W HE N AT O MS BE HAVE AS WAVES: B OSE-EI NSTEI N C ONDENSATI ON AND T HE AT O M LASER

Nobel Lecture, Dece mber 8, 2001 by

W OLFGA NG K ETTERLE * Depart ment of Physics, MI T- Harvard Center for Ultracold Ato ms, and Re- searc h Laboratory of Electro nics, Massac husetts I nstitute of Tec h nology, Ca m- bridge, Massac husetts, 02139, US A.

INTRODUCTION T he l ure of lo wer te m perat ures has attracte d p hysicists for t he past ce nt ury, and with each advance to wards absolute zero, ne w and rich physics has e merged. Laypeople may wonder why “freezing cold” is not cold enough. But i magi ne ho w ma ny aspects of nature we would miss if we lived o n t he surface of t he su n. Wit hout i nve nti ng refrigerators, we would o nly k no w gaseous mat- ter a nd never observe liquids or solids, a nd miss t he beauty of s no w flakes. Cooli ng to nor mal eart hly te mperatures reveals t hese dra matically differe nt states of matter, b ut t his is o nly t he begi n ni ng: ma ny more states a p pear wit h further cooling. The approach into the kelvin range was re warded with the discovery of superco nductivity i n 1911 a nd of super fluidity i n heliu m-4 i n 1938. Cooling into the millikelvin regi me revealed the super fluidity of heliu m-3 i n 1972. T he adve nt of laser cooli ng i n t he 1980s ope ned up a ne w approach to ultralo w te mperature physics. Microkelvin sa mples of dilute ato m clouds were generated and used for precision measure ments and st u dies of ultracol d collisio ns. Na nokelvi n te m perat ures were necessary to ex- plore quantu m-degenerate gases, such as Bose-Einstein condensates first realized i n 1995. Eac h of t hese ac hieve me nts i n cooli ng has bee n a major ad- v a n c e, a n d r e c o g niz e d wit h a N o b el priz e. T his paper describes t he discovery a nd study of Bose- Ei nstei n co nde nsates ( B E C) in ato mic gases fro m my personal perspective. Since 1995, this field has gro w n explosively, dra wi ng researc hers fro m t he co m mu nities of ato mic p hysics, qua ntu m optics, a nd co nde nsed matter p hysics. T he trapped ultra- cold vapor has e merged as a ne w qua ntu m syste m t hat is u nique i n t he preci- si o n a n d fl e xi bility wit h w hi c h it c a n b e c o ntr oll e d a n d m a ni p ul at e d. At l e ast thirty groups have no w created condensates, and the publication rate on Bose- Ei nstei n co n de nsatio n has soare d follo wi ng t he discovery of t he gaseo us co n de nsates i n 1995 (see Fig. 1).

* U R L: http://cua. mit.edu/ketterle_group/

1 1 8 Fi g ure 1. Annual nu mber of published papers, which have the words “ Bose” and “ Einstein” in t heir title, abstracts or key words. T he data were obtai ned by searc hi ng t he ISI (I nstitute for Scie nti fic I nfor matio n) database.

The pheno menon of Bose- Einstein condensation was predicted long ago, in a 1925 paper by Albert Einstein [1] using a method introduced by Satyendra Nath Bose to derive the black-body spectru m [2]. When a gas of boso nic ato ms is coole d belo w a critical te m perat ure T c , a large fracti o n of t he ato ms condenses in the lo west quantu m state. Ato ms at te mperature T a n d wit h m ass m can be regarded as quantu m- mechanical wavepackets that have a spatial extent on the order of a ther mal de Broglie wavelength λ d B = 2 1 / 2 ( 2 π / m k B T ) . T he val ue of λ d B is t he positio n u ncertai nty associate d wit h the ther mal mo mentu m distribution and increases with decreasing te mpera- ture. W he n ato ms are cooled to t he poi nt w here λ d B is c o m p ar a bl e t o t h e i n- terato mic separatio n, t he ato mic wavepackets “overlap” a nd t he gas starts to beco me a “qua ntu m soup” of i ndisti nguis hable particles. Boso nic ato ms u n- dergo a qua ntu m- mec ha nical p hase tra nsitio n a nd for m a Bose- Ei nstei n co n- de nsate (Fig. 2), a cloud of ato ms all occupyi ng t he sa me qua ntu m mec ha n- ical state at a precise te m perat ure ( w hic h, for a n i deal gas, is relate d to t he 3 peak ato mic de nsity n by n λ d B = 2.612). If t he ato ms are fer mio ns, cooli ng gradually bri ngs t he gas closer to bei ng a “Fer mi sea” i n w hic h exactly o ne ato m occ u pies eac h lo w-e nergy state. Cr e ati n g a B E C is t h us si m pl e i n pri n ci pl e: m a k e a g as e xtr e m ely c ol d u ntil t he ato mic wave packets start to overlap! Ho wever, i n most cases qua ntu m de- generacy would si mply be pre-e mpted by the more fa miliar transitions to a li q ui d or s oli d. T his m or e c o nv e nti o n al c o n d e ns ati o n i nt o a li q ui d a n d s oli d ca n o nly be avoided at extre mely lo w de nsities, about a hu ndred t housa ndt h t he de nsity of nor mal air. U nder t hose co nditio ns, t he for matio n ti me of mo- lec ules or cl usters by t hree-bo dy collisio ns ( w hic h is pro portio nal to t he i n- verse de nsity s q uare d) is stretc he d t o sec o n ds or mi n utes. Si nce t he rate of bi- nary elastic c ollisi o ns dr o ps o nly pr o p orti o nal t o t he de nsity, t hese c ollisi o ns are muc h more freque nt. T herefore, t her mal equilibriu m of t he tra nslatio n-

