dqg wkh SSDF duh qrw vhqvlwlyh wr srvlwurqv1 Wkh uvw SIU dwwhpsw zdv grqh zlwk wkh yrowdjh frq jxudwlrq ri Ilj1 <181 Wzr h{shulphqwv zhuh shuiruphg= wkh uvw zlwk dqwl0surwrqv dqg srvlwurqv/ dqg wkh vhfrqg rqo| zlwk dqwl0surwrqv1 Vxevwudfwlrq ri wkh vljqdo ri wkh vhfrqg h{shulphqw iurp wkh uvw frxog uhyhdo dq dqwl0k|gurjhq vljqdo/ li wkh edfnjurxqg vljqdo lv qrw wrr surqrxqfhg1 Lq Ilj1 <144 wkh ghwhfwhg vljqdo ri wkhvh wzr h{shulphqwv lv ghslfwhg1 Qr fohdu dqwl0k|gurjhq vljqdo fdq eh revhuyhg zkhq wkh uhvxowv ri wkh wzr h{shulphqwv duh frpsduhg/ srvvleo| gxh wr wkh idfw wkdw wkh dqwl0k|gurjhq vljqdo lv pxfk zhdnhu wkhq wkh edfnjurxqg vljqdo dqg vdwxudwlrq ri wkh ghwhfwru gxh wr wkh vxgghq gxps ri wkh dqwl0surwrq wuds1 453 <17 Sxovhg Ilhog Uhfrpelqdwlrq a positrons and anti-protons 0 5 10 15 b no positrons scintillator yield (arb. un.) (arb. yield scintillator 0 5 10 15 time (µs) Iljxuh <144= Iluvw dwwhpsw ri SIU1 d= SIU vfkhph zlwk srvlwurqv dqg dqwl0 surwrqv1 Wkh dqwl0surwrq dqqlklodwlrq |lhog lv sorwwhg dv d ixqfwlrq ri wkh wlph diwhu wkh srvlwurq odxqfk1 Dqwl0k|gurjhq vljqdo lv h{shfwhg diwhu q 4< v +vhh wh{w,1 e= SIU vfkhph zlwkrxw srvlwurqv/ wr phdvxuh wkh edfnjurxqg vljqdo1 Wr flufxpyhqw wklv edfnjurxqg sureohp/ d orqj zhoo zdv fuhdwhg iurp wkh KY hohf0 wurgh wr wkh GHJ hohfwurgh/ vr wkdw diwhu d SIU h{shulphqw wkh dqwl0surwrqv zrxog eh wudsshg dqg gr qrw frqwulexwh wr edfnjurxqg vljqdo +vhh Ilj1 <145,1 Wkh edfnjurxqg zdv juhdwo| uhgxfhg exw vwloo orvvhv zhuh vhhq iurpwklv orqj zhoo= lq Ilj1 <146d dqg <146e wkh uhfrughg orvvhv duh sorwwhg dv d ixqfwlrq ri wlph diwhu shuiruplqj d SIU h{shulphqw zlwkrxw srvlwurqv1 Wkh dprxqw ri orvv lv qrw ixoo| xqghuvwrrg/ exw fdq eh h{sodlqhg e| hohfwurgh lpshuihfwlrqv zklfk lqwurgxfh srwhqwldo glvfrqwlqxlwlhv1 Wkhvh glvfrqwlqxlwlhv fdq eh vhyhuh hqrxjk iru orz nlqhwlf hqhuj| sduwlfohv wr nlfn wkhprxw ri wkh wuds1 Uhjdugohvv ri wkh orvvhv dq dwwhpsw zdv pdgh wr surgxfh dqwl0k|gurjhq lq wklv frq jx0 udwlrq1 Lq Ilj1 <146 wkh uhvxowv ri dq h{shulphqw zlwk/ dqg zlwkrxw srvlwurqv duh ghslfwhg1 Fohduo| wkh edfnjurxqg lv juhdwo| uhgxfhg hqdeolqj xv wr gljlwl}h wkh dqdorjxh vljqdo iurp wkh dqwl0surwrq ghwhfwruv lq rughu wr frxqw vlqjoh dqwl0surwrq dqqlklodwlrq hyhqwv1 Qr vwdwlvwlfdo vljql fdqw vljqdo lv revhuyhg zklfk fdq eh dwwulexwhg wr dqwl0k|gurjhq/ zkhq dq h{shulphqw zlwk dqwl0surwrqv dqg srvlwurqv lv shuiruphg1 Gxh wr wkh orz uhshwlwlrq udwh ri dq h{shulphqw + ku, lw zdv lpsrvvleoh wr dyhudjh ryhu pxowlsoh h{shulphqwv wr h{wudfw d vljql fdqw dqwl0k|gurjhq vljqdo rxw ri wkh qrlvh1 Lw zdv h{shfwhg wkdw f32 dqwl0k|gurjhq dwrpv frxog eh revhuyhg zlwk wkh ghqvlwlhv xvhg lq wkhvh h{shulphqwv1 Wkh odfn ri vljqdo fdq eh h{sodlqhg e| wkuhh olplwlqj idfwruv1 Wkh orqj zhoo fdq dwwulexwh wr d orvv lq ghwhfwlrq vlqfh wkh hohfwulf hogv dvvrfldwhg zlwk wklv orqj zhoo duh vxevwdqwldo hqrxjk dw wkh rxwhu hqgv ri wklv zhoo wr hog lrql}h wkh fuhdwhg U|gehuj dqwl0k|gurjhq dwrpv1 Wkhuhiruh wkh zhoo zdv pdgh dv orqj dv srvvleoh wr lqfuhdvh wkh vrolg ghwhfwlrq dqjoh dv pxfk dv srvvleoh1 Li dqwl0k|gurjhq lv pdlqo| surgxfhg 454 Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ 8 0 -8 -16 a -24 8 0 potential (eV) potential -8 -16 b -24 12 15 18 21 24 27 z-position (cm) Iljxuh <145= Wkh h hfw ri d orqj zhoo iru dqwl0surwrqv1 Ehiruh d SIU h{shulphqw/ srvlwurqv duh wudsshg dw hohfwurgh W5/ dqg dqwl0surwrqv duh wudsshg dw hohfwurgh W; +d,1 Diwhu d SIU h{shulphqw/ wkh srvlwurqv duh xqwudsshg dqg zloo jlyh edfnjurxqg vljqdo rq wkh EJR ghwhfwru/ exw wkh| zloo qrw eh ghwhfwhg e| wkh rwkhu vflqwloodwruv/ vlqfh wkhvh duh lqvhqvlwlyh wr srvlwurqv1 Gxh wr wkh orqj zhoo/ wkh xquhfrpelqhg dqwl0surwrqv vkrxog eh wudsshg/ vr wkdw wkh| zloo qrw dwwulexwh wr d edfnjurxqg vljqdo1 zlwk d yhorflw| dorqj wkh }0d{lv/ wkhq wkh qxpehu ri ghwhfwhg dqwl0k|gurjhq dwrpv zloo eh vljql fdqwo| orzhu wkdq rxu hvwlpdwh1 Wkh vhfrqg olplwlqj idfwru lv lrql}dwlrq e| wkh prwlrqdo Vwdun h hfw1 Wkh prwlrqdo Vwdun hog zloo eh sursruwlrqdo wr wkh yhorflw| shushqglfxodu wr wkh pdjqhwlf hog +}0d{lv,1 Wklv phdqv wkdw wkh lrql}lqj h hfw zloo eh pruh vxevwdqwldo iru dqwl0k|gurjhq dwrpv surgxfhg zlwk d yhorflw| gluhfwhg shushqglfxodu wr wkh }0d{lv1 D wklug olplwlqj idfwru rq wkh ghwhfwlrq ri dqwl0k|gurjhq/ lv wkdw wkh ryhuods yroxph ri wkh srvlwurq dqg wkh dqwl0surwrq forxg lv yhu| vpdoo/ uhvxowlqj lq d orz qxpehu ri uhfrpelqdwlrqv1 <18 Ixwxuh Gluhfwlrq Lq wklv fkdswhu/ d uhsruw lv suhvhqwhg lq zklfk zh ghvfulehg wkh surjuhvv lq wkh fuhdwlrq ri dqwl0k|gurjhqdwwkhDWUDSh{shulphqwdwFHUQ1Zhkdyhvkrzqwkdwsrvlwurqsxovhv zlwk d ghqvlw| ri fS f. fp3 fdq eh surgxfhg ri 53 qv gxudwlrq iurpd wuds/ zklfk fdq eh fdxjkw lq d vsdwldoo| vhsdudwhg wuds zlwk ff ( h!flhqf|1 Dgglwlrqdo h{shulphqwv zhuh shuiruphg wr fdoleudwh wkh hohfwulf hog lq d vshfl f uhjlrq lq wkh wuds1 Ilqdoo|/ wkh uvw dwwhpswv ri SIU zhuh pdgh zlwk dqwl0surwrqv dqg srvlwurqv1 Zh zhuh krzhyhu qrw deoh wr ghwhfw dq| fuhdwhg dqwl0k|gurjhq1 Zh sursrvh wkuhh lpsuryhphqwv iru ixwxuh h{shulphqwv zlwk SIU wr lqfuhdvh wkh suredelolw| ri ghwhfwlqj dqwl0k|gurjhq1 455 <18 Ixwxuh Gluhfwlrq Iljxuh <146= d= Uhfrughg orvvhv iurp dqwl0surwrqv/ diwhu wkh| zhuh odxqfkhg lq wkh orqj zhoo e| wkh SIU vfkhph1 Diwhu 419 pv/ 4;69 frxqwv zhuh uhfrughg1 e= Uhfrughg vljqdo diwhu shuiruplqj d SIU h{shulphqw zlwk srvlwurqv dqg dqwl0 surwrqv lq d orqj dqwl0surwrq zhoo frq jxudwlrq1 Diwhu 419 pv/ 4979 frxqwv zhuh uhfrughg1 Uhfruglqj wkhvh wudfhv wrrn rqh qljkw1 Wkh wrwdo qxpehu ri dqwl0surwrqv xvhg lq wkh wzr h{shulphqwv lv doprvw wkh vdph vlqfh diwhu 419 pv d vlplodu orvv qxpehu lv uhfrughg +4;69 frxqwv yv 4979 frxqwv, Wkh uvw lpsuryhphqw zrxog eh wr uhgxfh wkh pdjqhwlf hog vwuhqjwk/ wr uhgxfh wkh prwlrqdo Vwdun hog1 Fodvvlfdo fdofxodwlrqv suhglfw wkdw wkh hog uhtxluhg wr lrql}h d U|gehuj vwdwh/ uhodwhv wr wkh sulqflsdo txdqwxpqxpehu dv iroorzv= ' 8 ' +<15, z ?e zkhuh 8 lv wkh prwlrqdo Vwdun hog vwuhqjwk/ dqg z lv wkh yhorflw| ri wkh +dqwl0,dwrp shushqglfxodu wr wkh pdjqhwlf hog1 Fodvvlfdoo|/ wkh . whup/ gxh wr wkh prwlrqdo Vwdun hog/ jlyhv ul}h wr d vwdelol}lqj pdjqhwurq0olnh ^45:` ruelw ri wkh srvlwurq durxqg wkh qxfohxv1 Li wkh udglxv ri wkh pdjqhwurq ruelw lv odujhu wkdq wkh srvlwlrq ri wkh vdggohsrlqw/ wkh v|vwhplrql}hv1 Zh nqrz wkdw o ' /dqgT ' n 85/ iru dq hohfwulf hog lq wkh ?2 o s }0gluhfwlrqv1 Wkh srvlwlrq ri wkh vdggohsrlqw lv orfdwhg dw= 5 ' *8 / dqg wkxv lw fdq eh xqghuvwrrg wkdw ' 8 ' 1 Qrwlfh wkh dqdorjxh zlwk wkh fodvvlfdo hoglrql}dwlrq z ?e odz lq wkh fdvh ri mxvw wkh suhvhqfh ri dq hohfwulf hog +Fkdswhu 5,= 8 ' +<16, S?e Lq wklv fdvh lrql}dwlrq rffxuv zkhq wkh + hog iuhh, elqglqj hqhuj| ri d U|gehuj vwdwh lv vpdoohu wkdq wkh hqhujhwlf srvlwlrq ri wkh vdggohsrlqw1 Wkxv . ' / T ' n 85/ 2?2 o 456 Sxovhg Ilhog Uhfrpelqdwlrq dw FHUQ s dqg wkh orfdwlrq ri wkh vdggohsrlqws lv 5 ' *8 1 Wkh dprxqw ri hqhuj| e| zklfk wkh vdggoh0srlqw lv orzhuhg lv= T '2 8 /ohdglqjwr8 ' 1 S?e Wkh fodvvlfdo fdofxodwlrqv zhuh edvhg rq d 5G qxphulfdo lqwhjudwlrq ri wkh htxdwlrqv ri prwlrq ri d srvlwurq ruelwlqj dq dqwl0surwrq lq d pdjqhwlf hog furvvhg zlwk dq hohfwulf hog lq wkh fhqwhu ri pdvv iudph1 Wkh ydoxh ri wkh hohfwulf hog fruuhvsrqgv wr wkh ydoxh ri wkh prwlrqdo Vwdun hog h{shulhqfhg e| d U|gehuj dwrp ri 715 N1 Orzhulqj wkh pdjqhwlf hog wr 2 W zrxog douhdg| suhyhqw lrql}dwlrq ri d ? 'HfU|gehuj vwdwh +vhh Ilj1 <147,1 Lw lv qrw |hw fohdu krz wkh orzhulqj ri wkh pdjqhwlf hog h hfwv wkh wudsslqj h!flhqf| ri wkh dqwl0surwrqv iurpwkh DG0ulqj/ dqg wklv vkrxog eh lqyhvwljdwhg wr vhw d orzhu olplw rq wkh pdjqhwlf hog vwuhqjwk1 Iljxuh <147= Pdjqhwlf hog uhtxluhg wr hog lrql}h dq dqwl0k|gurjhq dwrp zlwk d yhorflw| shushqglfxodu wr wkh pdjqhwlf hog/ fruuhvsrqglqj wr wkh yhorflw| ri d 715 N sduwlfoh1 Wkh rshq wuldqjohv uhsuhvhqw wkh uhvxowv iurp wkh 50G fodvvlfdo fdofxodwlrq1 Wkh grwwhgt olqh fruuhvsrqgv wr +dwrplf xqlwv duh xvhg,= 2&A yzE @ I @ ?e / zlwk yz @ 6 /dqgW @ 7=5 N1 Lw vkrxog eh qrwhg wkdw wkh ehkdylru ri U|gehuj dwrpv lq furvvhg pdjqhwlf dqg hohfwulf hogv dw wkhvh kljk sulqflsdo txdqwxpqxpehuv kdv qrw |hw ehhq lqyhvwljdwhg1 Wkh olihwlph ri U|gehuj vwdwhv zklfk fdq fodvvlfdoo| lrql}h/ frxog eh vljql fdqw/ dqg wkhuh fdq hyhq eh fkdrwlf vwdeoh vwdwhv lq . hogv1 Lq idfw Zlhexvfk hw do1 ^46;` kdyh vkrzq wkdw fhuwdlq vwdwhv vxusdvvlqj wkh vdggohsrlqw lq . hogv kdyh orqj olihwlphv1 Li wkh olihwlph ri wkh fuhdwhg U|gehuj vwdwhv lv orqjhu wkdq wkh wlph lw wdnhv wkh dqwl0k|gurjhq wr klw wkh zdoo/ lw fdq eh ghwhfwhg1 Wkh dqwl0k|gurjhq dwrpv zlwk d vpdoo z frpsrqhqw/ kdugo| h{shulhqfh dq| prwlrqdo Vwdun h hfw dqg wkhuhiruh zloo qrw lrql}h li wkh lqgxfhg hohfwulf hog lv vpdoo hqrxjk1 Zkhq d orqj zhoo lv