1 1 9 al degree of freedo m of t he ato mic gas is reac hed muc h faster t ha n c he mical equilibriu m, and quantu m degeneracy can be achieved in an effectively metastable gas p hase. Ho wever, suc h ultralo w de nsity lo wers t he te mperature require ment for quantu m degeneracy into the nano- to microkelvin range. T he ac hieve me nt of Bose- Ei nstei n co nde nsatio n required first t he ide nti fi- catio n of a n ato mic syste m w hic h would stay gaseous all t he way to t he B E C tra nsitio n, a nd seco nd, t he develop me nt of cooli ng a nd trappi ng tec h niques to reac h t he required regi me of te mperature a nd de nsity. Eve n arou nd 1990, it was not certai n t hat nature would provide us wit h suc h a syste m. I ndeed, many people doubted that B E C could ever be achieved, and it was regarded as a n elusive goal. Ma ny believed t hat pursui ng B E C would result i n ne w a nd interesting physics, but whenever one would co me close, so me ne w pheno- me no n or tec h nical li mitatio n would s ho w up. A ne ws article i n 1994 quoted Steve Chu: “I a m betting on nature to hide Bose condensation fro m us. The last 15 years s he’s bee n d oi ng a great j o b” [3]. I n brief, t he co nditio ns for B E C i n alkali gases are reac hed by co mbi ni ng t wo cooli ng met hods. Laser cooli ng is used to precool t he gas. T he pri nciple of laser cooli ng is t hat scattere d p hoto ns are o n average bl ue-s hifte d wit h re- s pect to t he i nci de nt laser bea m. As a res ult, t he scattere d lig ht carries a way more e nergy t ha n has bee n absorbed by t he ato ms, resulti ng i n net cooli ng. Bl ue-s hifts are ca use d by D o p pler s hifts or ac Stark s hifts. T he differe nt laser cooli ng sc he mes are described i n t he 1997 Nobel lectures i n p hysics [4–6]. After t he precooli ng, t he ato ms are cold e noug h to be co n fi ned i n a mag ne- tic trap. Wall-free co n fi ne me nt is necessary, ot her wise t he ato ms would stick to t he surface of t he co ntai ner. It is note wort hy t hat si milar mag netic co n- fine ment is also used for plas mas which are too hot for any material con- tai ner. After mag netically trappi ng t he ato ms, forced evaporative cooli ng is applied as t he seco nd cooli ng stage [7–9]. I n t his sc he me, t he trap dept h is reduced, allo wing the most energetic ato ms to escape while the re mainder rether malize at steadily lo wer te mperatures. Most B E C experi ments reach quantu m degeneracy bet ween 500 n K and 2 µ K, at de nsities bet wee n 10 1 4 a n d 1 0 1 5 c m - 3 . T he largest co n de nsates are of 100 millio n ato ms for so di u m, a n d a billio n for hydroge n; t he s mallest are just a fe w hu ndred ato ms. Depe ndi ng o n t he mag netic trap, t he s hape of t he co nde nsate is eit her approxi mately r o u n d, wit h a di a m et er of 1 0 t o 5 0 µ m, or ci g ar-s h a p e d wit h a b o ut 1 5 µ m i n dia meter a nd 300 µ m i n le ngt h. T he f ull cooli ng cycle t hat pro d uces a co n- de nsate may take fro m a fe w seco n ds to as lo ng as several mi n utes. After t his s hort overvie w, I wa nt to provi de t he historical co ntext for t he search for B E C and then describe the develop ments which led to the obser- vatio n of B E C i n sodiu m at MI T. Fi nally, so me exa mples will illustrate t he novel physics which has been explored using Bose- Einstein condensates. A more detailed account of the work of my group has been presented in four co mpre he nsive revie w papers [8, 10–12].

1 2 0 Fi g ure 2. Criteri o n f or B ose- Ei nstei n co n de nsatio n. At hig h te m perat ures, a weakly i nteract- i ng gas ca n be treate d as a sys- t e m of “ billi ar d b alls.” I n a si m- pli fied qua ntu m descriptio n, t he ato ms ca n be regarded as wavepackets wit h a n exte nsio n of t heir de Broglie wavele ngt h

λ d B . At t he B E C tra nsitio n te m- perat ure, λ d B beco mes co mpar- able to t he dista nce bet wee n ato ms, and a Bose condensate for ms. As t he te mperature ap- proac hes zero, t he t her mal clo u d disa p pears, leavi ng a p ure Bose co nde nsate.

BEC AND C ONDENSED- MATTER P HYSICS Bose- Einstein condensation is one of the most intriguing pheno mena pre- dicte d by q ua nt u m statistical mec ha nics. T he history of t he t heory of B E C is very i nteresti ng, a n d is nicely describe d i n t he biogra p hies of Ei nstei n [13] and London [14] and revie wed by Griffin [15]. For instance, Einstein made his predictio ns before qua ntu m t heory had bee n fully developed, a nd before the differences bet ween bosons and fer mions had been revealed [16]. After Einstein, i mportant contributions were made by, most notably, London, Landau, Tisza, Bogoliubov, Penrose, Onsager, Feyn man, Lee, Yang, Huang, Beliaev a n d Pitaevskii. A n i m porta nt iss ue has al ways bee n t he relatio ns hi p be- t wee n B E C a nd super fluidity i n liquid heliu m, a n issue t hat was hig hly co n- troversial bet wee n Lo ndo n a nd La ndau (see ref. [14]). Works by Bogoliubov, Beliaev, Grif fi n a nd ot hers s ho wed t hat Bose- Ei nstei n co nde nsatio n gives t he microscopic picture behind Landau’s “quantu m hydrodyna mics.” BE C is closely related to superco nductivity, w hic h ca n be described as bei ng due to Bose- Einstein condensation of Cooper pairs. Thus Bose- Einstein condensa- tio n is at t he heart of several macroscopic qua ntu m p he no me na. B E C is u ni q u e i n t h at it is a p ur ely q u a nt u m-st atisti c al p h as e tr a nsiti o n, i. e., it occ urs eve n i n t he abse nce of i nteractio ns. Ei nstei n describe d t he tra nsitio n as co nde nsatio n “ wit hout attractive forces” [16]. T his makes B E C a n i mpor- ta nt para dig m of statistical mec ha nics, w hic h has bee n disc usse d i n a variety of co ntexts i n co n de nse d- matter, n uclear, particle a n d astro p hysics [17]. O n t he ot her ha n d, real-life particles will al ways i nteract, a n d eve n t he weakly- i nteracti ng Bose gas be haves q ualitatively differe ntly fro m t he i deal Bose gas