xvhg wr vxssuhvv edfnjurxqg vljqdo/ wkhvh dqwl0k|gurjhq dwrpv zlwk vpdoo z fdqqrw eh ghwhfwhg vlqfh wkh| zloo hog lrql}h zkhq wkh| uhdfk wkh hgjh ri wkh orqj zhoo gxulqj wkhlu wudyho dorqj wkh }0d{lv1 Rq wkh rwkhu kdqg rqh frxog xvh wklv hog lrql}dwlrq zkhq wkh dqwl0k|gurjhq dwrpv uhdfk wkh rxwhu vlghv ri wkh orqj zhoo/ wr ghwhfw 457 <18 Ixwxuh Gluhfwlrq 6 6 a b 3 3 trapped positron 0 0 . trapped V=300 m/s . -3 anti-H -3 anti-proton potential (eV)potential potential (eV) potential -6 -6 9 121518212427 9 121518212427 position along z-axis (cm) position along z-axis (cm) Iljxuh <148= Xvlqj d orqj dqwl0surwrq zhoo wr ghwhfw dqwl0k|gurjhq1 Li dqwl0 k|gurjhq lv surgxfhg zlwk d fhuwdlq yhorflw| dorqj wkh }0gluhfwlrq/ lw zloo uhdfk wkh rxwhu zdoo ri wkh orqj dqwl0surwrq zhoo diwhu d fhuwdlq wlph +d,1 Gxh wr wkh hohfwulf hog dw wklv srwhqwldo zdoo/ wkh dqwl0k|gurjhq dwrp zloo hog lrql}h/ dqg wkh srvlwurq lv fdswxuhg lq wkh srvlwurq zhoo orfdwhg rq wkh vlgh ri wklv srwhqwldo zdoo/ zkloh wkh dqwl0surwrq lv wudsshg lq wkh orqj zhoo +e,1 dqwl0k|gurjhq dwrpv1 Wklv fdq eh grqh e| lpsohphqwlqj dgglwlrqdo zhoov iru srvlwurqv rq wkh wzr vlghv ri wkh orqj zhoo1 Hdfk wlph dq dqwl0k|gurjhq dwrp hog lrql}hv/ wkh orqj zhoo lv oohg zlwk dq dqwl0surwrq dqg wkh srvlwurq zhoo rq wkh vlgh lv oohg e| d srvlwurq +vhh Ilj1 <148,1 Diwhu doo wkh uhfrpelqhg dqwl0k|gurjhq dwrpv kdyh hog lrql}hg/ wkh srvlwurq zhoo fdq eh wudqvsruwhg wr d kduprqlf uhjlrq lq wkh wuds/ vr wkdw wkh srvlwurqv fdq eh frxqwhg1 Wkh vhfrqg lpsuryhphqw zrxog eh wr xvh idvwhu sxovh jhqhudwruv wr surgxfh idvwhu hohfwulf hog wxuq r v1 Wkh lqwhudfwlrq yroxph lv pdlqo| ghwhuplqhg e| wkh wlph lw wdnhv wr wxuq r wkh hohfwulf hog/ vlqfh lw kdv wr eh wxuqhg r zlwklq wkh ruelwlqj shulrg ri wkh fuhdwhg U|gehuj vwdwh1 Wkhuhiruh/ d idvwhu hohfwulf hog wxuq r uhvxowv lq d vwdwh glvwulexwlrq zlwk pruh ghhso| erxqg vwdwhv dqg pruh uhfrpelqdwlrqv iru wkh vdph fkdujhg sduwlfoh ghqvlwlhv1 Pruhryhu/ ghhshu erxqg vwdwhv duh ohvv vxvfhswleoh wr h{whuqdo hohfwulf hogv dqg wkxv wkh prwlrqdo Vwdun h hfw zloo eh vxssuhvvhg1 Wkh qdo lpsuryhphqw zrxog eh wr orzhu wkh whpshudwxuh ri wkh dqwl0surwrqv e| vlghedqg frrolqj ^45:/ 463`/ dv lv grqh zlwk wkh srvlwurqv/ wr uhgxfh wkh pdjqhwurq ruelw ri wkh dqwl0surwrqv1 Wkh wudsshg dqwl0surwrqv duh eholhyhg wr kdyh odujh pdjqhwurq udgll/ vlqfh d odujh iudfwlrq ri wkh dqwl0surwrqv gr qrw hqwhu wkh wuds dorqj wkh fhqwudo d{lv ri wkh wuds1 Wklv uhvxowv lq d udwkhu odujh forxg vl}h1 Wkh srvlwurq forxg krzhyhu/ lv vlghedqg0frrohg diwhu wkh wudsslqj vfkhph ri srvlwurqv/ uhvxowlqj lq d srvvleoh vpdoohu forxg vl}h wkhq wkh dqwl0surwrqv1 Li wkh forxg vkdshv gl hu yhu| pxfk/ wkh ryhuods lq d SIU h{shulphqw zloo eh yhu| vpdoo1 Rqo| gxulqj wkh odvw vkliw ri ehdp wlph/ wkh d{ldo uhvrqdqfh ri wkh dqwl0surwrqv lq d kduprqlf wudsslqj srwhqwldo frxog eh ghwhfwhg/ dqg wkxv wkh h hfw ri vlghedqg frrolqj ri dqwl0surwrqv lq d SIU h{shulphqw vkrxog vwloo eh lqyhvwljdwhg1 458 Fkdswhu 43 Vxppdu| 4314 Prwlydwlrq ri wkh Uhvhdufk Lq wklv wkhvlv/ wkh pdnlqj +Fkdswhu 9/ :/ ;/ dqg <, dqg wkh euhdnlqj +Fkdswhu 5/ 6/ 7/ dqg 8, ri U|gehuj dwrpv lv lqyhvwljdwhg1 Wkh pdnlqj ri dq dwrp fdq riwhq eh grqh e| wkh wlph lqyhuvh ri d phfkdqlvp zklfk euhdnv dq dwrp1 Euhdnlqj ri dwrpv fdq eh dffrpsolvkhg e| wlph ydu|lqj hohfwulf hogv +Fkdswhu 5,/ ru skrwrq hogv +Fkdswhu 6/ dqg 7,1 Wlph ydu|lqj hohfwulf hogv fdq dovr eh xvhg wr iuxvwudwh wkh euhdnlqj +Fkdswhu 8,/ e| gldedwlfdoo| vzlwfklqj dq lrql}lqj vwdwh ri dq dwrplqwr d erxqg vwdwh1 Wkh fduhixo h{dplqdwlrq ri wkh euhdnlqj ru wkh iuxvwudwhg euhdnlqj ri d U|gehuj dwrp riwhq uhyhdov dwrplf g|qdplfv/ pdnlqj wkhp lghdo wr frqvwuxfw dqg whvw +txdqwxp, wkhrulhv1 Lq Fkdswhu 9 zh ghprqvwudwh wkdw wkh wlph lqyhuvh ri d surfhvv ghvfulehg lq Fkdswhu 5 +Vhohfwlyh Ilhog Lrql}dwlrq,/ fdq eh xvhg wr pdnh d U|gehuj vwdwh iurp d iuhh hohfwurq dqg d iuhh lrq +Sxovhg Ilhog Uhfrpelqdwlrq,1 Pdnlqj dq dwrpe| uhfrpelqlqj dq hohfwurq dqg d surwrq lv qrw vlpsoh1 Wkh uh0 frpelqdwlrq lv rqo| srvvleoh zkhq d wklug remhfw fduulhv dzd| wkh h{fhvv hqhuj| ri wkh fdswxuhg hohfwurq1 Wklv wklug sduwlfoh fdq eh d vhfrqg hohfwurq +wklv surfhvv lv nqrzq dv wkuhh0erg| uhfrpelqdwlrq,/ ru d skrwrq +udgldwlyh uhfrpelqdwlrq,1 Sxovhg Ilhog Uh0 frpelqdwlrq +SIU, ^<;/ <<` fdq eh uhjdughg dv lqwhuphgldwh ehwzhhq wkh udgldwlyh dqg wkh wkuhh0erg| surfhvv1 Rqh fdq vd| wkdw wkh h hfw ri wkh wklug erg|/ vwlpxodwlqj wkh uhfrpelqdwlrq wkurxjk lwv wlph ghshqghqw hohfwulf hog/ lv qrz dssolhg e| kdqg lq wkh irupri wdloruhg sxovhv1 Lq Fkdswhu 9/ :/ dqg ; wklv qryho dqg h!flhqw uhfrpelqdwlrq vfkhph lv glvfxvvhg lq ghwdlo1 Lq Fkdswhu < d surjuhvv uhsruw lv suhvhqwhg rq wkh lpsohphqwdwlrq ri SIU iru wkh surgxfwlrq ri frog +e2 N, dqwl0k|gurjhq1 Wkh h{shulphqwv zhuh shuiruphg dw FHUQ iru wkh DWUDS frooderudwlrq1 Wklv surgxfwlrq ri qhxwudo dqwl0pdwwhu zrxog hqdeoh wkh gluhfw frpsdulvrq ri qhxwudo pdwwhu zlwk qhxwudo dqwl0pdwwhu/ zklfk fdq eh xvhg wr whvw FSW lqyduldqfh dqg wkh Zhdn Htxlydohqfh Sulqflsoh +ZHS,1 Wr surgxfh vxfk frog dqwl0pdwwhu lv wkh uvw jrdo ri wkh DWUDS +Dqwl0k|gurjhq Wuds, frooderudwlrq ^5;`1 Lq wklv fkdswhu zh vxppdul}h h{shulphqwv lq zklfk zh xvh ruglqdu| pdwwhu wr vwxg| wkh uhfrpelqdwlrq g|qdplfv ri wkh SIU vfkhph1 Iroorzlqj wkh lqlwldo ghprqvwudwlrq ri 45: Vxppdu| SIU lq Ue/ zh frqwlqxhg wkh h{shulphqwv e| uhfrpelqlqj hohfwurqv/ lqlwldoo| wudsshg lq d Shqqlqj wuds/ zlwk Ol lrqv1 Wkhuh zhuh wkuhh pdmru prwlydwlrqv iru shuiruplqj wkhvh h{shulphqwv1 Wr whvw li wkh SIU vfkhph frxog lqghhg eh xvhg wr uhfrpelqh oljkwhu lrqv zlwk iuhh hohfwurqv/ zh kdyh xvhg olwklxplrqv lqvwhdg ri uxelglxplrqv/ zklfk zhuh xvhg lq suhylrxv h{shulphqwv1 Olwklxp ehlqj 45 wlphv oljkwhu wkdq uxelglxp uhvhpeohv pxfk pruh d surwrq/ dowkrxjk lw lv vwloo : wlphv khdylhu1 Wkh vhfrqg prwlydwlrq zdv wr vwxg| SIU lq d frq jxudwlrq zklfk kdg d juhdwhu uhvhpeodqfh zlwk wkh DWUDS h{shulphqw dw FHUQ/ zkhuh uhfrpelqdwlrq ri wudsshg srvlwurqv dqg wudsshg dqwl0surwrqv zloo eh vwxglhg lq Shqqlqj wudsv ^43;`1 Wkh odvw prwlydwlrq zdv wr lqfuhdvh wkh uhfrpelqdwlrq h!flhqf| ri wkh SIU vfkhph1 Pruhryhu/ zh sursrvh wkdw SIU fdq eh xvhg lq fdwlrq vshfwurvfrs| rq prohfxodu vshflhv iru zklfk odvhu0h{flwdwlrq ri d U|gehuj vwdwh idlov +Fkdswhu ;,1 Lq Skrwr0lqgxfhg Lqiud0Uhg Lrql}dwlrq +SLUL, vshfwurvfrs| ^43843:`/ wkh fdwlrq vshfwuxpri d prohfxoh lv uhfrughg zlwk wkh dlg ri d U|gehuj vwdwh lq wkdw vshfl f prohfxoh1 Prvw frpprqo|/ vxfk d U|gehuj vwdwh lv suhsduhg e| odvhu0h{flwdwlrq1 Iru frpsoh{ prohfxohv odvhu0h{flwdwlrq ri d zhoo gh qhg U|gehuj vwdwh fdq idlo/ vr wkdw wkh SLUL whfkqltxh fdq qrw eh dssolhg1 Uhfhqwo| zh kdyh vkrzq wkdw wkh SIU phwkrg fdq eh xvhg wr uhfrpelqh d iuhh hohfwurq n zlwk d odujh lrqlf fduerq foxvwhu vxfk dv FSf/ lqgxflqj d kljko| h{flwhg erxqg vwdwh ri vxfk d prohfxoh +? r Hf, ^<<`1 Wklv zdv wkh uvw wlph wkh h{lvwhqfh ri FSf U|gehuj vwdwhv zdv revhuyhg frqylqflqjo|1 Lq dgglwlrq/ d wkhruhwlfdo ghvfulswlrq lv suhvhqwhg zlwk vhpl0fodvvlfdo fdofxodwlrqv1 Wkhvh vhpl0fodvvlfdo fdofxodwlrqv jlyh ghhshu lqvljkw rq wkh vwdwhv zklfk duh ehlqj iruphg lq wkh uhfrpelqdwlrq surfhvv dqg fdq eh xvhg wr sureh uhfrpelqdwlrq g|qdplfv qrw surehg e| wkh h{shulphqwv1 4315 Vfkhph dqg H!flhqf| Lq Ilj1 4314 wkh SIU vfkhph lv vnhwfkhg1 Dq lrq lv vlwxdwhg lq d vwdwlf hohfwulf hog wkdw prgl hv wkh Frxorpe srwhqwldo vxfk wkdw d vdggoh srlqw lv fuhdwhg +Ilj1 4314d,1 Li dq hohfwurq sdvvhv ryhu wkh vdggoh srlqw lq wkh prgl hg Frxorpe srwhqwldo/ lw zloo wdnh d vpdoo/ exw qrw qhjoljleoh/ dprxqw ri wlph wr uhwxuq wr wkh vdggoh srlqw dqg hvfdsh iurp wkh lrq +Ilj1 4314d,1 Li wkh vwdwlf hog lv wxuqhg r +Ilj1 4314e, ehiruh wkh hohfwurq uhwxuqv wr wkh vdggoh srlqw/ lw zloo uhpdlq erxqg lq d kljko| h{flwhg vwdwh +Ilj1 4314f,1 Wkh wlph uhtxluhg iru wkh hohfwurq wr wudyho iurpwkh vdggoh srlqw/ wr wkh qxfohxv/ dqg edfn wr wkh vdggoh srlqw lv derxw 4 qv iru wkh hogv dqg hqhujlhv xvhg lq wkhvh h{shulphqwv1 Wklv wlph lv frpsdudeoh wr wkh wxuq r wlph ri wkh vwdwlf hohfwulf hog +bfI $ fI lq 31; qv,1 Lq Ilj1 4314g wkh h{shulphqwdoo| ghwhuplqhg h!flhqf| +qxpehu ri uhfrpelqhg dwrpv glylghg e| wkh qxpehu ri iuhh lrqv, ri wklv vfkhph lv ghslfwhg dv d ixqfwlrq ri wkh ghod| ri wkh idvw hog wxuq r 1 Wklv ghod| lv zlwk uhvshfw wr wkh wlph zkhq wkh iuhh hohfwurq kdv lwv wxuqlqj srlqw lq wkh hohfwulf hog1 Fohduo|/ d pd{lpxp qxpehu ri uhfrpelqdwlrq hyhqwv lv uhfrughg dw }hur ghod|1 D frpsdulvrq zlwk suhylrxv h{shulphqwv zlwk uxelglxp lrqv vkrzv wkdw wkh h!flhqf| + f f3 ^<;`/ Fkdswhu 9, kdv jrqh xs e| doprvw dq rughu ri 45; 4316 H{shulphqwdo a b c E z rubidium:Rb: Chapter previous 6 experiment lithium:Li: Chapter this 7experiment 2.0 d 1.5 1.0 efficiency (%)efficiency 0.5 0.0 -10-8-6-4-20 2 4 6 810 closing pulse delay (ns) Iljxuh 4314= +d0f,= Vfkhpdwlf uhsuhvhqwdwlrq ri wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph +vhh wh{w,1 +g,= H{shulphqwdoo| revhuyhg h!flhqf| dv d ixqfwlrq ri wkh ghod| ri wkh txlfn wxuqr 1 Wkh rshq flufohv uhsuhvhqw uhfrpelqdwlrq ri iuhh hohfwurqv dqg olwklxp lrqv zlwk wkh xvh ri dq hohfwurq wuds +Fkdswhu :,1 Wkh vrolg flufohv uhsuhvhqw gdwd zkhuh zh vwxglhg uhfrpelqdwlrq ri iuhh hohfwurqv dqg uxelglxp lrqv lq d wudsohvv jhrphwu| +Fkdswhu 9,1 pdjqlwxgh +2f f32/ Fkdswhu :, dqg wkdw wkh hohfwurq sxovhv duh pxfk vkruwhu1 Wkh lqfuhdvh lq h!flhqf| lv pdlqo| gxh wr wkh idfw wkdw wkh hohfwurq sxovhv duh vkruwhu lq wlph +iurp44 qv ^<;` wr 61; qv, dqg wkdw zh kdg ehwwhu frqwuro ryhu wkh ryhuods yroxphri wkh lrq forxg dqg wkh yroxph ri wkh hohfwurq sxovhv1 Zh dfklhyhg wkh kljkhvw h!flhqf| +9(, vr idu zkhq zh xvhg wkh SIU vfkhph wr uhfrpelqh iuhh hohfwurqv zlwk iuhh lrqlf fduerq foxvwhuv lq d wudsohvv hqylurqphqw ^<<`1 Qrwh wkdw zh kdyh vkrzq wkdw SIU fdq eh xvhg lq wkh jhrphwu| ri wudsshg hohfwurqv dqg oljkw lrqv1 4316 H{shulphqwdo Zh kdyh xvhg wzr gl huhqw vhwxsv wr vwxg| Sxovhg Ilhog Uhfrpelqdwlrq1 Zlwk wkh uvw vhwxs zh kdyh vwxglhg uhfrpelqdwlrq zlwk uxelglxp lrqv +Fkdswhu 9, dqg uhfrpelqdwlrq zlwk lrqlf fduerq foxvwhuv +Fkdswhu ;,1 Wkh vhfrqg vhwxs +Fkdswhu :, zdv ghvljqhg wr plplf dv forvho| dv srvvleoh wkh frqglwlrqv xqghu zklfk dqwl0surwrqv dqg srvlwurqv vkrxog eh uhfrpelqhg dw FHUQ wr surgxfh frog dqwl0k|gurjhq1 Wkh hvvhqwldo gl huhqfh ehwzhhq wkh vhwxsv lv wkh hohfwurq vrxufh1 Iru wkh lqlwldo h{shulphqwv +Fkdswhu 9/ dqg ;, zh xvhg 45< Vxppdu| a electrons ions trapped electrons ions b B=0-64 mT Iljxuh 4315= Vnhwfk ri wkh wzr h{shulphqwdo vhwxsv xvhg wr vwxg| SIU1 d= Wkh vhwxs zlwk zklfk zh vwxglhg uhfrpelqdwlrq ri iuhh hohfwurqv zlwk Uen dqg n zlwk FSf1 e= Wkh vhwxs zlwk zklfk zh vwxglhg uhfrpelqdwlrq ri iuhh hohfwurqv/ ruljlqdwhg iurp dq hohfwurq wuds/ zlwk Oln1 skrwrhohfwurqv/ zkloh wkh odwhu h{shulphqwv zhuh shuiruphg zlwk hohfwurqv iurp d Shqqlqj wuds1 431614 Skrwrhohfwurq Vhwxs Lq wkh uvw vhwxs d sxovhg hohfwurq vrxufh zdv fuhdwhg e| skrwrlrql}lqj olwklxpdwrpvlq d vpdoo vwdwlf hohfwulf hog zlwk d g|h odvhu1 W|slfdoo| hohfwurq sxovhv ri 44 qv gxudwlrq/ zlwk derxw fe hohfwurqv lq d yroxph ri 3135 pp zhuh surgxfhg1 Lq dqrwkhu uhjlrq d forxg ri lrqv lv dzdlwlqj wkh hohfwurqv1 W|slfdoo| f Ue0lrqv zhuh surgxfhg lq d yroxph ri 513 pp 1 Wkh uxelglxplrqv zhuh surgxfhg e| skrwrlrql}lqj uxelglxpdwrpvlq d vwdwlf hohfwulf hog ri 4183 Y2fp/ 83 qv ehiruh wkh olwklxp dwrpv zhuh lrql}hg/ lq d wzr0skrwrq surfhvv1 Wkh frq jxudwlrq lv ghslfwhg lq Ilj1 4315d1 Wkh lrqlf fduerq foxvwhuv zhuh surgxfhg e| skrwrlrql}lqj dqg iudjphqwlqj jdv0skdvh FSf prohfxohv lq d vwdwlf hohfwulf hog1 Wkh skrwrlrql}dwlrq pdlqo| surgxfhv wkh kljkhu lrqlf fduerq foxvwhuv1 Wkh lrqlf fduerq forxg uhvhpeohv d f|olqghu zlwk d udglxv ri 68 >p lq wkh }0dqg |0gluhfwlrq dqg d ohqjwk ri 43 pp lq wkh {0gluhfwlrq/ zlwk derxw f lrqv1 Lq wkh lrq vrxufh uhjlrq wkh hohfwurqv duh ghfhohudwhg e| wkh hohfwulf hog ri 4183 Y2fp/ dqg kdyh wkhlu wxuqlqj srlqw dw wkh srvlwlrq ri wkh lrq forxg1 Dw wkdw wlph wkh hog lv wxuqhg r e| glsslqj wkh yrowdjh rq wkh fdwkrgh sodwh iurp04183 Y wr 03153 Y1 Wkh hohfwulf hog wxuq r lv uhdol}hg e| frqqhfwlqj dq lpshgdqfh pdwfkhg/ idvw sxovh jhqhudwru wr wkh fdwkrgh sodwh1 463 4317 Uhfrpelqdwlrq ri Olwklxp dqg Uxelglxp 431615 Shqqlqj Wuds Vhwxs Wkh vhfrqg vhwxs zdv ghvljqhg wr plplf dv forvho| dv srvvleoh wkh DWUDS h{shulphqw dw FHUQ/ zkhuh rqh zloo vwxg| uhfrpelqdwlrq ri wudsshg srvlwurqv dqg wudsshg dqwl0surwrqv lq Shqqlqj wudsv ^43;`1 Lq wklv vhwxs zh vwxglhg uhfrpelqdwlrq vwduwlqj rxw zlwk wudsshg hohfwurqv dqg iuhh lrqv1 Zh kdyh xvhg VLPLRQ ^46<` wr fdofxodwh wkh vkdsh ri wkh srwhqwldo zhoo/ fuhdwhg e| d vshfl f vhw ri hohfwurghv/ lq rughu wr ghvljq d sodwh frq jxudwlrq zklfk surgxfhv dv pxfk dv srvvleoh d kduprqlf srwhqwldo lq rughu wr plplf wkh frqglwlrqv ri wkh DWUDS vhwxs dw FHUQ1 Lq wkhvh h{shulphqwv zh oohg dq hohfwurq wuds e| skrwrlrql}lqj jdv0skdvh olwklxp dwrpv1 E| frqqhfwlqj d idvw sxovh jhqhudwru rq rqh ri wkh hohfwurghv wkh yrowdjh frxog eh vzlwfkhg1 Wklv hqdeohg xv wr hpsw| wkh wuds dw dq| wlph dqg surgxfh hohfwurq sxovhv ri 61; qv gxudwlrq1 Fduh zdv wdnhq iru fruuhfw lpshgdqfh0pdwfklqj ri wkh sxovh jhqhudwru wr wkh wuds hohfwurgh1 Zh frxog oo wkh wuds zlwk derxw fD fS hohfwurqv dqg wkh uhfrughg olihwlph zdv derxw 418 pv ghshqglqj rq wkh edfnjurxqg suhvvxuh +f3S Wruu,1 Olwklxplrqv zhuh surgxfhg 6 fpdzd| iurpwkh hohfwurq wuds e| xvlqj lrql}lqj odvhu oljkw1 W|slfdoo| zh zrxog surgxfh d f|olqgulfdoo| vkdshg lrq forxg frqwdlqlqj f2 f lrqv/ zlwk d gldphwhu ri 5 pp dqg d ohqjwk ri 43 pp1 Wkh odvw sodwh zdv frqqhfwhg wr d idvw sxovh jhqhudwru zklfk frxog udps wkh yrowdjh grzq iurp 0418 Y wr dq| yrowdjh lq ehwzhhq 0418 Y dqg . 413 Y zlwklq 31; qv1 Djdlq fduh zdv wdnhq wr pdwfk wkh lpshgdqfh ri wkh sdudooho fdsdflwru sodwh wr wkh rxwsxw ri wkh idvw sxovh jhqhudwru1 Wkh zkroh sodwh frq jxudwlrq zdv sodfhg lq wkh khduw ri 5 frlov lq wkh Khopkrow} frq jxudwlrq surgxflqj d wxqdeoh pdjqhwlf hog ri ff Sef pW1 Wkh sodwh frq jxudwlrq lv ghslfwhg lq Ilj1 4315e1 Lq doo wkh h{shulphqwv d vpdoo vwdwlf hohfwulf hog lv suhvhqw lq wklv uhjlrq ri 533 pY2fp wr hqvxuh wkdw dq| xquhfrpelqhg iuhh hohfwurq lv dffhohudwhg rxw ri wklv uhjlrq dqg wr suhyhqw wkh h hfw ri wudsslqj wkh hohfwurqv lq wkh dwwudfwlyh srwhqwldo ri wkh lrq forxg1 Iru wkh yroxphv dqg ghqvlwlhv xvhg lq wkh h{shulphqwv/ wkh hohfwurqv ihho dq dwwudfwlyh hog ri 43 pY2fp dw wkh hgjh ri wkhvh yroxphv1 Vxfk d orz ghqvlw| sodvpd lv wkhuhiruh qrw vwdeoh zkhq wkh lrq uhjlrq lv eldvhg zlwk dq hohfwulf hog ri 533 pY2fp1 Wkh h{shulphqwv zhuh shuiruphg lq d ydfxxp fkdpehu zlwk d edfnjurxqg suhvvxuh ri D f3. Wruu1 Wkh uhfrughg h!flhqf| zdv doprvw dq rughu ri pdjqlwxgh kljkhu lq wklv vhwxs frp0 sduhg wr wkh skrwrhohfwurq vhwxs +vhh Ilj1 4314g,/ exw wkh glvdgydqwdjh lv wkdw d Shqqlqj wuds uhtxluhv d pdjqhwlf hog1 Lq wkh h{shulphqwv shuiruphg lq wklv vhwxs/ wkh pd{lpxp hogvwuhqjwk zdv 9713 pW/ zkloh dw wkh DWUDS h{shulphqw dw FHUQ wkh pdjqhwlf hog0 vwuhqjwk lq wkh Shqqlqj wuds lv dv kljk dv 9 W1 Lq Fkdswhu < zh glvfxvv krz vxfk d vwurqj pdjqhwlf hog pljkw shuwxue wkh surgxfwlrq ri dqwl0k|gurjhq e| SIU1 4317 Uhfrpelqdwlrq ri Olwklxp dqg Uxelglxp Wlplqj lv hvvhqwldo lq d SIU h{shulphqw1 Wklv fdq eh vhhq lq Ilj1 4314g= li zh wxuq r wkh vwdwlf hohfwulf hog ehiruh wkh hohfwurqv uhdfk wkh lrqv kdoizd| ehwzhhq wkh sdudooho fdsdflwru sodwhv/ wkh hohfwurqv zloo kdugo| eh vorzhg grzq dqg zloo sdvv wkh lrqv zlwkrxw 464 Vxppdu| ehlqj uhfrpelqhg1 Li zh wxuq r wkh vwdwlf hohfwulf hog wrr odwh wkh hohfwurqv zloo wxuq durxqg dw wkh lrqv exw zloo jdlq nlqhwlf hqhuj| djdlq gxh wr wkh vwdwlf hohfwulf hog dqg zloo ohdyh wkh lrq uhjlrq lq wkh rssrvlwh gluhfwlrq zlwkrxw ehlqj uhfrpelqhg1 Li zh wxuq r wkh vwdwlf hohfwulf hog dw wkh prphqw wkh hohfwurqv wxuq dqg ryhuods zlwk wkh lrqv/ zh uhfrug d pd{lpxpuhfrpelqdwlrq h!flhqf| ri 513 (1 IurpIlj1 4314g zh dovr uhwulhyh wkh wlph sur oh iurp wkh hohfwurq sxovhv vlqfh zh uhfrug d Jxdvvldq sur oh zlwk d zlgwk ri 61; qv +vrolg olqh, zklfk phdqv wkdw zh kdyh fuhdwhg hohfwurq sxovhv ri 61; qv1 Lq wklv fdvh wkh hohfwurq sxovhv duh surgxfhg e| sxovlqj rshq wkh hohfwurq wuds lq 31; qv dqg wkhuhiruh rqh fdq h{shfw wkdw hohfwurq sxovhv duh fuhdwhg ri 31; qv +Fkdswhu :,1 Wkh idfw wkdw wkh sxovh gxudwlrq lv 9 wlphv orqjhu lv pdlqo| gxh wr Frxorpe uhsxovlrq zklfk uhvxowv lq dq hqodujhphqw ri wkh hohfwurq forxg1 Wkh hqodujhphqw ri wkh hohfwurq forxg lv pdlqo| uhvwulfwhg lq wkh }0gluhfwlrq vlqfh wkh suhvhqfh ri wkh pdjqhwlf hog suhyhqwv wkh forxg iurpeorzlqj xs lq gluhfwlrqv shushqglfxodu wr wkh }0d{lv1 Wklv/ lq wxuq/ zloo uhvxow lq gl huhqw wudyhoolqj wlphv wrzdugv wkh lrqv dqg wkhuhiruh d eurdghqlqj ri wkh wlph gxudwlrq ri wkh hohfwurq sxovhv1 Qrwh wkdw wklv wlph gxudwlrq ri wkh hohfwurq sxovhv lv pxfk vkruwhu wkdq lq wkh h{shulphqwv zlwk Ue +Fkdswhu 9, zkhuh wkh +skrwr0,hohfwurq sxovh gxudwlrq zdv olplwhg e| wkh gxudwlrq ri wkh odvhu sxovhv +q f qv,/ dqg wkdw SIU zrunv iru erwk khdy| +Ue, lrqv dv iru oljkw +Ol, lrqv1 D iuhh hohfwurq lv prvw olnho| wr jhw uhfrpelqhg zlwk wkh SIU vfkhph zkhq lw lv forvh wr wkh qxfohxv zlwk }hur nlqhwlf hqhuj|/ exw wkh frruglqdwhv +iru d fhuwdlq {hg glvwdqfh wr wkh lrq, ri wkh hohfwurq uhodwlyh wr wkh lrq gr qrw sod| dq hvvhqwldo uroh1 Wklv phdqv wkdw lw lv qrw dssursuldwh wr fkdudfwhul}h SIU zlwk d furvv vhfwlrq dv lw lv zlwk prvw rwkhu uhfrpelqdwlrq surfhvvhv1 Wkhuhiruh zh lqwurgxfhg dq lqwhudfwlrq yroxph +T?|/dwkrurxjk glvfxvvlrq ri T?