1 2 1 [18]. It was believe d for q uite so me ti me t hat i nteractio ns wo ul d al ways lea d to “ordi nary” co nde nsatio n (i nto a solid) before Bose- Ei nstei n co nde nsatio n would happe n. Liquid heliu m was t he o nly cou nter-exa mple, w here t he lig ht mass a nd co nco mita nt large zero-poi nt ki netic e nergy preve nts solidi ficatio n eve n at zero kelvi n. Er wi n Sc hrödi nger wrote i n 1952 i n a textbook o n t her- modyna mics about B E C: “ The densities are so high and the te mperatures so lo w – t hose req uire d to ex hibit a noticeable de part ure [fro m classical stati- stics] – t hat t he va n der Waals correctio ns are bo u n d to coalesce wit h t he pos- si ble effects of dege nerati o n, a n d t here is little pr os pect of ever bei ng a ble t o se parate t he t wo ki n ds of effect” [19]. W hat he di d n’t co nsi der were dil ute sys- te ms i n a metastable gaseous p hase! T he q uest to realize B E C i n a dil ute, weakly i nteracti ng gas was p urs ue d i n at least t hree differe nt directio ns: liq ui d heli u m, excito ns a n d ato mic gases. Ex peri me ntal [20, 21] a n d t heoretical work [22] s ho we d t hat t he o nset of s u- per fl ui dity for liq ui d heli u m i n Vycor has feat ures of dil ute-gas Bose- Ei nstei n condensation. At sufficiently lo w coverage, the heliu m adsorbed on the po- rous spo nge-like glass be haved like a dilute t hree-di me nsio nal gas. Ho wever, t he i nter pretatio n of t hese res ults is not u na mbig uo us [23]. Excito ns, w hic h co nsist of weakly-bo u n d electro n- hole pairs, are co m posite boso ns. T he p hysics of excito ns i n se mico nductors is very ric h a nd i ncludes t he for matio n of a n electro n- hole liq ui d a n d biexcito ns. As nicely disc usse d i n refs. [24, 25], t here are syste ms w here excito ns for m a weakly i nteracti ng gas.

Ho wever, t he i nitial evide nce for Bose- Ei nstei n co nde nsatio n i n Cu 2 O [26] was retracted [27]. Rece nt work i n coupled qua ntu m- well structures is very pro misi ng [28]. W he n excito ns stro ngly i nteract wit h lig ht i n a cavity, t hey for m polarito ns. I n suc h polarito n syste ms, sti mulated scatteri ng a nd no n- equilibriu m co nde nsates have bee n observed rece ntly [29–31].

SPIN-P OLARIZED HYDR OGEN Dil ute ato mic gases are disti ng uis he d fro m t he co n de nse d- matter syste ms dis- c usse d above by t he abse nce of stro ng i nteractio ns. I nteractio ns at t he de nsi- ty of a liq ui d or a soli d co nsi derably mo dify a n d co m plicate t he nat ure of t he p hase tra nsitio n. Hec ht[32], a nd St walley a nd Nosa no w [33] used t he qua n- tu m t heory of correspo ndi ng states to co nclude t hat spi n-polarized hydroge n would re main gaseous do wn to zero te mperature and should be a good can- didate to realize Bose- Ei nstei n co nde nsatio n i n a dilute ato mic gas. T hese suggestio ns triggered several experi me ntal efforts, most notably by Silvera and Walraven in A msterda m, by Greytak and Kleppner at MI T, and by others at M os c o w, T ur k u, Britis h C ol u m bi a, C or n ell, H ar v ar d, a n d Ky ot o. T h e st a bi- lizatio n of a spi n-polarized hydroge n gas [34, 35] created great excite me nt about the prospects of exploring quantu m-degenerate gases. Experi ments were first do ne by filli ng cryoge nic cells wit h t he spi n-polarized gas a nd by co mpressing it, and since 1985, by magnetic trapping and evaporative cooli ng. B E C was fi nally acco mplis hed i n 1998 by Klepp ner, Greytak a nd col- la b orat ors [36]. See refs. [9, 37–39] a n d i n partic ular ref. [40] f or a f ull ac-

1 2 2 cou nt of t he pursuit of Bose- Ei nstei n co nde nsatio n i n ato mic hydroge n. Evi- de nce for a p hase tra nsitio n i n t wo di me nsio ns was reported i n 1998 [41]. T he work i n alkali ato ms is based o n t he work i n spi n-polarized hydroge n i n several res pects: • Studies of spin-polarized hydrogen sho wed that syste ms can re main in a metastable gaseo us state close to B E C co n ditio ns. T he c halle nge was t he n to fi nd t he wi ndo w i n de nsity a nd te mperature w here t his metastability is suf- fi ci e nt t o r e aliz e B E C. • Many aspects of B E C in an inho mogeneous potential [42–44], and the the- ory of c ol d c ollisi o n pr ocesses (see e.g. [45]) devel o pe d i n t he 1980s f or hy- dr o g e n c o ul d b e a p pli e d dir e ctly t o t h e al k ali syst e ms. • T he tec h nique of evaporative cooli ng was developed first for hydroge n [7, 46] a n d t he n use d for alkali ato ms.