| lv jlyhq lq Fkdswhu :, wr ghvfuleh wkh revhuyhg h!flhqf|/ zklfk lv wkh yroxph lq vsdfh durxqg wkh lrq lq zklfk wkh hohfwurq kdv wr eh zlwk d fhuwdlq yhorflw| wr eh uhfrpelqhg1 D vlpsoh irupxod wkhq suhglfwv zkdw wklv T?| vkrxog eh= oeS ' 4e4J?TJeoT?| +4314, zkhuh QoeS lv wkh qxpehu ri uhfrughg dwrpv +43,/ 4e lv wkh hohfwurq ghqvlw| lq wkh hohfwurq e D 3 sxovhv/ 4J? lv wkh lrq ghqvlw| +f f fp ,/ dqg TJeo lv wkh ryhuods yroxph ri wkh hohfwurq forxg dqg wkh lrq forxg1 Wkh vl}h ri TJeo lv ghwhuplqhg e| wkh vpdoohvw forxg= 3f 3 lq rxu fdvh wkh hohfwurq forxg1 Zh wkxv rewdlq d T?| rq wkh rughu ri 43 fp 1Vxfkdq lqwhudfwlrq yroxph zrxog fruuhvsrqg wr d U|gehuj vwdwh durxqg ? r Hf1Zhwkhuhiruh eholhyh wkdw kljk U|gehuj vwdwhv duh surgxfhg durxqg ? r Hf/e|phdqvriwkhSIU vfkhph1 Wr yhuli| wklv k|srwkhvlv zh xvhg wkh whfkqltxh ri Vhohfwlyh Ilhog Lrql}dwlrq +VIL,/ dv glvfxvvhg lq Fkdswhu 5/ wr sureh wkh erxqg vwdwh glvwulexwlrq diwhu wkh uhfrpelqdwlrq hyhqw1 Hyhu| erxqg vwdwh lq dq dwrplf ru prohfxodu v|vwhp kdv d vwdwlf hohfwulf hog dvvrfldwhg zlwk lw e| zklfk lw zloo eh lrql}hg1 D kljko| h{flwhg vwdwh zloo eh lrql}hg e| d uhodwlyh vpdoo hohfwulf hog frpsduhg wr d pruh ghhso| erxqg vwdwh1 Wkh uhodwlrq ehwzhhq wkh ydoxh ri wkh hohfwulf hog dw zklfk hog lrql}dwlrq fodvvlfdoo| rffxuv dqg wkh sulqflsdo 465 4318 Uhfrpelqdwlrq ri Fduerq Foxvwhuv txdqwxpqxpehu q lv +lq dwrplf xqlwv,= . 8 'E 2 ' +4315, 2 S?e Li rqh udpsv wkh vwdwlf hohfwulf hog lq wlph dqg prqlwruv dw zklfk wlph lrql}dwlrq rf0 fxuv rqh fdq ghgxfh wkh erxqg vwdwh glvwulexwlrq ri dq dwrplf ru prohfxodu v|vwhp1 Lq Ilj1 4316d d VIL wudfh lv ghslfwhg ri wkh uhfrpelqhg vwdwhv zkhq gxulqj wkh uhfrpelqdwlrq hyhqw wkh hohfwulf hog lq wkh lrq uhjlrq lv vzlwfkhg iurp613 Y2fpwr 3153 Y2fplq 31; qv +vrolg wuldqjohv,1 Wkh VIL ghwhfwlrq vwduwhg 417 >v diwhu wkh uhfrpelqdwlrq hyhqw1 Fohduo| lw lv vhhq wkdw zh pdlqo| surgxfh vwdwhv zklfk duh lrql}hg e| wkh orzhvw VIL hogv1 Li zh xvh htxdwlrq+4315, wr ghwhuplqh zklfk erxqg vwdwhv zh kdyh surgxfhg zh lqghhg revhuyh wkdw zh duh pdnlqj U|gehuj vwdwhv zlwk d sulqflsdo txdqwxp qxpehu durxqg qr Hf/lq shuihfw djuhhphqw zlwk wkh sulqflsdo txdqwxp qxpehu zh hvwlpdwhg iurp rxu revhuyhg h!flhqf| dqg wkh T?| ghgxfhg iurplw1 D qxphulfdo hvwlpdwh ri T?| lv rewdlqhg e| vroylqj Qhzwrq*v htxdwlrqv wr ghwhu0 plqh wkh erxqg vwdwh glvwulexwlrq diwhu d SIU h{shulphqw1 Dq lqwhudfwlrq yroxph ri 3f f2D fs fp lv irxqg1 Xvlqj wkh rewdlqhg vwdwh glvwulexwlrq + ?: 'Hfzlwk {? ' ?2 : ?:2 '2f, wkh VIL wudfh lv fdofxodwhg +xvlqj wkh Odqgdx0]hqhu dssur{lpdwlrq/ Fkdswhu 5, dqg d yhu| jrrg djuhhphqw ehwzhhq wkhru| dqg h{shulphqw lv revhuyhg +Ilj1 4316d/ wklq olqh,1 4318 Uhfrpelqdwlrq ri Fduerq Foxvwhuv Wkh h!flhqf| zh rewdlqhg zkhq lrqlf fduerq foxvwhuv duh uhfrpelqhg zlwk iuhh hohfwurqv zlwk wkh SIU vfkhph +Fkdswhu ;, zdv dv kljk dv SE e f32 ^<<`1 W|slfdoo| zh ghwhfwhg derxw 48 uhfrpelqhg prohfxohv1 Wkh idfw wkdw lq wklv h{shulphqw wkh kljkhvw h!flhqf| zdv uhfrughg/ lv dwwulexwhg wr dq rswlpdo ryhuods yroxph ri wkh hohfwurqlf dqg lrqlf forxgv/ n dqg wkh lqhuwld ri wkh odujh prohfxodu lrqv +d FSf lrq lv :53 wlphv khdylhu wkdq d surwrq,1 Iurpwkh dfklhyhg h!flhqf| zh djdlq frqfoxgh zlwk wkh khos ri htxdwlrq +4314, wkdw zh duh surgxflqj kljk U|gehuj vwdwhv durxqg ? r 2ff Lq Ilj1 4316e/ wkh U|gehuj vwdwh glvwulexwlrq diwhu uhfrpelqdwlrq zlwk SIU lv ghslfwhg iru uhfrpelqdwlrq ri wkh fduerq foxvwhuv +FDf 0FSf,/ vkrzlqj wkdw wkh vwdwh glvwulexwlrq shdnv iru vpdoo VIL hogv/ dqg wkxv iru yhu| kljk U|gehuj vwdwhv1 Vlqfh wkh 4 qv wxuq r uhgxfhv wkh hohfwulf hog wr 315 Y2fp/ vwdwhv zlwk d sulqflsdo txdqwxp qxpehu eh|rqg ? '2ffduh qrw vwdeoh1 IurpIlj1 4316e/ lw lv ghgxfhg wkdw U|gehuj vwdwhv duh surgxfhg durxqg ? ' bf1 Wkh fdofxodwlrq ghslfwhg lq Ilj1 4316e vkrzv d gluhfw frpsdulvrq ehwzhhq wkhru| dqg h{shulphqw/ dqg fohduo| jrrg djuhhphqw lv rewdlqhg1 Wr rewdlq wklv ohyho ri djuhhphqw/ wkh srodul}delolw| ri wkh lrqlf fduerq foxvwhuv dqg dxwrlrql}dwlrq ri wkh uhfrpelqhg fduerq foxvwhuv lv lqfoxghg lq wkh wkhru|1 Dxwrlrql}dwlrq ri wkh U|gehuj n vwdwhv e| wkh lqwhudfwlrq ri wkh U|gehuj hohfwurq zlwk wkh krw FSf/ lv lqfoxghg wkurxjk d prgho wkdw doorzv wkh hohfwurq hqhuj| wr fkdqjh hyhu| wlph wkh uhfrpelqhg hohfwurq jhwv forvh wr wkh fruh1 Zkhq wkh hohfwurq jhwv zlwklq 8 dwrplf xqlwv ri wkh lrqlf fruh/ lw uhfhlyhv 466 Vxppdu| n=200 n=142 n=123 0.4 experimental theory -1 ) / Vcm ) / 3 cm -10 (x10 int V a 0.0 0.2 0.8 1.4 8.5 experimental theory ) -1 /Vcm 3 cm -11 (x10 int V b 0.0 0.2 0.8 1.4 SFI field (V/cm) Iljxuh 4316= d= Fdofxodwhg vwdwh glvwulexwlrq +gdvkhg olqh, ri wkh uhfrpelqhg U|gehuj dwrpv frpsduhg wr wkh h{shulphqwdo vwdwh glvwulexwlrq +vrolg olqh,1 Wkh h{shulphqwdoo| ghwhuplqhg lqwhudfwlrq yroxph ++4=3 3=:, 433f fp , lv ydulhg zlwklq lwv huuru wr rswlpl}h wkh frpsdulvrq zlwk wkhru| +Y ?| @ 3=6 433f fp ,1 e= Fdofxodwhg vwdwh glvwulexwlrq +grwwhg olqh, ri wkh uhfrp0 elqhg U|gehuj foxvwhuv/ frpsduhg wr wkh h{shulphqwdo vwdwh glvwulexwlrq +vrolg olqh,1 Wkh h{shulphqwdoo| ghwhuplqhg lqwhudfwlrq yroxph lv ydulhg zlwklq lwv xqfhuwdlqw| wr rswlpl}h wkh frpsdulvrq zlwk wkhru|1 d nlfn lq d udqgrpgluhfwlrq vr wkdw wkh hqhuj| ri wkh hohfwurq lv mxvw dv olnho| wr lqfuhdvh dv wr ghfuhdvh1 Li wkh nlfn lqfuhdvhv wkh hqhuj|/ wkh hohfwurq ohdyhv +dxwrlrql}dwlrq,1 Li wkh nlfn ghfuhdvhv wkh hqhuj|/ wkh hohfwurq zloo eh lq d orzhu U|gehuj vwdwh1 Iru wklv n ghhshu erxqg vwdwh wkh wlph wr uhwxuq wr wkh FSf ghfuhdvhv/ vr wkh hohfwurq zloo udslgo| jhw nlfnhg djdlq1 Wklv lv olnh d udqgrpzdon zkhuh wkh wlphehwzhhq vwhsv ghfuhdvhv lq rqh gluhfwlrq dqg wkh wlph ehwzhhq vwhsv lqfuhdvhv lq wkh rwkhu gluhfwlrq1 Wkh uhvxowlqj 3 T?| iurpwklv fdofxodwlrq lv f. f fp / lq jrrg djuhhphqw zlwk wkh h{shulphqwdo revhuydwlrq= E 2 f3 fp 1 Iurpwkh fdofxodwlrq iroorzv wkdw q :8( ri wkh ruljlqdoo| uhfrpelqhg hohfwurqv duh hmhfwhg ehiruh wkh VIL ghwhfwlrq1 4319 Dqwl0K|gurjhq Lq Uhi1 ^<7` d frpelqhg wuds lv ghvfulehg/ zkhuh w|slfdoo| : fD surwrqv dqg fS hohfwurqv +fruuhvsrqglqj ghqvlw|= 43H fp3 , zhuh ghwhfwhg lq wkh frpelqhg wuds1 Dw FHUQ/ wkh DWUDS frooderudwlrq hpsor|v vxfk d wuds wr frq qh srvlwurqv dqg dqwl0surwrqv zlwk vlplodu sduwlfoh qxpehuv1 Lpsohphqwlqj SIU lq vxfk d frq jxudwlrq dqg li wkh ryhuods 467 431: Frqfoxvlrqv dqg Rxworrn yroxph lv pd{lpdo +wkh dqwl0surwrq sodvpd wdnhv xs wkh vdph yroxph dv wkh srvlwurq sodvpd,/ wkh srvlwurq ghqvlw| lv f. fH fp3 / dqg wkh qxpehu ri wudsshg dqwl0surwrqv lv fD/ rxu vfkhph fdq surgxfh f2 f uhfrpelqhg dqwl0k|gurjhq dwrpv lq d vlqjoh h{shulphqw +dvvxplqj wkh vdph T?| dv lv revhuyhg lq rxu phdvxuhphqwv,1 Wkh h{dfw lp0 sohphqwdwlrq ri SIU iru wkh h{shulphqwdo uhdol}dwlrq ri dwrplf dqwl0k|gurjhq surgxfwlrq lv wkh wrslf ri Fkdswhu <1 Lq wkdw fkdswhu zh ghvfuleh uhfhqw dgydqfhv ri wkh surgxf0 wlrq ri frog dqwl0k|gurjhq e| SIU dw FHUQ iru wkh DWUDS frooderudwlrq1 Slorw vwxglhv zhuh shuiruphg ghprqvwudwlqj d phwkrg wr fdoleudwh wkh hohfwulf hogv lq wkh wuds/ dqg ghprqvwudwlqj wkdw srvlwurqv sxovhv zlwk d wlph gxudwlrq ri q 2f qv fdq eh pdgh iurp d wuds1 Xqiruwxqdwho|/ wkh uvw dwwhpswv wr surgxfh dqwl0k|gurjhq zlwk SIU lq wkh DWUDS frq jxudwlrq glg qrw vxffhhg1 Srvvleoh h{sodqdwlrqv/ dqg ixwxuh gluhfwlrqv duh jlyhq lq Fkdswhu<1Lq5334qhzdwwhpswvzlooehpdghwrsurgxfhfrogdqwl0k|gurjhqzlwkSIU dw FHUQ1 431: Frqfoxvlrqv dqg Rxworrn D ghwdlohg vwxg| ri wkh Sxovhg Ilhog Uhfrpelqdwlrq vfkhph lv suhvhqwhg lq zklfk zh kdyh vkrzq wkdw SIU lv dq xqlyhuvdo phwkrg wr uhfrpelqh d iuhh hohfwurq zlwk dq| vruw ri lrq1 Wkhuhiruh zh sursrvh wkdw SIU fdq eh xvhg lq wkh sxuvxlw ri wkh surgxfwlrq ri frog dqwl0k|gurjhq1 Pruhryhu/ zh kdyh vkrzq wkdw SIU fdq eh xvhg wr fuhdwh d U|gehuj vwdwh lq d odujh fduerq foxvwhu vxfk dv FSf1 Wkh uhfrpelqdwlrq g|qdplfv iru wkhvh odujh prohfxohv zdv vkrzq wr eh wkh vdph/ exw wkh vxuylydo0 dqg VIL0ghwhfwlrq0g|qdplfv gl hu1 D vlpsoh prgho/ lqfoxglqj dxwrlrql}dwlrq lv suhvhqwhg wr xqghuvwdqg wkh vxuylydo g|qdplfv1 Zh sursrvh wkdw SIU fdq eh xvhg iru fdwlrq vshfwurvfrs|1 468 Fkdswhu 44 Vdphqydwwlqj 4414 PdnhqhqeuhnhqydqU|gehujdwrphq Lq glw surhivfkuliw zrugw rqghu}rfkw krh hhq dwrrprseuhhnw lq hhq hohnwurq hq hhq lrq +lrql}dwlh, hq krh hhq dwrrpjhpddnw ndq zrughq xlw hhq lrq hq hhq hohnwurq +uhfrpel0 qdwlh,1 Klhuyrru zrugw khw U|gehuj dwrrpjheuxlnw1 Hhq U|gehuj dwrrplv hhq dwrrp zddu ììq ydq gh hohnwurqhq }lfk lq hhq +krrj, ddqjhvodjhq wrhvwdqg ehylqgw +}lh Krrigvwxn 415,1 Lq gh hhuvwh khoiw ydq glw surhivfkuliw +Krrigvwxnnhq 507, zrugw yhuvodj jhjhyhq ydq yhuvfkloohqgh lrql}dwlh phwkrghv ydq hhq U|gehuj dwrrp1 Whuzlmo lq gh wzhhgh khoiw hhq qlhxzh pdqlhu zrugw jhlqwurgxfhhug rp hhq hohnwurq hq hhq lrq wh uhfrpelqhuhq wrw hhq U|gehuj dwrrp1 Gh}h uhfrpelqdwlh phwkrgh khhiw dov krriggrho rp qhxwudoh dqwlpdwhulh +dqwlzdwhuvwri, wh pdnhq1 Khw rseuhnhq ydq U|gehuj dwrphq zrugw yhhodo jhuhdolvhhug phw ehkxos ydq odvhuv1 Odvhuv nxqqhq h{wuhph hljhqvfkdsshq kheehq1 Hu }lmq elmyrruehhog qdxzedqgljh odvhuv glh olfkw surgxfhuhq ydq yulmzho ììq nohxu/ pddu phw hhq odqjh sxovgxxu1 Hu }lmq rrn xowud0 vqhooh odvhuv phw hhq }hhu nruwh sxovgxxu/ pddu zdduydq gh nohxu doohuplqvw jhgh qlhhug lv +euhhgedqgljh odvhu,1 Gh qdxzedqgljh odvhu zrugw lqjh}hw dov zh gh hqhujlh qlyhdxv ydq hhq dwrrpqdxznhxulj zloohq ehsdohq ri hhq jrhg jhgh qlîhugh U|gehuj wrhvwdqg lq hhq dwrrpzloohq h{flwhuhq1 Gh xowud0vqhooh odvhu zrugw lqjh}hw dov gh dwrpdluhuhvsrqv qd gh h{flwdwlh ydq hhq dwrrpdov ixqfwlh ydq gh wlmg zrugw ehvwxghhug1 Gh sxovgxxu ydq hhq xowud0vqhooh odvhu prhw nruw }lmq rpgdw gh dwrpdluh g|qdplfd yddn }hhu vqho lv +lq khw slfrvhfrqgh/ f32 v/ uhjlph,1 Yhuyrojhqv prhw hu rrn gh ehvfklnnlqj }lmq ryhu hhq ghwhfwlh phfkdqlvph phw digrhqgh wlmgv0uhvroxwlh1 Lq Krrigvwxn 7 zrughq h{shulphqwhq ehvfkuhyhq zddu hhq xowud0vqhooh ghwhfwru +gh dwrplf vwuhdn fdphud, zrugw lqjh}hw rp rs slfrvhfrqgh vfkddo wh phwhq krh hhq dwrrp xlw honddu ydow grru h{flwdwlh phw hhq xowud0vqhooh odvhu1 Gh}h lqirupdwlh zrugw yhujhohnhq phw gh lqirupdwlh yhunuhjhq xlw h{0 shulphqwhq zddu khw hqhujlh vshfwuxpydq khw ehwuh hqgh dwrrpzhug rsjhphwhq phw hhq qdxzedqgljh odvhu1 ]rgrhqgh zhughq +qlhxzh, lq}lfkwhq ryhu gh dwrrpg|qdplfd yhunuhjhq1 Khwhohnwurqlq}lmqjherqghqwrhvwdqgzrugwelmkhwlrqjhkrxghqgrrukhwddqwuhnnhqgh hohnwulvfkh yhog ydq gh wzhh whjhqjhvwhog jhodghq ghhowmhv1 Khw lv gxv qlhw yhudvvhqg gdw 46: Vdphqydwwlqj hhq h{whuq hohnwulvfk yhog gh}h elqglqj ndq ehlqyorhghq1 Lq gh h{shulphqwhq ehvfkuhyhq lq glw surhivfkuliw jheuxlnhq zh yhhodo wlmgv0dikdqnholmnh hohnwulvfkh yhoghq rpddqjhvod0 jhq wrhvwdqghq ydq hhq dwrrp wh ndudnwhulvhuhq1 Glw lv prjholmn rpgdw hu hhq hhqgxlgljh uhodwlh ehvwddwv wxvvhq gh vwhunwh ydq khw hohnwulvfkh yhog gdw qrglj lv rpkhw ddqjhvod0 jhq dwrrprs wh euhnhq hq lq zhonh ddqjhvodjhq wrhvwdqg khw dwrrp}lfk ehylqgw1 Gh}h ndudnwhulvdwlh vwddw ehnhqg rqghu gh qddpVhohfwlyh Ilhog Lrql}dwlrq +Krrigvwxn 5,1 Rrn zrugw hu yhuvodj jhjhyhq +Krrigvwxn 8, ydq hhq h{shulphqw zddu zrugw ddqjhwrrqg gdw vqhooh hohnwulvfkh yhog sxovhq khw rseuhnhq ydq hhq dwrrpnxqqhq yhuklqghuhq1 Khw wzhhgh khoiw ydq khw surhivfkuliw +Krrigvwxnnhq 90<, kdqghow ryhu khw lq honddu }hwwhq ydq hhq dwrrpxlw hhq hohnwurq hq hhq lrq1 Glw surfhv khhw uhfrpelqhuhq +}lh rrn Krrigvwxn 418,1 Zhghurpzrugw jheuxln jhpddnw ydq hhq wlmgv0dikdqnholmn hohnwulvfk yhog1 Khw eolmnw gdw hhq yulm hohnwurq hq hhq yulm lrq nxqqhq zrughq jhuhfrpelqhhug dov zh hhq lrq lq hhq hohnwulvfk yhog }hwwhq hq khw yhog vqho xlw }hwwhq rs khw prphqw gdw hhq hohnwurq phw }hhu zhlqlj vqhokhlg khw lrq wrw }hhu glfkwelm lv jhqdghug + >6,1 Lq Krrigvwxn 90; zrugw phw ehkxos ydq glyhuvh h{shulphqwhq gh}h qlhxzh hq h!flhqwh uhfrpelqdwlh phwkrgh wrhjholfkw1 Gh phwkrgh zhug vxffhvyro wrhjhsdvw rs uxelglxp lrqhq +Krrigvwxn 9,/ olwklxplrqhq +Krrigvwxn :, hq jurwh prohfxodluh lrqhq +khw F Sf prohfxxo/ Krrigvwxn ;,1 Yhurqghuvwhog zrugw gdw gh qlhxzh uhfrpelqdwlh phwkrgh lqjh}hw ndq zrughq rp hon vrruw dwrrp +prohfxxo, wh pdnhq xlw hhq hohfwurq hq hhq +prohfxodlu0,lrq hq gxv rrn hhq dqwl0dwrrpwh ideulfhuhq xlw hhq dqwl0hohnwurq +srvlwurq, hq hhq dqwl0surwrq1 Krrigvwxn < ehvfkulmiw gh hhuvwh srjlqjhq rpqhxwudoh dqwlpdwhulh wh pdnhq grru hhq srvlwurq hq hhq dqwl0lrq +dqwl0surwrq, phw ehkxos ydq gh qlhxzh phwkrgh wh uhfrpelqhuhq1 Lq gh uhvw ydq gh}h vdphqydwwlqj zrugw gh prwlydwlh yrru khw pdnhq ydq qhxwudoh dqwlpdwhulh wrhjholfkw1 4415 Zdw lv dqwlpdwhulhB Yrru hon hohphqwdlu ghhowmh ehvwddw hu hhq dqwlghhowmh phw hhq whjhqjhvwhogh odglqj1 Dov hhq dqwlghhowmh rs hhq ghhowmh erwvw eolmiw hu qlhwv ryhu/ ehkdoyh hhq krrs vwudolqjvhqhujlh yrojhqv Hlqvwhlq*v H@pf21 Khw ehvwddq ydq dqwlpdwhulh zhug *rqwghnw* grru Gludf wrhq klm lq 4<5; eh}lj zdv phw khw irupxohuhq ydq }lmq yhuvlh ydq gh txdqwxpphfkdqlfd1 Xlw }lmq wkhrulh yrojgh khw ehvwddq ydq dqwl0hohnwurqhq glh rpklvwrulvfkh uhghqhqhq srvlwur0 qhq zrughq jhqrhpg1 ]rdov dwrphq }lmq rsjherxzg xlw surwrqhq/ qhxwurqhq +ri rs qrj ixqgdphqwhohu qlyhdx= txdunv, hq hohnwurqhq/ }r }lmq dqwl0dwrphq vdphqjhvwhog xlw dq0 wlsurwrqhq/ dqwlqhxwurqhq hq srvlwurqhq1 Whjholmnhuwlmg phw Vfkuùglqjhu hq Khlvhqehuj zdv Gludf eh}lj phw }lmq irupxohulqj ydq gh txdqwxpwkhrulh1 Gludf zdv hfkwhu ydq phqlqj gdw }lmq txdqwxpwkhrulh prhvw yrogrhq ddq Hlqvwhlqv vshfldoh uhodwlylwhlwvwkhrulh= gh wkhrulh prhw gh mxlvwh hqhujlh0lpsxovuhodwlh 2 2 e 2 2 yrruvshoohq= . ' 6fS n R S hq lqyduldqw }lmq rqghu hhq Oruhqw}0wudqvirupdwlh1 Gh}h wkhrulh ohyhugh wzhh rsphunholmnh yrruvshoolqjhq rs= khw ehvwddq ydq hohnwurq0vslq hq ydq dqwlpdwhulh1 Klhurqghu zrugw gh wkhruhwlvfkh d hlglqj jhvfkhwvw glh wrw gh}h oddwvwh frqfoxvlh ohlgw1 46; 4415 Zdw lv dqwlpdwhulhB Gh wzhh edvlvsulqflshv ydq gh txdqwxpphfkdqlfd }lmq gh txdqwlvdwlh ydq khw hohfwur0 pdjqhwlvfk yhog hq khw jroindudnwhu ydq ghhowmhv= 2Z . ' k/ hq R ' k& phw & ' b Gh qlhw0uhodwlylvwlvfkh xlwguxnnlqj ydq gh hqhujlh ydq hhq yulm ghhowmh lv= T2 . ' +4414, 26 Gh jro xqfwlh zrugw jhjhyhq grru hhq yodnnh jroi= Ehc| 'eE!fh3/| +4415, Zh hlvhq qx gdw gh jro xqfwlh hhq hljhqixqfwlh lv ydq gh hqhujlh0 hq gh lpsxovrshudwru +,e hq Te,= ,e ' . k/ dqg Te ' T k! Gdq prhwhq gh rshudwruhq gh yrojhqgh yrup kheehq= Y ,e ' k c Te ' ku +4416, Y| Jheuxlnpdnhqg ydq yjo1 4414/ 4415 hq 4416 jhhiw gh Vfkuùglqjhu0yhujholmnlqj ydq hhq yulm ghhowmh= Y k2 k @ u2 Y| 26 Dov zh hfkwhu ehjlqqhq phw gh uhodwlylvwlvfkh hqhujlh ydq hhq yulm ghhowmh= 2 2 2 2 e . ' R S n 6fS yhunulmjhq zh/ jheuxlnpdnhqg ydq yjo1 4415 hq 4416/ gh Nohlq0Jrugrq0yhujholmnlqj= Y2 k2 k2S2u2 n 62Se 'f Y|2 f Dov zh qx zhhu hhq yodnnh jroi dov uhsuhvhqwdwlh ydq hhq yulm ghhowmh jheuxlnhq/ nulmjhq zh= t 2 2 2 2 2 2 e 2 2 2 e Ek / n S k ! n 6fS 'f ', . k/ ' S T n 6fS +4417, 3/| Glw uhvxowhhuw lq wzhh vhwv jro xqfwlhv= n b e phw hhq srvlwlhyh hljhqzddugh 2 n/| ydq gh hqhujlh +hq hhq plqlpxp zddugh ydq n6fS ,hqhhqvhwjro xqfwlhv=3 b e 2 phw hhq qhjdwlhyh hljhqzddugh ydq gh hqhujlh +hq hhq pd{lpxp zddugh ydq 6fS ,1 Gludfv lqwhusuhwdwlh zdv qx gdw gh}h qhjdwlhyh0hqhujlhwrhvwdqghq zho ghjholmn ehvwddq/ 46< Vdphqydwwlqj materie antimaterie -electron positron m = me m = m - + e q = e q = -e proton antiproton m = m m = m + p - p q = -e q = e antiwaterstof hydrogen - + + - Iljxuh 4414= Vfkhpdwlvfkh zhhujdyh ydq zdwhuvwri/ dqwlzdwhuvwri hq kxq erxz0 vwhqhq1 pddu gdw gh}h dooh jhyxog }lmq phw hohnwurqhq1 Sdxol*v xlwvoxlwlqjvsulqflsh }rujw huyrru gdw hohnwurqhq phw srvlwlhyh hqhujlh qlhw nxqqhq yhuydoohq lq hhq uhhgv eh}hwwhs qhjdwlhyh0 2 e hqhujlhwrhvwdqg1 Wzhh 0irwrqhq phw hhq jh}dphqolmnh hqhujlh ydq . '2 6fS @4135 PhY nxqqhq hhq qhjdwlhyh0hqhujlhwrhvwdqg h{flwhuhq qddu hhq srvlwlhyh0hqhujlhwrhvwdqg1 Hu eolmiw gdq hhq jdw dfkwhu lq gh}h qhjdwlhyh0hqhujlhwrhvwdqg1 Glw jdw zrugw jhòq0 whusuhwhhug dov hhq hohnwurq phw srvlwlhyh odglqj= khw dqwlghhowmh ydq khw hohnwurq/ khw srvlwurq1 Nruw qd Gludfv irupxohulqj +4<5;,/ zhug khw hhuvwh srvlwurq zddujhqrphq grru Fduo Dqghuvrq +4<64, ^54/ 55`1 Lq kdoijhohlghu0i|vlfd zrugw Gludfv xlwohj ydq gh qhjdwlhyh0hqhujlhwrhvwdqghq qrj vwhhgv phw jurrw vxffhv wrhjhsdvw1 Lq ghhowmhvi|vlfd khhiw gh yhunodulqj khw qdghho gdw gh}h qlhw wrhjhsdvw ndq zrughq rs ervrqhq/ zddu khw Sdxol0xlwvoxlwlqjvsulqflsh qlhw yrru jhogw/ whuzlmo ervrqhq hq dqwlervrqhq zho ghjholmn ehvwddq1 Qd gh wkhruhwlvfkh yrruvshoolqj ydq dqwlpdwhulh +4<5;, hq gh rqwghnnlqj ydq srvlwur0 qhq/ zhug lq gh mduhq ylmiwlj khw dqwlsurwrq zddujhqrphq +hq qlhw yhho odwhu khw dqwlqhx0 wurq,1 Khw zhug wrhq sdv prjholmn rp hhq yrogrhqgh jurwh krhyhhokhlg hqhujlh wh pdnhq +31< JhY, yrru glw ghhowmh phw jurwh pdvvd1 Gh lqjuhglîqwhq yrru dqwlzdwhuvwri +K,/ gh jherqghq wrhvwdqg ydq hhq dqwlsurwrq hq hhq srvlwurq +}lh Ilj1 4414,/ }lmq gxv do jhuxlph wlmg ddqzh}lj1 Wrfk khhiw khw wrw 4<<9 jhgxxug wrwgdw gh hhuvwh < dqwlzdwhuvwridwrphq }lmq zddujhqrphq elm FHUQ ^59/ <5`1 Glw yrupgh khw hhuvwh h{shulphqwhoh ehzlmv yrru khw ehvwddq ydq qhxwudoh dwrpdluh dqwlpdwhulh lq khw xqlyhuvxp1 Rp h{shulphqwhho wh rqghu}rhnhq lq krhyhuuh dwrpdluh dqwlpdwhulh }lfk dov pdwhulh jhguddjw/ lv lq 4<<: khw DWUDS0surmhfw ^5;` elm khw FHUQ lq Jhqëyh ydq vwduw jhjddq1 Lq glw surmhfw/ gdw zrugw jhohlg grru suri1 J1 Jdeulhovh ydq gh Kduydug Xqlyhuvlwhlw/ zhunhq 473 4416 Zdw pddnw dqwlzdwhuvwri lqwhuhvvdqwB < lqwhuqdwlrqdoh rqghu}rhnvjurhshq vdphq/ zddurqghu dwrrpi|vlfl ydq gh Xqlyhuvlwhlw ydq Dpvwhugdp hq khw DPROI1 Gh DWUDS0vdphqzhunlqj khhiw dov hhuvwh grho }hhu nrxgh +A e N, dqwlzdwhuvwridwrphq