LASER C O OLI NG Laser cooling opened a ne w route to ultralo w te mperature physics. Laser cooling experi ments, with roo m te mperature vacuu m cha mbers and easy op- tical access, look very differe nt fro m cryoge nic cells wit h m ulti-layer t her mal s hieldi ng arou nd t he m. Also, t he nu mber of ato mic species t hat ca n be studi- ed at ultralo w te mperatures was greatly extended fro m heliu m and hydrogen t o all of t he alkali at o ms, metasta ble rare gases, several eart h-alkali at o ms, a n d ot h ers (t h e list of l as er- c o ol e d at o mi c s p e ci es is still gr o wi n g ). A f ull a c c o u nt of t he releva nt laser cooli ng tec h niques a nd t heir develop me nt is give n i n refs. [47–49] and in the 1997 Nobel lectures of Chu, Cohen- Tannoudji and P hilli ps [ 4 – 6 ]. So me papers a nd proposals writte n i n t he early a nd mid 1980s, before a nd d uri ng t he develo p me nts of t he basic cooli ng a n d tra p pi ng tec h niq ues, liste d qua ntu m dege neracy i n a gas as a visio nary goal for t his ne w e mergi ng field [50–52]. Ho wever, major li mitatio ns of laser cooli ng a nd trappi ng were soo n ide nti fied. Alt houg h t here is no fu nda me ntal lo w te mperature li mit, t he fi nal te mperature provided by polarizatio n gradie nt cooli ng – about te n ti mes t he r e c oil e n er gy – w as r e g ar d e d as a pr a cti c al li mit. S u b-r e c oil l as er c o oli n g t e c h- niques, especially i n t hree di me nsio ns, were harder to i mple me nt, a nd re- quired lo ng cooli ng ti mes. T he nu mber a nd de nsity of ato ms were li mited by i nelastic, lig ht-i n d uce d collisio ns (lea di ng to tra p loss [53, 54]) a n d by ab- sor ptio n of scattere d laser lig ht [55], w hic h res ults i n a n o ut war d ra diatio n pressure ( weakening the trapping potential and li miting the density). Further more, since the lo west te mperatures could not be achieved at the hig hest de nsities [56–58], most trappi ng a nd cooli ng tec h niques reac hed a 3 - 5 maxi mu m phase-space density of around n λ d B = 1 0 ; a n d a val ue of 2.612 is needed for B E C. T his was t he situatio n w he n t he aut hor joi ned t he field of cold ato ms i n 1990. It was o nly more rece ntly t hat major i ncreases i n p hase- s pace de nsity were ac hieve d by laser cooli ng [59–61], b ut so far laser cooli ng by its elf h as n ot b e e n a bl e t o r e a c h B E C.

1 2 3 T HE EFF ORT AT MIT 1990–1996 I mprovi ng laser cooli ng W he n I tea me d u p wit h Dave Pritc har d at MI T i n 1990 as a post doc, t he i nitial goal was to b uil d a n i nte nse so urce of col d ato ms to st u dy col d collisio ns a n d pure lo ng-ra nge molecules. Ho wever, Dave a nd I freque ntly talked about t he li mitatio ns i n de nsity a n d te m perat ure of t he c urre nt tec h niq ues a n d trie d to develop ideas o n ho w to get arou nd t he m. O ne li mitatio n of mag netic traps is that they can hold ato ms only in weak-field seeking hyperfine states. T herefore, a collisio n bet wee n t wo trapped ato ms ca n lead to a spi n flip, a nd t he Zee ma n e nergy is co nverted i nto ki netic e nergy (dipolar relaxatio n). T his process has bee n a major li mitatio n to t he experi me nts i n ato mic hydroge n. First, we aske d o urselves if t he i ncl usi o n of electric a n d gravitati o nal fiel ds would allo w t he stable co n fi ne me nt of ato ms i n t heir lo west hyper fi ne states- – but the ans wer was negative [62]. One loophole was ti me-dependent mag- netic fiel ds, a n d b uil di ng o n a n earlier pro posal [63], I desig ne d a n ex peri- me nt to co n fi ne sodiu m ato ms wit h ac mag netic fields w hic h looked feasible. Ho wever, we lear nt t hat Eric Cor nell at Bo ul der ha d develo pe d a si milar i dea a nd experi me ntally i mple me nted it [64] – so we left t he idea o n t he dra wi ng boar d. It was n’t t he last ti me t hat Eric a n d I wo ul d develo p si milar i deas i n- depe nde ntly a nd al most si multa neously! Trappi ng ato ms i n t he lo west hyper fi ne state was not necessary to acco m- plis h B E C. Alrea dy i n 1986, Pritc har d correctly esti mate d t he rate co nsta nts of elastic a n d i nelastic c ollisi o ns f or alkali at o ms [52]. Fr o m t hese esti mates o ne could easily predict t hat for alkali ato ms, i n co ntrast to hydroge n, t he so- calle d goo d collisio ns (elastic collisio ns necessary for t he eva poratio n pro- cess) wo ul d clearly do mi nate over t he so-calle d ba d collisio ns (i nelastic t wo- a nd t hree-body collisio ns); t herefore, evaporative cooli ng i n alkalis would probably not be li mited by i ntri nsic loss a nd heati ng processes. Ho wever, there was pessi mis m [65] and skepticis m, and the above- mentioned experi- me ntal [64] a n d t heoretical [62] work o n tra ps for stro ng- fiel d seeki ng ato ms h as t o b e s e e n i n t his c o nt e xt. I n t hose years, t here were so me suggestio ns t hat ti me-depe nde nt pote ntials could lead to substa ntial cooli ng, but we s ho wed t hat t his was not possible [66]. Real cooli ng needs a n ope n syste m w hic h allo ws e ntropy to be re moved fro m t he syste m – i n laser cooli ng i n t he for m of scattere d p hoto ns, i n eva po- rative cooli ng i n t he for m of discarded ato ms. Dave a nd I brai nstor med about novel laser cooling sche mes. In 1991, at the Varenna su m mer school, Dave prese nted a ne w t hree-level cooli ng sc he me [67]. I nspired by t hese ideas, I developed a sc he me usi ng Ra ma n tra nsitio ns. Replaci ng t he six laser bea ms i n optical molasses by cou nterpropagati ng bea ms drivi ng t he Doppler-se nsi- tive Ra ma n tra nsitio n, we hoped to realize Doppler molasses wit h a li ne widt h t hat was proportio nal to t he optical pu mpi ng rate, a nd t herefore adjustable. We had started setting up radio-frequency (rf) electronics and magnetic shields for Ra man cooling when we heard that Mark Kasevich and Steve Chu were worki ng o n Ra ma n cooli ng usi ng laser pulses [68]. For t his reaso n, a nd also because around the sa me ti me we had developed the idea for the Dark 1 2 4 SP O T (spo nta neous force optical tray; see later i n t his sectio n), trap, we stopped our work on Ra man cooling. Our experi me ntal work i n t hose years focused first o n ge nerati ng a large flux of slo w ato ms. In my first months at MI T when I overlapped with Kris Hel merso n a nd Mi n Xiao, we built a sodiu m vapor cell mag neto-optical trap ( M O T). The idea was inspired by the Boulder experi ment [69], and our ho pe was to vastly i ncrease t he loa di ng rate by a d ditio nal freq ue ncies or fre- q ue ncy c hir ps a d de d to t he re d si de of t he D 2 r es o n a n c e li n e. T h e i d e a f ail e d – we first suspected t hat nearby hyper fi ne levels of sodiu m may have adverse- ly i nterfere d, b ut it was later s ho w n t hat it di d n’t work for cesi u m eit her [70] beca use of t he u nfavorable d uty cycle of t he c hir p. Still, exce pt for a cryo- ge nic setup w hic h was soo n aba ndo ned, it was t he first mag neto-optical trap built at MI T ( Dave Pritc hard’s earlier work o n mag neto-optical trappi ng was carried out at Bell Labs in collaboration with Steve Chu’s group). We ( Mic hael Joffe, Alex Marti n, Dave Pritc hard a nd myself) t he n put our efforts on bea m slo wing, and got distracted fro m pursuing Zee man slo wing by the i dea of isotro pic lig ht slo wi ng [71]. I n t his sc he me, ato ms are se nt t hro ug h a cavity wit h diff usely re flecti ng walls a n d ex pose d to a n isotro pic lig ht fiel d. For re d- det u ne d lig ht t he ato ms prefere ntially absorb lig ht fro m a for war d di- rectio n a nd are slo wed. T he experi me nt worked very well a nd it was a lot of fu n to do. Ho wever, t he require me nts for laser po wer a nd t he velocity capture ra nge of t his met hod were i nferior to Zee ma n slo wi ng, so we decided to build a n opti mized Zee ma n slo wer. We adopted t he ne w desig n by Greg Lafyatis w here t he mag netic field i n- creases rat her t ha n decreases as i n a co nve ntio nal Zee ma n slo wer [72]. We realized that at the magnetic field maxi mu m it would be possible to apply so me additio nal tra nsverse laser cooli ng to colli mate t he slo w bea m. Mic hael Joffe, a graduate stude nt, wou nd a sole noid w hic h had radial access for four extra laser bea ms. The colli mation worked [73], but not as well as we had hoped, a nd we felt t hat t he s mall gai n was not wort h t he added co mplexity. Still, even without colli mation, our Zee man slo wer provided one of the largest slo w-ato m fluxes reported until then, and soon after we had a mag- neto-optical trap with a large cloud of sodiu m ato ms. In hindsight, I a m a mazed at ho w ma ny differe nt sc he mes we co nsidered a nd tried out, but t his may have bee n necessary to distill t he best a p proac h. The 1991 Varenna su m mer school on laser cooling was me morable to me f or several reas o ns. I ha d j oi ne d t he fiel d of c ol d at o ms j ust a year earlier, a n d t here I met ma ny colleag ues for t he first ti me a n d establis he d lo ng-lasti ng re- lationships. I still have vivid me mories of one long afternoon where Dave Pritc hard a nd I sat outside t he meeti ng place, w hic h offered a spectacular vie w on Lake Co mo, and brainstor med about the big goals of our field and ho w to approach the m. Dave’s encourage ment was crucial to me and helped to i ncrease my self-co n fide nce i n my ne w field of researc h. We co nsidered op- tio ns a nd strategies o n ho w to co mbi ne laser cooli ng a nd evaporative cooli ng, so mething which had been on our mind for so me ti me. Follo wing the exa mple of the spin-polarized hydrogen experi ment at MI T

1 2 5 [7], eva poratio n co ul d be do ne i n a mag netic tra p usi ng rf i n d uce d s pi n- fli ps, as suggested by Pritc hard a nd collaborators i n 1989 [74]. Mag netic traps a nd laser cooli ng had already bee n used si multa neously i n t he first experi me nts on magnetic trapping at NIS T [75] and MI T [76], and on Doppler cooling of magnetically trapped ato ms at MI T [74, 77]. In 1990, a magnetic trap was loaded fro m a magneto-optical trap and optical molasses in Boulder [69]. The laser cooling route to BE C was su m marized by Monroe, Cornell and Wie ma n i n ref. [78]. So most of t he pieces to get to B E C were k no w n i n 1990, but t here was doubt about w het her t hey would fit toget her. Laser cooli ng works best at lo w de nsities w here lig ht absor ptio n a n d lig ht- i nduced collisio ns are avoided, w hereas evaporative cooli ng requires a hig h collisio n rate a n d hig h de nsity. T he proble m is t he m uc h hig her cross sectio n f or lig ht scatteri ng of ~ 10 - 9 c m 2 , w hile t he cr oss secti o n f or elastic scatteri ng of ato ms is a t ho usa n d ti mes s maller. I n hi n dsig ht, it wo ul d have bee n s uf fi- cie nt to provide tig ht mag netic co mpressio n after laser cooli ng a nd a n ex- tre mely good vacuu m to obtai n a lifeti me of t he sa mple t hat is muc h lo nger t ha n t he ti me bet wee n collisio ns, as de mo nstrated at Rice U niversity [79]. Ho wever, our assess ment was that one major i mprove ment had to be done to laser cooli ng to bridge t he gap i n de nsity bet wee n t he t wo cooli ng sc he mes. Dave a n d I disc usse d possibilities o n ho w to circ u mve nt t he de nsity-li miti ng processes i n mag neto-optical traps. We co nsidered co here nt-populatio n trap- pi ng sc he mes w here ato ms are put i nto a co here nt superpositio n state w hic h d o es n ot a bs or b t h e li g ht. W e d ev el o p e d s o m e i d e as o n h o w at o ms n e ar t h e ce nter of t he trap would be pu mped i nto suc h a dark state, but t he nu mbers were not too pro misi ng. A fe w mo nt hs later, a si m ple i dea e merge d. If t he so- called repu mping bea m of the magneto-optical trap would have a shado w in t he ce nter, ato ms would stay t here i n t he lo wer hyper fi ne state a nd not absorb t he trappi ng lig ht, w hic h is near-reso na nt for ato ms i n t he upper hyper fi ne st at e. I n a M O T, t h e d e nsity is li mit e d by l oss es d u e t o e x cit e d-st at e c ollisi o ns a nd by multiple scatteri ng of lig ht, w hic h results i n a n effective repulsive force bet wee n ato ms. W he n ato ms are kept i n t he dark, t he trappi ng force de- creases by a factor w hic h is pro portio nal to t he probability of t he ato ms to be i n t he reso na nt hyper fi ne state. Ho wever, t he repulsive force requires bot h ato ms to be reso na nt wit h t he lig ht a n d decreases wit h t he sq uare of t his fac- tor. T herefore, t here is net gai n i n co n fi ne me nt by keepi ng ato ms i n t he dark. Of course, t here is a li mit to ho w far you ca n pus h t his co ncept, w hic h is reac hed w he n t he size of t he cloud is no lo nger deter mi ned by t he bala nce of tra p pi ng a n d re p ulsive forces, b ut by t he fi nite te m perat ure of t he clo u d. The gain in density of this sche me, called Dark SP O T, over the standard M O T is bigger when the nu mber of trapped ato ms is large. So in 1992, we t weaked up the M O T to a huge size before we i mple mented the idea. It worked al most i m me diately, a n d we got very excite d abo ut t he dark s ha do ws cast by t he trapped ato ms when they were illu minated by a probe bea m. We inferred that t he probe lig ht had bee n atte nuated by a factor of more t ha n e -100 [80]. T his i mplied t hat we had created a cl o u d of c ol d at o ms wit h a n u n pr e c e d e nt e d c o m- bi n ati o n of n u m b er a n d d e nsity.