wh pdnhq hq gh}h rs wh voxlwhq lq hhq pdjqhwlvfkh ydo1 4416 Zdw pddnw dqwlzdwhuvwri lqwhuhvvdqwB Khw pdnhq hq lqydqjhq ydq dwrpdluh dqwlpdwhulh lv hljhqolmn hhq prghuqh yrup ydq dofkhplh1 Gh zdduqhplqj ydq gh hhuvwh qhjhq dqwlzdwhuvwridwrphq lq 4<<9 ghhg yhho vwri rszddlhq1 Qlhw }r}hhu rpgdw hu yhho jhî{shulphqwhhug nrq zrughq phw glh ghhowmhv +}h yorjhq phw uhodwlylvwlvfkh vqhokhlg whjhq gh zdqg, pddu rpgdw hu hhq qlhxzh yrup ydq pdwhulh zdv jhpddnw1 Qrj lqwhuhvvdqwhu }rx khw }lmq rp gh}h dqwl0dwrphq yrru odqjhuh wlmg lq khw oderudwrulxpehvfklneddu wh kheehq/ e1y1 grru }h di wh nrhohq hq zdqgyulm rs wh voxlwhq lq hhq pdjqhwlvfkh hv1 Gdw jhhiw gh prjholmnkhlg rp zhunholmn lhwv wh phwhq ddq dqwlpdwhulh1 Krh jhguddjw dqwlpdwhulh }lfk elmyrruehhog rqghu lqyorhg ydq gh }zdduwhnudfkwB Yro0 jhqv khw htxlydohqwlh0sulqflsh ydq Hlqvwhlq +dojhphqh uhodwlylwhlwvwkhrulh, lv hu jhhq yhu0 vfklo wxvvhq gh lqyorhg ydq gh }zdduwhnudfkw rs hhq ghhowmh hq }lmq frpsohphqwdluh dq0 wlghhowmh1 Glw sulqflsh yrruvshow lpphuv gdw hhq +dqwl,ghhowmh lq yulmh ydo }lfk suhflhv }r jhguddjw dov zdqqhhu hu jhhq lqyorhg ydq gh }zdduwhnudfkw lv1 Yhuvfkloohqgh yhuvlhv ydq khw Htxlydohqwlh Sulqflsh zrughq jheuxlnw/ glh }lfk ehshunhq wrw yhuvfkloohqgh vrruwhq ihqrphqhq1 Khw ]zdnnh Htxlydohqwlh Sulqflsh ehshunw }lfk wrw phfkdqlvfkh jurrwkhghq hq yrruvshow gdw dooh pdwhulh gh}hoigh }zdduwhnudfkwvyhuvqhoolqj rqghujddw1 Rp h{shul0 phqwhho ydvw wh vwhoohq krh jrhg khw htxlydohqwlh sulqflsh rsjddw/ lv jhhq jhpdnnholmnh rsjdyh1 Yrru edoolvwlvfkh h{shulphqwhq +oddw dqwlpdwhulh ydoohq hq nlmn qddu gh yhusoddw0 vlqj dov ixqfwlh ydq gh wlmg, lv nrxgh +oddj0hqhujhwlvfkh, dqwlpdwhulh qrglj glh wrw qrj wrh doohhq jhsurgxfhhug lv lq jhodghq yrup1 Hhq }zdduwhnudfkwvh{shulphqw phw jhodghq ghhowmhv lv hfkwhu h{wuhhpjhyrholj yrru hohnwulvfkh yhoghq hq h{shulphqwhho qdxzholmnv xlw wh yrhuhq1 Gh }zdduwhnudfkw rs hhq dqwlsurwrq zrugw elmyrruehhog do jhfrpshqvhhug grru hhqhohnwulvfkyhogydq433b Y2fp1 Hhq edoolvwlvfk h{shulphqw phw qhxwudoh pdwhulh/ }rdov hhq nrxg dqwlzdwhuvwridwrrp/ pddnw khw prjholmn rp gh }zdduwhnudfkw wh ehsdohq }rqghu vwruhqgh lqyorhghq ydq hohnwurpdjqhwlvfkh nudfkwhq1 Hhq dqghuh ehodqjulmnh yuddj lv ri gh hqhujlhqlyhdxv ydq hhq dqwl0dwrrpgh}hoigh }lmq dov glh ydq jhzrrq zdwhuvwri1 Dov khw dqwzrrug rs gh}h yuddj ehyhvwljhqg lv gdq rqghu0 vwhxqw glw khw }rjhkhwhq FSW0lqyduldqwlhsulqflsh1 Yrojhqv glw sulqflsh lv hon i|vlvfk surfhv lqyduldqw rqghu gh jhfrpelqhhugh rshudwlh ydq odglqjvfrqmxjdwlh +F,/ sdulwhlwvlqyhuvlh +S,/ hq wlmgvrpnhulqj +W,1 Odglqjvfrqmxjdwlh lv gh rshudwlh glh hhq ghhowmh wudqviruphhuw lq }lmq dqwlghhowmh1 Sdulwhlwvlqyhuvlh lv gh rshudwlh glh hhq v|vwhhplqyhuwhhuw grru gh rruvsurqj ydq khw frùuglqddwv|vwhhp1 Wlmgvrpnhulqj nrsshow hhq surfhv ddq khw surfhv yhunuhjhq grru whuxj wh orshq lq gh wlmg1 Hljhqolmn lv khw ehwhu wh vsuhnhq ydq ehzhjlqjvrpnhulqj1 Gh qdxznhxuljvwh whvw ydq FSW0lqyduldqwlh wrw qx wrh lv gh yhujholmnlqj ydq gh pdvvd*v ydq khw gf phvrq hq }lmq dqwlghhowmh1 Rs jurqg ydq gh}h phwlqjhq ndq zrughq jhfrqfoxghhug gdw FSW0lqyduldqwlh yrru phvrqhq ehkrxghq lv wrw rs rs hhq rqjhoriholmnh suhflvlh ydq 474 Vdphqydwwlqj f3H1 Yrru ohswrqhq +yhujholmnlqj ydq en hq e3, lv gh ehuhlnwh suhflvlh f321Ghehvwh FSW0whvwv yrru edu|rqhq kheehq qx hhq qdxznhxuljkhlg ydq f3f/ hq }lmq jhedvhhug rs khw yhujholmnhq ydq gh yhukrxglqj ydq odglqj hq pdvvd ydq khw surwrq +R,hqkhw dqwlsurwrq +R ^473` hq khw M30lrq hq khw dqwlsurwrq ^474`1 Gh hqhujlhqlyhdxv ydq khw K0dwrrp}lmq exlwhqjhzrrq qdxznhxulj wh ehsdohq phw ehkxos ydq odvhuvshfwurvfrslh1 Glw jhogw lq khw elm}rqghu yrru gh phwlqj ydq gh iuhtxhq0 wlh ydq gh 4V05V wzhh0irwrq ryhujdqj glh prjholmn lv phw hhq phhwqdxznhxuljkhlg ydq f3e ^5:`1 Grru phwlqjhq ddq gh}h ryhujdqj ndq }hhu suhflhv zrughq ydvwjhvwhog ri gh vshfwud ydq zdwhuvwri hq dqwl0zdwhuvwri vdphqydoohq/ zddugrru hhq yhuehwhugh FSW0whvw yrru edu|rqhq prjholmn lv1 Phq }rx }lfk nxqqhq diyudjhq zddurpkhw yhujholmnhq ydq khw vshfwuxpydq hhq zdwhuvwridwrrp phw }lmq dqwlghhowmh hljhqolmn hhq FSW0whvw lv1 Lpphuv khw yhuydqjhq ydq hhq ghhowmh grru }lmq dqwlghhowmh jhehxuw shu gh qlwlh grru gh rshudwlh F1 Zddu nrphq glh S hq W rshudwlhv gdq whyrruvfklmq1 Khw dqwzrrug lv rqjhyhhu dov yrojw= Vwho zh ehjlqqhq phw hhq zdwhuvwridwrrp lq hhq pdjqhwlvfk yhog hq zh jheuxlnhq hhq flufxodlu +jn, jhsrodulvhhugh odvhuexqgho rphhq rswlvfkh ryhujdqj wh pdnhq +lq glw jhydo yhudqghuw khw pdjqhwlvfkh txdqwxpjhwdo phw .4,1 Dov zh qx rs glw khoh h{shulphqw lq jhgdfkwhq gh rshudwlh F wrhsdvvhq yhudqghuw qlhw doohhq khw K0dwrrplq }lmq dqwlghhowmh pddu rrn khw pdjqhhwyhog nhhuw ydq whnhq rp/ rpgdw gh hohnwurqhq lq gh pdjqhhwvsrho yhuydqjhq zrughq grru srvlwurqhq1 Dov zh yhuyrojhqv gh rshudwlh W wrhsdvvhq vwddw khw pdjqhhwyhog zhhu lq gh rruvsurqnholmnh ulfkwlqj/ pddu qx nhhuw gh yrruwsodqwlqjvulfkwlqj ydq khw olfkw rp1 Sdvvhq zh wrw vorw gh rshudwlh S wrh gdq kheehq zh hhq vlwxdwlh glh dov wzhh guxsshov zdwhu olmnw rs gh rruvsurqnholmnh/ pddu phw wzhh yhuvfkloohq= khw dwrrp lv yhuydqjhq grru }lmq dqwlghhowmh hq gh srodulvdwlh ydq khw olfkw lv rpjhnhhug +lq glw yrruehhog j3,1 FSW0 lqyduldqwlh }hjw gxv gdw gh iuhtxhqwlh ydq gh jn ryhujdqj lq zdwhuvwri suhflhv jholmn lv ddq glh ydq gh j3 ryhujdqj yrru khw dqwl0dwrrphq glw ndq h{shulphqwhho jhyhul hhug zrughq grru ehlgh ghhowmhv lq hhq lghqwlhnh pdjqhwlvfkh ydo rs wh voxlwhq1 4417 Lqjuhglîqwhq yrru nrxg dqwlzdwhuvwri Yrrugdw srvlwurqhq hq dqwlsurwrqhq vdphq hhq qhxwuddo dwrrp nxqqhq yruphq/ prhw khw hhq hq dqghu jhehxuhq1 Gh dqwlsurwrqhq zrughq ddqjhohyhug phw hhq hqhujlh glh 43 rughv ydq jurrwwh krjhu lv gdq gh zddugh qrglj rp}h lq wh nxqqhq ydqjhq lq hhq Shqqlqj ydo1 Gh}h hqhujlh +w|slvfk hqnhoh PhY, zrugw phw ehkxos ydq hhq yhuvfkhlghqkhlg ddq phwkrghv jhuhgxfhhug wrw hqnhoh Nhoylq +phY,1 Gh oddwvwh vwds ydq glw nrhosurfhv jddw dov yrojw= gh Shqqlqj ydo lv uhhgv jhyxog phw hhq zron hohnwurqhq1 Gh}h }lmq }r olfkw gdw }h yld fdsdflwlhyh nrssholqj kxq hqhujlh glvvlshuhq lq hhq zhhuvwdqg glh lq hhq edg yorhleddu kholxp kdqjw1 ]hhu vqho nrpw glw lqjhydqjhq hohnwurqhqjdv lq wkhuplvfk hyhqzlfkw phw khw yorhleddu kholxp1 Gh dqwlsurwrqhq nrhohq qx yld erwvlqjhq phw glw hohnwurqhqjdv1 Srvlwurqhq nxqqhq grru kxq whjhqjhvwhogh odglqj qlhw vdphq phw dqwlsurwrqhq lq gh}hoigh Shqqlqj ydo zrughq jhydqjhq1 Khw lv zho prjholmn rp gh surwrqhq lq hhq whjhqjh0 srrogh Shqqlqj ydo qdelm glh yrru gh dqwlsurwrqhq wh ydqjhq1 Gh srvlwurqhqeurq lv hhq 475 4417Lqjuhglîqwhqyrrunrxgdqwlzdwhuvwri Iljxuh 4415= K|eulgh Shqqlqj ydo zddulq }rzho dqwlsurwrqhq dov srvlwurqhq lqjhydqjhq }lmq/ xlw Uhi1 ^<7`1 udglrdfwlhi suhsduddw +ehwdn0vwudohu,1 Rrn klhu jhogw zhhu gdw hhq hqruph krhyhhokhlg hqhujlh prhw zrughq jhglvvlshhug yrrugdw gh ghhowmhv lq gh Shqqlqj ydo lqjhydqjhq nxq0 qhq zrughq1 Qhjhq gdjhq yrru khw voxlwhq ydq gh Orz Hqhuj| Dqwlsurwrq Ulqj +OHDU, lq FHUQ/ glh oddj0hqhujhwlvfkh dqwlsurwrqhq ohyhugh/ zhug grru gh WUDS vdphqzhunlqj hhq doohv ri qlhwv srjlqj jhgddq yrru gh surgxfwlh ydq nrxg dqwlzdwhuvwri1 Yhhoehoryhqgh krhyhhokhghq dqwlsurwrqhq hq srvlwurqhq +phhu gdq hhq plomrhq ydq hon, nrqghq di}rq0 ghuolmn zrughq lqjhydqjhq lq hhq k|eulgh Shqqlqj ydo +}lh Ilj 4415,1 Khw whjholmnhuwlmg lqydqjhq ydq nrxgh +7N, dqwlsurwrqhq hq srvlwurqhq lq gh}h uxlpwh ohyhugh khoddv ydq ehlgh yhho odjhuh ddqwdoohq rs ^<7`1 Yruplqj ydq dqwl0zdwhuvwri zhug qlhw jhrevhuyhhug1 Khw rshqhq ydq ydq gh Dqwlsurwrq Ghfhohudwru +DG, pdfklqh elm FHUQ lq 4<<< ehwhn0 hqgh hhq qlhxzh vwduw yrru khw dqwlzdwhuvwrirqghu}rhn grru DWUDS hq gh frqfxuhuhqgh DWKHQD vdphqzhunlqj1 Qx lv khw vlpshozhj vdphqeuhqjhq ydq hhq srvlwurq phw hhq dqwlsurwrq rrn qlhw yrogrhqgh rpdqwlzdwhuvwri wh yruphq1 Gh uhdfwlh= R n en $ M lv qlhw prjholmn/ rpgdw klhuelm +elqglqjv0,hqhujlh yulmnrpw1 Qrupddo jhvsurnhq ndq gh uh0 dfwlh gddurpdoohhq soddwvylqghq zdqqhhu hu hhq ghugh ghhowmh +irwrq/ hohnwurq ri srvlwurq, ddq gh uhdfwlh ghhoqhhpw }rgdw gh yulmnrphqgh hqhujlh klhuddq ndq zrughq dijhvwddq1 Glw surhivfkuliw kdqghow ryhu hhq qlhxzh uhfrpelqdwlh0phwkrgh/ glh gh ehwurnnhqkhlg ydq hhq ghugh ghhowmh ryhuerglj pddnw ^<;/ < 476 Vdphqydwwlqj Iljxuh 4416= Vwho gdw hhq hohnwurq hhq lrq qdghuw lq hhq hohnwulvfk yhog/ }r gdw khw hohnwurq qhw ryhu khw yhog0jhòqgxfhhugh }dghosxqw nrpw lq gh Frxorpe sr0 whqwlddo1 Xlwhlqgholmn }do khw hohnwurq khw lrq zhhu yhuodwhq ryhu khw}hoigh yhog0 jhòqgxfhhugh }dghosxqw1 Khw hohnwurq grhw rqjhyhhu 4 qdqrvhfrqgh +43 3b v, ryhu khw rpguddlhq urqg khw lrq1 Gh fux{ ydq gh uhfrpelqdwlh phwkrgh }lw khp qx lq khw yrogrhqgh uhgxfhuhq ydq khw hohnwulvfk yhog zdqqhhu khw hohn0 wurq glfkwelm khw lrq lv1 Rs gh}h pdqlhu hlqgljw khw hohnwurq rqghu khw }dghosxqw lq hhq U|gehuj0wrhvwdqg hq ndq qlhw phhu rqwvqdsshq1 Qhw }rdov gh zhvs doohhq lq khw mdpsrwmh }do zrughq jhydqjhq dov gh ghnvho rs khw mxlvwh wlmgvwls zrugw glfkw jhgddq1 gh ehkddogh uhfrpelqdwlh h!flîqwlh +ddqwdo jhuhfrpelqhhugh dwrphq2ddqwdo yulmh lrqhq f32/ Krrigvwxn :, rughv ydq jurrwwh krjhu lv gdq elm phwkrghv zdduelm hhq ghugh ghhowmh ehwurnnhq lv1 Gh hhuvwh srjlqjhq rp phw gh}h phwkrgh dqwlzdwhuvwri wh pdnhq yrru khw DWUDS surmhfw/ vwddq ehvfkuhyhq lq Krrigvwxn <1 Zdqqhhu qlhw yrrunrphq ndq zrughq gdw gh dqwl0dwrphq phw gh zdqg erwvhq/ }xoohq }h pddu nruwvwrqglj ehvwddq1 ]rgud khw oxnw rp nrxg dqwlzdwhuvwri wh pdnhq/ zdfkw gddurpgluhnw gh yrojhqgh rsjdyh rpglw zdqgyulm rs wh voxlwhq1 Phw gh zdqgyulmh nrho0 lqj hq rsvoxlwlqj ydq dwrphq lv gh dijhorshq mduhq gdqn}lm odvhunrholqj whfkqlhnhq jurwh yrruxlwjdqj jherhnw1 Zdwhuvwridwrphq nxqqhq elm yrogrhqgh odjh whpshudwxuhq zrughq lqjhydqjhq lq hhq vwdwlvfk pdjqhhwyhog hq lq vlwx zrughq ehvwxghhug phw ehkxos ydq odvhuvshfwurvfrslh ^475/ 476`1 Khw frpelqhuhq ydq hhq Shqqlqj ydo yrru jhodghq ghhow0 mhv phw hhq pdjqhwlvfkh ydo yrru dwrphq lv qrj qlhw h{shulphqwhho yhuwrrqg1 Phw hhq ghujholmnh ydo ndq gh hhqpddo jhydqjhq dqwlpdwhulh lq dooh uxvw rqghu}rfkw zrughq qddu }lmq hljhqvfkdsshq1 477 Eleolrjudsk| ^4`M1U1U|gehuj/Sklo1Pdj18| Vhu1 5 ^5` W1I1 Jdoodjkhu/ U|gehuj Dwrpv/ +Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ XN/ 4<<7,> ^6`G1\rx/U1U1Mrqhv/S1K1Exfnvedxp/Rsw1Ohww14;/ 5<3 +4<<6,> ^7`U1U1Mrqhv/G1\rx/S1K1Exfnvedxp/Sk|v1Uhy1Ohww1:3/ 4569 +4<<6,> ^8` D1 whq Zrogh / O1G1 Qrrugdp/ D1 Odjhqglmn/ K1E1 ydq ghq Olqghq ydq ghq Khxyhoo/ Sk|v1Uhy1Ohww194/ 53<< +4<;;,> ^9` M1D1 \hd}hoo/ P1 Pdoodolhx/ F1U1 Vwurxg/ Mu1/ Sk|v1 Uhy1 Ohww1 97/ 533: +4<<3,> ^:` J1P1 Odqnkxlm}hq/ O1G1 Qrrugdp/ Sk|v1 Uhy1 Ohww1 :9/ 4:;7 +4<<9,> ^;` Z1F1 Uùqwjhq/ Qdwxuh 86/ 5:7 +4;<9,> ^<` K1D1 Ehwkh/ H1H1 Vdoshwhu/ Txdqwxp Phfkdqlfv ri Rqh dqg Wzr Hohfwurq Dwrpv +Vsulqjhu0Yhuodj/ Ehuolq/ 4<8:,> ^43` G1U1 Edwhv/ D1 Gdojduqr/ Dwrplf dqg Prohfxodu surfhvvhv +Dfdghplf Suhvv/ Qhz \run/ 4<95,> ^44` J1 Jdeulhovh/ V1O1 Urovwrq/ O1 Kdduvpd/ Z1 Nhoov/ Sk|v1 Ohww1 D 45 ^45`K1V1Z1Pdvvh|/G1U1Edwhv/Uhs1rqSurju1lqSk|v1 ^46` Uhfrpelqdwlrq ri Dwrplf Lrqv/hglwhge|Z1J1Judkdp/Z1Iulwvfk/\1Kdkq/M1D/ Wdqlv/ +SohqxpSuhvv/ Qhz \run 4<<5,> ^47` D1 Pÿoohu/ D1 Zroi/ K|s1 Lqw1 43 ^48` U1 Iodqqhu|/ Dwrplf/ Prohfxodu/ dqg Rswlfdo Sk|vlfv Kdqgerrn/+DLSSuhvv/Zrrg0 exuu|/ Q\/ 4<<9,> ^49` I1E1 \rxvli/ S1 ydq ghu Grqn/ ]1 Nxfkhuryvn|/ M1 Uhlv/ H1 Eudqqhq/ M1E1D1 Plwfkhoo/ Sk|v1Uhy1Ohww19:/ 59 +4<<4,> 478 ELEOLRJUDSK\ ^4:` X1 Vfkudpp / M1 Ehujhu/ P1 Julhvhu/ G1 Kdev/ H1 Mdhvfknh/ J1 Nlojxv/ G1 Vfkzdop/ D1 Zroi/ U1 Qhxpdqq/ U1 Vfkxfk/ Sk|v1 Uhy1 Ohww1 9:/ 55 +4<<4,> ^4;` P1O1 Urjhovwdg/ I1E1 \rxvli/ W1M1 Prujdq/ M1E1D1 Plwfkhoo/ M1 Sk|v1 E 63/ 6<46 +4<<:,> ^4<` N1N1 Gduurz/ Hohfwulfdo Skhqrphqd lq Jdvvhv/ +Zlooldpv dqg Zlonlqv/ Edowlpruh/ 4<65,> ^53` D1 Pxoohu/ Frpp1 Dw1 Pro1 Sk|v1 6/ 476 +4<<9,> ^54` F1G1 Dqghuvrq/ Vflhqfh :9/ 56; +4<65,> ^55` F1G1 Dqghuvrq/ Sk|v1 Uhy1 76/ 7<4 +4<66,> ^56` G1U1 Edwhv/ D1H1 Nlqjvwrq/ U1Z1S Pf Zkluwhu/ Surf1 U1 Vrf1 D 59:/ 5<: +4<95,> ^57` E1 Pdnlq/ M1 Nhfn/ Sk|v1 Uhy1 Ohww1 44/ 5;4 +4<96,> ^58`M1Vwhyhow/M1Erxophu/M1I1Ghoshfk/Sk|v1Uhy1D45/ 4579 +4<:8,> ^59`J1Edxu/J1Erhur/V1Eudxnvlhsh/D1Ex}}r/Z1H|ulfk/U1Jh|hu/G1Ju}rqnd/M1 Kdx h/ N1 Nlooldq/ P1 OrYhwhuh/ P1 Pdful/ P1 Prrvexujhu/ U1 Qhoohq/ Z1 Rhohuw/ V1 Sdvvdjjlr/ D1 Sr}}r/ N1 Uùkulfk/ N1 Vdfkv/ J1 Vfkhshuv/ W1 Vhi}lfn/ U1V1 Vlprq/ U1 Vwudwpdqq/ I1 Vwlq}lqj/ P1 Zronh/ Sk|v1 Ohww1 E 69;/ 584 +4<<9,> ^5:` P1 Qlhulqj/ U1 Kro}zduwk/ M1 Uhlfkhuw/ S1 Srndvry/ Wk1 Xghp/ P1 Zhlw}/ W1Z1 Kçqvfk/ S1 Ohprqgh/ J1 Vdqwduhool/ P1 Dejudoo/ S1 Odxuhqw/ F1 Vdorprq/ D1 Fodlurq/ Sk|v1Uhy1Ohww1;7/ 87<9 +5333,> ^5;` kwws=22kxvvoh1kduydug1hgx2dwuds2> ^5<` W1I1 Jdoodjkhu/ O1P1 Kxpskuh|/ U1P1 Kloo/ V1D1 Hghovwhlq/ Sk|v1 Uhy1 Ohww1 6:/ 4798 +4<:9,> ^63` W1I1 Jdoodjkhu/ O1P1 Kxpskuh|/ Z1H1 Frrnh/ V1D1 Hghovwhlq/ U1P1 Kloo/ Sk|v1 Uhy1 D 49/ 43<; +4<::,> ^64` M1O1 Yldooh/ K1W1 Gxrqj/ M1 Sk|v1 E 45/ 473: +4<:<,> ^65` J1 Ohxfkv/ K1 Zdowhu/ ]1 Sk|v1 D 5<6/ <6 +4<:<,> ^66` W1K1 Mh|v/ J1Z1 Irow}/ N1D1 Vplwk/ H1M1 Ehlwlqj/ I1J1 Nhoohuw/ I1E1 Gxqqlqj/ U1I1 Vwheelqjv/ Sk|v1 Uhy1 Ohww1 77/ 6<3 +4<;3,> ^67` M1K1P1 Qhlm}hq/ D1 Grqv}hopdqq/ M1 Sk|v1 E 48/ O;: +4<;5,> ^68` I1E1 Gxqqlqj/ U1I1 Vwheelqjv/ U|gehuj vwdwhv ri dwrpv dqg prohfxohv/+Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ 4<;6,> 479 ELEOLRJUDSK\ ^69`O1J1Jud|/N1E1PdfDgdp/M1Sk|v1E5:/ 6388 +4<<7,> ^6:` N1 Pxoohu0Ghwkohiv/ P1 Vdqghu/ H1Z1 Vfkodj/ Fkhp1 Sk|v1 Ohww1 445/ 5<4 +4<;7,> ^6;` H1Z1 Vfkodj/ ]HNH Vshfwurvfrs|/ +Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ XN/ 4<<;,> ^6<` G1D1 Kduplq/ S1Q1 Sulfh/ Sk|v1 Uhy1 D 7 ^73` G1D1 Kduplq/ Sk|v1 Uhy1 D 89/ 565 +4<<:,> ^74` J1P1 Odqnkxlm}hq/ O1G1 Qrrugdp/ Sk|v1 Uhy1 Ohww1 :7/ 668 +4<<8,> ^75` G1D1 Kduplq/ Sk|v1 Uhy1 D 59/ 5989 +4<;5,> ^76` W1 \dpdeh/ D1 Wdfkledqd/ K1M1 Vloyhuvwrqh/ Sk|v1 Uhy1 D 49/ ;:: +4<::,> ^77` G1 Edqnv/ M1J1 Ohrsrog/ M1 Sk|v1 E 44/ O8 +4<:;,> ^78` F1 R1 Uhlqrog/ P1 Phoohv/ K1 Vkdr/ M1 Exujgùuihu/ M1 Sk|v1 E 4 ^79` Q1H1 Wlhonlqj/ W1M1 Ehqvn|/ U1U1 Mrqhv/ Sk|v1 Uhy1 D 84/ 66:3 +4<<8,> ^7:` M1 Eurpdjh/ F1U1 Vwurxg/ Sk|v1 Uhy1 Ohww1 ;6/ 7<96 +4<<<,> ^7;`P1Z1Qrho/Z1P1Jul!wk/W1I1Jdoodjkhu/Sk|v1Uhy1Ohww1;6/ 4:7: +4<<<,> ^7<` M1K1 Krrjhquddg/ U1E1 Yulmhq/ O1G1 Qrrugdp/ Sk|v1 Uhy1 D 83/ 7466 +4<<7,> ^83`I1Urelfkhdx{/F1Zhvgrus/O1G1Qrrugdp/Sk|v1Uhy1D95/ 76737 +5333,> ^84` Z1 Vdqgqhu/ N1D1 Vd q|d/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 D 66/ 433; +4<;9,> ^85` G1Z1 Vfkxpdfkhu/ E1M1 O|rqv/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 Ohww :;/ 768< +4<<:,> ^86` E1M1 O|rqv/ G1Z1 Vfkxpdfkhu/ G1L1 Gxqfdq/ U1U1 Mrqhv/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 D 8:/ 6:45 +4<<;,> ^87` J1P1 Odqnkxlm}hq/ O1G1 Qrrugdp/ Sk|v1 Uhy1 D 88/ 5349 +4<<8,> ^88` G1D1 Kduplq/ Sk|v1 Uhy1 D 57/ 57<4 +4<;4,> ^89`I1Urelfkhdx{/M1Vkdz/Sk|v1Uhy1D89/ 5:; +4<<:,> ^8:`I1Urelfkhdx{/M1Vkdz/Sk|v1Uhy1Ohww1::/ 7487 +4<<9,> ^8;` O1G1 Qrrugdp/ U1U1 Mrqhv/ Mrxuqdo ri Prghuq Rswlfv 77/ 5848 +4<<:,> ^8<`I1Urelfkhdx{/F1Zhvgrus/O1G1Qrrugdp/Sk|v1UhyD93/ U66:: +4<<<,> ^93` G1D1 Kduplq/ Frpp1 Dw1 Pro1 Sk|v1 48/ 5;4 +4<;8,> 47: ELEOLRJUDSK\ ^94` Z1H1 Huqvw/ W1S1 Vriwoh|/ U1Q1 ]duh/ Sk|v1 Uhy1 D 6:/ 74:5 +4<;;,> ^95` D1 Nùqlj/ M1 Qhxndpphu/ K1 Klhurq|prxv/ K1 Ulqqhehuj/ Sk|v1 Uhy1 D 76/ 5735 +4<<4,> ^96` G1M1 Dupvwurqj/ F1K1 Juhhqh/ U1S1 Zrrg/ M1 Frrshu/ Sk|v1 Uhy1 Ohww1 :3/ 56:< +4<<7,> ^97` G1M1 Dupvwurqj F1K1 Juhhqh/ Sk|v1 Uhy1 D 83/ 7<89 +4<<7,> ^98` W1S1 Vriwoh|/ D1M1 Kxgvrq/ U1 Zdwvrq/ M1 Fkhp1 Sk|v1 439/ 4374 +4<<:,> ^99` X1 Idqr/ Sk|v1 Uhy1 457/ 4;99 +4<94,> ^9:` J1 P1 Odqnkxlm}hq/ O1 G1 Qrrugdp/ Rsw1 Frppxq1 45 ^9;` D1 whq Zrogh/ O1G1 Qrrugdp/ D1 Odjhqglmn/ K1E1 ydq Olqghq ydq ghq Khxyhoo/ Sk|v1 Uhy1 D 73 / 7;8 +4<;<,> ^9<` U1J1 Uroihv/ G1E1 Vplwk/ N1E1 PdfDgdp/ M1 Sk|v1 E= Dw1 Pro1 Sk|v1 49/ O8680O86; +4<;6,> ^:3` G1U1 Pduldql/ Z1 ydq gh Zdwhu/ S1P1 Nrfk/ W1 Ehujhpdq/ Sk|v1 Uhy1 Ohww1 4:/ 4594 +4<;6,> ^:4` K1E1 ydq Olqghq ydq ghq Khxyhoo/ U1 Ndfkux/ Q1K1 Wudq/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 Ohww1 53/ 4<34 +4<;7,> ^:5` K1E1 ydq Olqghq ydq ghq Khxyhoo/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 D 65/ 47<8 +4<;8,> ^:6` W1I1 Jdoodjkhu/ F1U1 Pdkrq/ S1 Sloohw/ Sdqplqj Ix/ M1 E1 Qhzpdq/ Sk|v1 Uhy1 D 6 ^:7` S1 Sloohw/ K1E1 ydq Olqghq ydq ghq Khxyhoo/ Z1Z1 Vplwk/ U1 Ndfkux/ Q1K1 Wudq/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 D 63/ 5;3 +4<;7,> ^:8`S1Nulvwhqvhq/J1P1Odqnkxlm}hq/O1G1Qrrugdp/M1Sk|v1E=Dw1Pro1Rsw1Sk|v1 63/ 47;4 +4<<:,> ^:9` J1P1 Odqnkxlm}hq/ O1G1 Qrrugdp/ Sk|v1 Uhy1 Ohww1 :7/ 668 +4<<8,> ^::`P1Jdw}nh/E1Eurhuv/O1G1Qrrugdp/U1E1Zdwnlqv/W1I1Jdoodjkhu/Sk|v1Uhy1D 83/ 5835 +4<<7,> ^:;`W1M1Ehqvn|/P1E1Fdpsehoo/U1U1Mrqhv/Sk|v1Uhy1Ohww1;4/ 6445 +4<<;,> ^:<`E1Eurhuv/M1I1Fkulvwldq/M1K1Krrjhquddg/Z1M1ydqghu]dqgh/K1E1ydqOlqghq ydq ghq Khxyhoo/ O1G1 Qrrugdp/ Sk|v1 Uhy1 Ohww1 :4/ 677 +4<<6,> 47; ELEOLRJUDSK\ ^;3` P1 Jdyulod/ Dwrpv lq Lqwhqvh Odvhu Ilhogv/ +Dfdghplf Suhvv Olplwhg/ Orqgrq/ uvw hglwlrq/ 4<<5,> ^;4` W1I1 Jdoodjkhu/ Sk|v1 Uhy1 Ohww1 53/ 5637 +4<;;,> ^;5` W1I1 Jdoodjkhu/ W1M1 Vfkro}/ Sk|v1 Uhy1 D 73/ 5:95 +4<;<,> ^;6` E1L1 Juhhqh/ M1I1 Ihghulfl/ G1U1 G|nddu/ U1U1 Mrqhv/ S1 K1 Exfnvedxp/ Dsso1 Sk|v1 Ohww1 8 ^;7`Y1O1Mdfrev/M1Gdylv/S1F1Nhssoh/Sk|v1Uhy1Ohww16:/ 46<3 +4<:9,> ^;8` Y1O1 Mdfrev/ M1 Gdylv/ Sk|v1 Uhy1 D 4 ^;9` D1 Pÿoohu/ E1V1 Eholf/ E1G1 GhSdrod/ Q1 Gmxulf/ J1K1 Gxqq/ G1Z1 Pxhoohu/ F1 Wlpphu/ Sk|v1 Uhy1 Ohww1 89/ 45: +4<;9,> ^;:`I1Urelfkhdx{/P1V1Slqg}rod/Sk|v1Uhy1Ohww1: ^;;` O1 Nr/ Y1 Nolphqnr/ W1I1 Jdoodjkhu/ Sk|v1 Uhy1 D 8 ^;<` G1U1 Edwhv/ Sk|v1 Uhy1 ::/ :4; +4<83,> ^<3` H1D1 