1 2 6 Co mbi ni ng laser cooli ng a nd evaporative cooli ng The follo wing weeks and months were quite dra matic. What should we do next? Dave Pritc hard had pla n ned to use t his trap as a n excelle nt starti ng point for the study of cold collisions and photoassociation – and indeed ot her groups had major successes alo ng t hese li nes [81, 82]. But t here was also t he exciti ng pros pect of co mbi ni ng laser cooli ng wit h eva porative cooli ng. We esti mated t he elastic collisio n rate i n t he Dark SP O T trap to be arou nd 100 Hz [80] which appeared to be more than sufficient to start runa way evaporatio n i n a mag netic trap. After so me discussio ns, t he w hole group decid- ed to go for t he more a mbitious a nd speculative goal of evaporative cooli ng. It was one of those rare mo ments where suddenly the whole group’s effort gets refocused. Even before we wrote the paper on the Dark SP O T trap, we placed orders for esse ntial co mpo ne nts to upgrade our experi me nt to ultra- hig h vacuu m a nd to mag netic trappi ng. All resources of t he lab were no w di- rected to wards t he evaporative cooli ng of sodiu m. T he Dark SP O T trap was a huge i mprove ment to wards co mbining high ato m nu mber and high density i n laser cooli ng. It t ur ne d o ut to be cr ucial to t he B E C work bot h at Bo ul der [83] a nd at MI T [84] a nd see ms to be still necessary i n all curre nt B E C ex- p eri m e nts wit h s o di u m, b ut n ot f or r u bi di u m. T he next step was t he desig n of a tig htly co n fi ni ng mag netic trap. We de- cided to use t he sp herical quadrupole trap, w hic h si mply co nsists of t wo op- posi ng coils – t his desig n was used i n t he first de mo nstratio n of mag netic trapping [75]. We knew that this trap would ulti mately be li mited by Majorana flops in the center of the trap where the magnetic field is zero. Near zero mag netic fiel d, t he ato mic s pi n does n’t precess fast e no ug h to fol- lo w t he c ha ngi ng directio n of t he mag netic fiel d---t he res ult is a tra nsitio n to another Zee man sublevel which is untrapped leading to trap loss. We esti- mated t he Majora na flop rate, but t here was so me u ncertai nty about t he nu- merical prefactor. Still, it see me d t hat Majora na flo ps wo ul d o nly beco me crit- ical after t he clo u d ha d s hr u nk d ue to eva porative cooli ng, so t hey s ho ul d n’t get i n t he way of de mo nstrati ng t he co mbi natio n of laser cooli ng a nd evapo- rative cooli ng. After Mic hael Joffe prese nted our approac h wit h t he quadru- pole trap at the Q E LS meeting in 1993, Eric Cornell infor med me that he had independently arrived at the sa me conclusion. In 1993, my group re- ported at the OS A meeting in Toronto the transfer of ato ms fro m the Dark SP O T trap i nto a mag netic trap, a nd t he effects of tru ncatio n of t he cloud usi n g rf i n d u c e d s pi n fli ps [ 8 5 ]. At about t his ti me, I joi ned t he MI T faculty as assista nt professor. Dave Pritchard made the unprecedented offer that if I stayed at MI T he would ha nd over to me t he ru n ni ng lab, i ncludi ng t wo gra nts. To make sure t hat I wo ul d receive t he f ull cre dit for t he work to war ds B E C, he deci de d not to stay i nvolved i n a field he had pio neered a nd gave me full respo nsibility a nd i n- depe nde nce. Dave told me t hat he wa nted to focus o n his ot her t wo experi- ments, the single-ion mass measure ment and the ato m interfero metry, al- t houg h w hat he gave up was his “ hottest” researc h activity. Eve n no w, I a m moved by his ge nerosity a nd u nusual me ntors hip. T he t wo graduate stude nts

1 2 7 o n t he project, Ke n Davis a nd Marc- Oliver Me wes, w ho had started t heir P h Ds in 1991 and 1992, respectively, deliberated whether they should stay with Dave Pritchard and work on one of his other experi ments, or to continue their work on B E C in a ne wly-for med group headed by a largely unkno wn as- sista nt professor. T hey bot h o pte d for t he latter a n d we co ul d p urs ue o ur ef- forts wit hout delay, alo ng wit h Mic hael A ndre ws, w ho joi ned t he group i n t he su m mer of 1993. For a fe w mo nt hs we got distracted fro m our goal of evaporative cooli ng. Our optical molasses te mperatures were higher than those reported by the NIS T gro u p [86], a n d we felt t hat we ha d to lear n t he state-of-t he-art before we could adva nce to eve n lo wer te mperatures. We suspected t hat t he hig her de n- sity of ato ms played a role, but we had to i mprove our tec h nique of te mpera- ture measure me nts. Our goal was to c haracterize t he i nterplay of para meters in “dark” molasses where most of the ato ms are pu mped into the dark hyper- fi ne state. It was also a goo d project for t he gra d uate st u de nts to ho ne t heir skills and develop independence. After a few months we had made so me progress, but I beca me concerned about the delay and the co mpetition fro m Boulder. We decided to drop t he project a nd resu me our work o n evaporative cooli ng. Up to t he prese nt day, we have never i mple me nted accurate diag nos- tics for t he te m perat ure obtai ne d i n laser cooli ng – it was j ust not i m porta nt. I n t he spri ng of 1994, we sa w first evide nce for a n i ncrease i n p hase-space de nsity by eva porative cooli ng. We re porte d t hese res ults at a n i nvite d talk at International Quantu m Electronics Conference (I Q E C) in May 1994. At the sa me meeti ng, t he Boulder group reported si milar results a nd t he li mitatio ns due to t he Majora na flops as t he te mperature was reduced. It was clear t hat t he next step was a n i mprove me nt of t he mag netic trap, to trap ato ms at a fi- nite bias field w hic h would suppress t he Majora na flops. Duri ng t he meeti ng, I ca me up with the idea of plugging the hole with a focused laser bea m: a blue-detuned laser bea m focused onto the zero- magnetic field point would exert re p ulsive di pole forces o nto t he ato ms a n d kee p t he m a way fro m t his re- gio n (Fig. 3). T his idea see med so obvious to me t hat I expected t he Boulder group to co me up wit h so met hi ng si milar. It was o nly at t he next co nfere nce (I C AP 1994) in Boulder [87], when I presented our approach, that I learnt about Eric Cor nell’s idea of suppressi ng Majora na flops wit h a rapidly rota- ti n g m a g n eti c fi el d – t h e s o- c all e d T O P tr a p [ 8 8 ]. H o w ev er, w e di d n’t i m pl e- ment the optical plug i m mediately. We wanted first to docu ment our obser- vatio n of evaporative cooli ng. We realized t hat our fluoresce nce diag nostics was inadequate and i mple mented absorption i maging which is no w the stan- dard tec h nique for observi ng Bose- Ei nstei n co nde nsatio n. I n t hose days, we foc use d o n direct i magi ng of t he tra p pe d clo u d ( wit ho ut ballistic ex pa nsio n), and Michael Andre ws and Marc- Oliver Me wes developed a sophisticated co m- puter code to si mulate absorption i mages in inho mogeneous magnetic fields. We t ho ug ht t hat t his wo ul d be a usef ul tool, b ut we ra pi dly a dva nce d to m uc h lo wer te mperatures where the inho mogeneous Zee man shifts were s maller t ha n t he li ne widt h, a nd never needed t he code agai n after our first paper o n eva p orative c o oli ng [89].

1 2 8 Fi g ure 3. Experi me ntal setup for cooli ng ato ms to Bose- Ei nstei n co nde nsatio n. Sodiu m ato ms are trapped by a strong magnetic field, generated by t wo coils. In the center, the magnetic field va nis hes, w hic h allo ws t he ato ms to spi n- flip a nd escape. T herefore, t he ato ms are kept a way fro m t he ce nter of t he tra p by a stro ng (3.5 W) argo n io n laser bea m (“o ptical pl ug”), w hic h exerts a re p ulsive force o n t he ato ms. Eva porative cooli ng is co ntrolle d by ra dio-freq ue ncy ra diatio n fro m a n a nte n na. T he rf selectively flips t he spi ns of t he most e nergetic ato ms. T he re mai ni ng ato ms ret her malize (at a lo wer te mperature) by collisio ns a mo ng t he mselves. Evaporative cooli ng is force d by lo weri ng t he rf freq ue ncy.

In late 1994, we had a “core meltdo wn”. The magnetic trap was s witched o n wit h o ut c o oli n g w at er, a n d t h e silv er s ol d er j oi nts of t h e c oils m elt e d. Si n c e in those days the magnetic coils were mounted inside the vacuu m cha mber, we had a catastrop hic loss of vacuu m a nd major parts of our setup had to be disasse mble d. I will never forget t he sig ht of coils dri p pi ng wit h water be hi n d a U H V vie wport. This happened just a fe w hours before MI T’s president, C harles Vest, visite d o ur lab to get first- ha n d i nfor matio n o n so me of t he re- searc h do ne o n ca mpus. He still re me mbers t his eve nt. We had lost weeks or mo nt hs of work i n a very co mpetitive situatio n. I was despo nde nt a nd sug- gested to t he group t hat we go out for a beer a nd t he n figure out w hat to do, b ut t he st u de nts i m me diately p ulle d o ut t he wre nc hes a n d starte d t he re pair. I was move d to see t heir de dicatio n a n d stre ngt h, eve n at t his dif fic ult ti me. We replaced t he mag netic trap by a muc h sturdier o ne. T his tur ned out to be crucial for t he i mple me ntatio n of t he plugged trap w here t he precise alig n- me nt of a laser bea m relative to t he mag netic- field ce nter was i mporta nt. So i n hi n dsig ht t he disaster may not have ca use d a major delay. I n early 1995, I ha d to tell my t hree gra d uate st u de nts t hat we were ra pi dly using up start-up money and urgently needed one of our t wo pending pro- posals approved. Other wise we would not be able to continue spending mo- ney i n t he way we had do ne u ntil t he n a nd would slo w do w n. Fortu nately, i n April 1995, t he NSF i nfor med me t hat my proposal was fu nded. It is i nteres-