Khvvhov/ G1P1 Krpdq/ P1M1 Fdydjqhur/ Sk|v1 Uhy1 D 8:/ 499; +4<<;,> ^<4` G1 Nodu/ P0Z Uxi/ K1 Krwrs/ Phdv1 Vfl1 Whfkqro1 8/ 457; +4<<7,> ^<5` J1 Eodqirug/ G1F1 Fkulvwldq/ N1 Jroozlw}hu/ P1 Pdqghonhuq/ F1W1 Pxqjhu/ M1 Vfkxow}/ J1 ]lrxodv/ Sk|v1 Uhy1 Ohww1 ;3/ 636: +4<<;,> ^<6` M1 Zdo}/ V1E1 Urvv/ F1 ]lpphupdqq/ O1 Ulffl/ P1 Suhyhghool/ W1Z1 Kdqvfk/ Sk|v1 Uhy1 Ohww1 :8/ 658: +4<<8,> ^<7` J1 Jdeulhovh/ G1V1 Kdoo/ W1 Urdfk/ S1 \hvoh|/ D1 Nkdeed}/ M1 Hvwudgd/ F1 Khlpdqq/ K1 Ndolqrzvn|/ Sk|v1 Ohww1 E 788/ 644 +4<<<,> ^<8` Qrq0Qhxwudo Sodvpd Sk|vlfv LLL/ hglwhg e| M1M1 Eroolqjhu/ U1O1 Vshqfhu/ U1F1 Gdylg0 vrq/ +DLS Frqi1 Surf1/ Sulqfhwrq/ Qhz Mhuvh|/ 4<<<,> ^<9` F1 Ghviudqfrlv/ K1 Degrxo0Fdulph/ M0S Vfkhupdqq/ Lqw1 M1 Prg1 Sk|v1 E 43/ 466< +4<<9,> ^<:`M1G1G1Pduwlq/M1Z1Khsexuq/Sk|v1Uhy1Ohww: ^<;` F1 Zhvgrus/ I1 Urelfkhdx{/ O1 G1 Qrrugdp/ Sk|v1 Uhy1 Ohww ;7/ 6:<< +5333,> ^<<` F1 Zhvgrus/ I1 Urelfkhdx{/ O1G1 Qrrugdp/ Fkhp1 Sk|v1 Ohww1 656/ 4<5 +5333,> ^433` Qlhov Erku dqg wkh Ghyhorsphqw ri Sk|vlfv/ hglwhg e| Z1 Sdxol/ s1 63 +Shujdprq Suhvv/ Qhz \run/ 4<88,> 47< ELEOLRJUDSK\ ^434` M1V1 Ehoo/ Surf1 Ur|1 Vrf1 D564/ 7<4 +4<88,> ^435` U1 Mrvw/ Wkh Jhqhudo Wkhru| ri Txdqwlvhg Ilhogv +Dp1 Pdwk1 Vrf1/ Surylghqfh/ 4<98,> ^436` D1 Hlqvwhlq/ Mdkue1 Udg1 Hohnwu1 7/ 744 +4<3:,> ^437` F1P1 Zloo/ Wkhru| dqg h{shulphqw lq Judylwdwlrqdo Sk|vlfv +Fdpeulgjh Xqlyhuvlw| Suhvv/ Fdpeulgjh/ 4<;4,> ^438`G1S1Wd|oru/M1J1Jrrgh/M1H1OhFodluh/S1P1Mrkqvrq/M1Fkhp1Sk|v1436/47 +4<<8,> ^439`D1Ixmll/D1Lzdvdnl/W1Hedwd/Q1Plndpl/M1Sk|v1Fkhp1434/ 8<96 +4<<:,> ^43:` P1 Jhukdugv/ P1 Vfklzhn/ F1 Xqwhuehuj/ N1 Nohlqhupdqqv/ Fkhp1 Sk|v1 Ohww1 5<:/ 848 +4<<;,> ^43;` G1 Zlqhodqg/ S1 Hnvwurp/ K1 Ghkphow/ Sk|v1 Uhy1 Ohww1 64/ 45:< +4<:6,> ^43<` G1M1 Zlqhodqg/ K1J1 Ghkphow/ M1 Dsso1 Sk|v1 79/ <4< +4<:8,> ^443` J1 Jdeulhovh/ Sk|v1 Uhy1 D 5:/ 55:: +4<;6,> ^444` F1V1 Zhlphu/ M1M1 Eroolqjhu/ I1O1 Prruh/ G1M1 Zlqhodqg/ Sk|v1 Uhy1 D 7 ^445`O1]kx/S1P1Mrkqvrq/M1Fkhp1Sk|v1<7/ 8:9< +4<<4,> ^446` K1 \dvxpdwvx/ W1 Nrqgrz/ K1 Nlwdjdzd/ N1 Vkredwdnh/ M1 Fkhp1 Sk|v1 437/ ;<< +4<<9,> ^447` H1E1 Jdoorjo|/ \lkdp0Edr/ Nhol0Kdq/ Kxd0Olq/ Z1P1 Mdfnvrq/ M1 Sk|v1 Fkhp1 <;/ 6454 +4<<7,> ^448` J1 yrq Khoghq/ L1 Kroohpdq/ J1P1K1 Nqlsshov/ D1I1J1 ydq ghu Phhu/ J1 Phlmhu/ Sk|v1Uhy1Ohww1: ^449` G1V1 Kdoo/ J1 Jdeulhovh/ Sk|v1 Uhy1 Ohww1 ::/ 4<95 +4<<9,> ^44:` S1 Zxu}/ N1U1 O|nnh/ M1 Fkhp1 Sk|v1 <8/ :33; +4<<4,> ^44;` H1H1E1 Fdpsehoo/ U1G1 Ohylqh/ dffhswhg iru sxeolfdwlrq lq Dqq1 Uhy1 Sk|v1 Fkhp1> ^44<` N1 Kdqvhq/ R1 Hfkw/ Sk|v1 Uhy1 Ohww1 45/ 566: +4<<:,> ^453` H1H1E1 Fdpsehoo/ J1 Xophu/ L1Y1 Khuwho/ Sk|v1 Uhy1 Ohww1 9:/ 4<;9 +4<<4,> ^454` P1U1 Shghuvrq/ D1D1 Txrqj/ Sk|v1 Uhy1 E 79/ 468;7 +4<<5,> 483 ELEOLRJUDSK\ ^455`D1D1Vfkhlghpdqq/Y1Y1Nuhvlq/Z1G1Nqljkw/Sk|v1Uhy1D7 ^456` Z1D1 Fkxsnd/ M1 Fkhp1 Sk|v1 <;/ 7853 +4<<6,> ^457` G1O1 Grurihhy/ E1D1 ]rq/ M1 Fkhp1 Sk|v1 439/ <93< +4<<:,> ^458`I1Phunw/U1Q1]duh/M1Fkhp1Sk|v434/ 67<8 +4<<7,> ^459` S1D1P1 Gludf/ Wkh Sulqflsohv ri Txdqwxp Phfkdqlfv/+7wkhg1R{irugXqlyhuvlw| Suhvv/ R{irug 4<8;,> ^45:`O1V1Eurzq/J1Jdeulhovh/Uhy1Prg1Sk|v18;/ 566 +4<;9,> ^45;` M1 Hvwudgd/ W1 Urdfk/ M1Q1 Wdq/ S1 \hvoh|/ J1 Jdeulhovh/ Sk|v1 Uhy1 Ohww1 ;7/ ;8< +5333,> ^45<` G1M1 Zlqhodqg/ K1J1 Ghkphow/ Lqwo1 M1 ri Pdvv Vshf1 dqg Lrq Sk|v1 49/ 66; +4<:8,> ^463` G1V1 Kdoo/ Srvlwurqv/ Dqwlsurwrqv/ dqg Lqwhudfwlrqv iru Frog Dqwlk|gurjhq/ +wkhvlv/ Kduydug Xqlyhuvlw| 4<<:,> ^464`G1Pùko/J1Shwuxffl/O1Wkruqgdko/V1ydqghuPhhu/Sk|v1Uhs18;/ :7 +4<;3,> ^465` V1 ydq ghu Phhu/ Sk|vlfv ri Sduwlfoh Dffhohudwruv/ s1 495; +hglwhg e| P1 Prqwk dqg P1Glhqhv/DLSFrqi1Surf1Qr1486/DLS/Qhz\run/4<;:,> ^466` G1V1 Kdoo/ J1 Jdeulhovh/ Sk|v1 Uhy1 Ohww1 ::/ 4<95 +4<<9,> ^467` G1K1H1 Gxelq/ Sk|vlfv ri Ioxlgv E 8/ 5<8 +4<<6,> ^468` M1M1 Eroolqjhu/ G1M1 Khlq}hq/ I1O1 Prruh/ Z1P1 Lwdqr/ G1M1 Zlqhodqg/ G1K1H1 Gx0 elq/Sk|v1Uhy1D7;/ 858 +4<<6,> ^469` G1K1H1 Gxelq/ W1P1 R*Qhlo/ Sk|v1 Uhy1 ohww1 93/ 844 +4<;;,> ^46:` F1 Zhvgrus/ I1 Urelfkhdx{/ O1 G1 Qrrugdp/ lq suhsdudwlrq> ^46;`J1Zlhexvfk/M1Pdlq/N1Nuÿjhu/K1Urwwnh/D1Krooh/N1K1Zhojh/Sk|v1Uhy1 Ohww1 95/ 5;54 +4<;<,> ^46<` Vlplrq Y 9133/ Orfnkhhg Pduwlq Lgdkr Whfkqrorjlhv/ Lgdkr Qdwlrqdo Hqjlqhhulqj Oderudwru|/ Xqlwhg Vwdwhv +4<<9,> ^473` J1 Jdeulhovh/ G1 Skloolsv/ Z1 Txlqw/ K1 Ndolqrzvn|/ W1 Wudlqru/ Z1 Nhoov/ Sk|v1 Uhy1 Ohww1 :7/ 6877 +4<<8,> ^474` J1 Jdeulhovh/ D1 Nkdeed}/ G1V1 Kdoo/ F1 Khlpdqq/ K1 Ndolqrzvn|/ Z1 Mkh/ Sk|v1 Uhy1 Ohww1 ;5/ 64<; +4<<<,> 484 ELEOLRJUDSK\ ^475` R1M1 Oxlwhq/ K1J1F1 Zhulm/ L1G1 Vhwlmd/ P1Z1 Uh|qrogv/ W1Z1 Klmpdqv/ M1W1P1 Zdoudyhq/ Sk|v1 Uhy1 Ohww1 :3/ 877 +4<<6,> ^476` N1V1H1 Hlnhpd/ M1 Zdo}/ W1Z1 Kçqvfk/ Sk|v1 Uhy1 Ohww1 ;6/ 6;5; +4<<<,1 485 Qdzrrug Khw lqglylgxhoh ndudnwhu ydq hhq surhivfkuliw lv doohuplqvw hhq pddw yrru khw ddqwdo phqvhq glh huddq kheehq phhjhzhunw1 Khw lv hhughu xlw}rqghulqj gdq uhjho gdw hhq surpryhqgxv doohhq ddq hhq h{shulphqwhoh rsvwhoolqj zhunw1 Eryhqglhq zrugw rs DPROI gh vdphqzhunlqj wxvvhq yhuvfkloohqgh jurhshq jhvwlpxohhug hq }lmq hu wdoulmnh lqwhuqh vdphqzhunlqjvyhuedqghq1 Plmq surprwru/ Eduw Qrrugdp/ khhiw hhq fhqwudoh uro yhuyxog lq gh uhdolvdwlh ydq glw erhnmh1 Glw erhnmh kdqghow elmyrruehhog ryhu hhq qlhxzh uhfrpelqdwlh0phwkrgh glh yroohglj ehgdfkw lv grru Eduw Qrrugdp1 Hhq ddqwdo mddu whuxj vfkhwvwh klm gh phwkrgh rs hhq yhoohwmh hq olhw gh}h }lhq ddq hhq wkhruhwlfxv1 Gh wkhruhwlfxv nrq qrj qhw }lmq odfkhq ehgzlqjhq hq phoggh gdw khw hhq ndqvorrv surmhfw zdv1 Qlhw rqwprhgljg zhug hu wrfk hhq srjlqj jhzddjg hq wzhh mddu odwhu/ wrhq khw h{shulphqw zdv jhoxnw/ prhvw gh}hoigh wkhruhwlfxv wrhjhyhq gdw glw +rrn lq wkhrulh, hhq }hhu nudfkwljh uhfrpelqdwlh0phwkrgh zdv1 Gh wkhruhwlfxv zdv qlhpdqg plqghu gdq Iudqflv Urelfkhdx{1 Iudqflv Urelfkhdx{ dqg Eduw Qrrugdpirupdq xqehdwdeoh whdplq dwrplfsk|vlfv1 Doprvwhyhu| zhhn L zurwh Iudqflv Urelfkhdx{ dq h0pdlo zlwk txhvwlrqv uhodwlqj wr dwrplf sk|vlfv1 Dq dyhudjh uhso| iurpd wkhruhwlfldq wkhq zrxog eh vr fu|swlf wkdw wkh dqvzhu zrxog eh xvhohvv1 Iudqflv Urelfkhdx{/lqfrqwudvw/zrxogfrphxszlwkdfohdudqvzhudozd|vvwduwlqjzlwk=dq hdv| zd| ri vhhlqj wklv 1111 Vshflddo zlo ln Kxle Ednnhu/ WrpKlmpdqv hq Zlpydq ghu ]dqgh ehgdqnhq yrru khw grruoh}hq hq ehrrughohq ydq glyhuvh pdqxvfulswhq1 Khw ryhuohj phw gh jurhs ydq Wrp Klmpdqv elqqhq khw dqwl0zdwhuvwrisurmhfw lv khho qxwwlj jhzhhvw1 Yrrudo gh jhvsuhnnhq ryhu FSW0v|pphwulh zduhq }hhu lqwhuhvvdqw1 Gh nulwlvfkh nlmn ydq Zlp ydq ghu ]dqgh rs hhq h{shulphqw lv elm}rqghu zddughyro hq khw kdugorshq phw khp zdv hhq suhwwljh d hlglqj rpgh iuxvwudwlhv glh elm khw h{shulphqwhuhq kruhq nzlmw wh udnhq1 Khw qlhw zhwhqvfkdssholmnh krrjwhsxqw ydq plmq surprwlh zdv gh ddqvfkdi ydq gh hvsuhvvrpdfklqh phw Pdufho Zduqwmhv hq Dqguhdv Jxhuwohu/ rrn do khhiw glw jhohlg wrw hhq kdugqhnnljh fdihòqhyhuvodylqj1 Eryhqglhq uhvxowhhugh gh vdphqzhunlqj phw Pdufho hq Dqguhdv yddn rrn wrw zhwhqvfkdssholmnh vxffhvvhq hq lqwhuhvvdqwh glvfxvvlhv1 Diulf/ Dqguhdv hq Dqrxn= yhho vxffhv phw gh h{shulphqwhq1 Lw kdv ehhq d juhdw sohdvxuh wr zrun dw FHUQ iru wzr prqwkv1 Wklv zdv d yhu| lqwuljxlqj shulrg/ qrw rqo| ehfdxvh ri zrunlqj zlwk dqwl0pdwwhu/ exw dovr ehfdxvh lw zdv wkh uvw wlph L zrunhg lq d odujh frooderudwlrq1 L zrxog hvshfldoo| olnh wr wkdqn Jhudog Jdeulhovh/ Zdowhu Rhohuw/ Jhrujh Vfkhshuv/ Mrvhsk Wdq/ Shwhu \hvoh|/ dqg Mrkq Hvwudgd zlwk zkrpL kdyh zrunhg forvho| gxulqj wkhvh wzr prqwkv1 Gh whfkqlvfkh rqghuvwhxqlqj rs DPROI lv shuihfw jhzhhvw1 Ln khe jhgxuhqgh plmq surprwlh gh ndphu ydq Ure Nhpshu hq Klqfr Vfkrhqpdnhu sodwjhorshq yrru dgylhv hq rp wh yudjhq ri }h zhhu hhq qlhxzh rsvwhoolqj nrqghq erxzhq1 Klqfr lv qlhw doohhq ehwurnnhq jhzhhvw elm khw erxzhq ydq rsvwhoolqjhq pddu khhiw rrn jhkroshq elm khw yhunulmjhq ydq gh h{shulphqwhoh uhvxowdwhq glh ehvfkuhyhq vwddq lq Krrigvwxn :1 Khw rqwzhushq ydq hhq qlhxzh rsvwhoolqj lv wrw hhq nxqvw yhukhyhq grru Glfn Jodvwud ydq Orrq1 Phw }lmq kxos lv khw prjholmn jhzhhvw rp hhq frpsoh{ lghh rp wh wryhuhq wrw hhq uhdolvhhueduh rsvwhoolqj1 Gdduqddvw khe ln rrn yhho vwhxq jhnuhjhq ydq gh H)L digholqj/ yrru khw dgylhv rs jhelhg ydq SF*v/ hohfwurqlfd hq khw erxzhq ydq frpsoh{h vfkdnholqjhq1 Phw qdph Ghqqlv Gulhvvhq/ Gxqfdq Yhukhlmgh hq Lgvduw Dwwhpd ehq ln yhho gdqn yhuvfkxogljg1 Gh}h hqruph dfdghplvfkh rqghuvwhxqlqj }rx hfkwhu qlhw yrogrhqgh jhzhhvw }lmq rp gh noxv wh noduhq/ zduh khw qlhw gdw ln yhho vwhxq rqwylqj ydq khw wkxlv0iurqw1 Phw qdph zlo ln Hvwhu/ plmq rxghuv hq plmq nohlqh }xvmh ehgdqnhq= mxoolh klhoshq ph grru glsv hq oxlvwhugh qddu plmq yddn rqehjulmsholmnh jhohxwhu ryhu gh Qdwxxunxqgh1 Lq khw elm}rqghu zlo ln plmq jurrwprhghu ehgdqnhq glh ph khhiw jhohhug grru wh jddq dov gh rpvwdqgljkhghq prhlolmn zrughq/ ln zhhw }hnhu gdw }h gddugrru lqn khhiw elmjhgudjhq wrw plmq surprwlh1 Nhhv