1 2 9 ti ng to look at so me of t he revie wers co m me nts no w, seve n years later: “It see ms that vast i mprove ments are required [in order to reach BE C] …the curre nt tec h niques are so far fro m striki ng ra nge for B E C t hat it is not yet possible to make...a n assess me nt …”; “ T he scie nti fic payoffs, ot her t ha n t he i mportance of producing a B E C itself, are unclear”. And a third revie wer: “ …t here have bee n fe w s peci fic (or realistic) pro posals of i nteresti ng ex peri- me nts t hat co ul d be do ne wit h a co n de nsate.” Des pite t he ske pticis m, all re- vie wers concluded that the proposed “experi ments are valuable and worth p urs ui ng”. After we receive d t he f u n di ng decisio n, t he w hole gro u p celebrat- ed wit h di n ner, a nd a fourt h graduate stude nt ( Dalli n Durfee), w ho had ex- presse d his i nterest alrea dy mo nt hs earlier, co ul d fi nally be s u p porte d. In late Dece mber 1994, our paper on evaporative cooling was sub mitted, a nd we were free to focus o n pluggi ng t he hole. We had to lear n ho w to alig n a po werful argo n io n laser bea m a nd i mage it t hroug h ma ny atte nuators wit h- o ut major distortio ns. W he n t he pl ug was alig ne d, t he res ult was s pectac ular (Fig. 4). We could i m mediately cool do wn to lo wer te mperatures and keep many more ato ms. During evaporation, the cloud beca me so cold and s mall t hat we could n’t resolve it a ny more. T he hig hest p hase space de nsity mea- sured was a factor of t hirty belo w B E C, but we may have bee n eve n closer. We had only a fe w runs of the experi ment before we ran into severe vacuu m pr o bl e ms. W e f o c us e d i niti ally o n s p ati al i m a gi n g a n d b e c a m e li mit e d by r e- solution, whereas ballistic expansion and ti me-of- flight i maging would not have suffered fro m t his li mitatio n. We also t houg ht t hat B E C would be ac- co m plis he d at lo wer de nsities a n d i n larger clo u ds, so we worke d o n a diabatic deco mpression and ran into proble ms with the zero of the magnetic field m ovi n g a w ay fr o m t h e pl u g. In those months, we were plagued by vacuu m proble ms. The coils inside the vacuu m sho wed so me strange outgassing behavior and the vacuu m slo wly deteriorated. We went through several bakeouts of the ultrahigh-vacuu m cha mber in the spring and su m mer of 1995. Further more, Ken Davis had to writ e his P h D t h esis a n d st o p p e d w or ki n g i n t h e l a b. It is i nt er esti n g t o r e c all my assess me nt of t he fiel d i n t hose mo nt hs; I di d n’t realize t hat B E C was j ust

Fi g ure 4. Absor ptio n i mages of ato m clo u ds tra p pe d i n t he o ptically pl ugge d tra p. Clo u d (a) is al- ready colder t ha n was attai nable wit hout t he “plug” ( Ar io n laser bea m). Cloud (b) s ho ws t he break- u p of t he clo u d i nto t wo “ pockets” i n t he t wo mi ni ma of t he pote ntial. T he size of clo u d (c) reac he d t he o ptical resol utio n of t he i magi ng syste m ( ≤ 1 0 µ m) still a bs or bi ng 90 % of t he pr o be light. This sets an upper bound on te mperature ( ≤ 1 0 µ K) a nd a lo wer bou nd o n de nsity (5 1 0 1 2 c m - 3 ).

1 3 0 around the corner. In To m Greytak’s and Dan Kleppner’s group the BE C tra nsitio n was approac hed to wit hi n a factor of 3.5 i n te mperature i n 1991 [90], but it took several more years to adva nce furt her. So I prepared for a lo ng haul to cover t he last order of mag nitude to B E C. By this ti me, the group was reinforced by Dan Kurn (no w Dan Sta mper- Kur n), a graduate stude nt, a nd Klaasja n va n Drute n, my first postdoc. After mo nt hs of worki ng o n vacuu m a nd ot her proble ms, we were just ready to ru n the machine again when we heard about the breakthrough in Boulder in Ju ne of 1995. We feveris hly made several atte mpts wit h traps plugged by fo- c use d laser bea ms a n d lig ht s heets, a n d trie d differe nt strategies of eva pora- tion without success. The clouds disappeared when they were very cold. We co njectured t hat so me jitter of t he laser bea m was respo nsible, a nd w he n ac- celero meters indicated vibrations of our vacuu m cha mbers, we i m mediately decided to eli minate all turbo and mechanical pu mps. Unfortunately, when we were exchanging the turbo pu mp on our oven cha mber against an ion pu mp, we caused a leak i n t he ultra hig h vacuu m part a nd had to go t hroug h a not her lo ng bake-out. We also i mple me nted a poi nti ng stabilizatio n for t he optical plug bea m. But when we finally obtained B E C, we realized that it di d n’t i m pr ov e t h e c o oli n g. T hese were dif ficult mo nt hs for me. T he Rice group had cooled lit hiu m to quantu m degeneracy [79]. A ne w subfield of ato mic physics was opening up, and I was afraid that our approach with sodiu m and the plugged trap would not be successful and we would miss the excite ment. I considered various strategies. Several peo ple s uggeste d t hat I a do pt t he s uccessf ul T O P tra p use d at Bo ul der. B ut I ha d alrea dy starte d to st u dy several possible co n fig uratio ns for mag netic co n fi ne me nt. I realized t hat a hig hly elo ngated Ioffe-Pritc hard trap with adjustable bias field could provide a good confine ment that was equivalent or superior to the T OP trap. Around August 1995, Dan Kurn worked out a n opti mized co n figuratio n, w hic h was t he cloverleaf wi ndi ng pat- tern [91]. I considered having the whole group work on this ne w approach, but several i n my group wa nted to give t he plugged trap a fe w more atte mpts a n d at least c haracterize ho w far we co ul d a p proac h B E C wit h o ur origi nal a p- proac h. Fort u nately, we follo we d t hat s uggestio n – it is al ways a goo d i dea to liste n t o y o ur c olla b orat ors.

B E C i n so di u m T his was t he situatio n o n Septe mber 29, 1995, w he n we observed B E C i n so- di u m for t he first ti me. T he goal of t he r u n was to meas ure t he lifeti me of t he trapped ato ms a nd c haracterize possible heati ng processes. For our ultra hig h vacuu m pressure, rather slo w evaporation should have been most efficient, b ut we fo u n d o ut t hat faster eva poratio n worke d m uc h better. T his was a clear sig n for so me ot her loss or heati ng process, e.g. d ue to fl uct uatio ns i n t he po- sitio n of t he pl ug. Aro u n d 11:30 p. m., a n e ntry i n t he lab book states t hat t he lifeti me measure me nts were not reliable, but t hey i ndicated lifeti mes arou nd ten seconds, enough to continue evaporation. A fe w minutes later we sa w

1 3 1 so me dark spots i n ti me-of- flig ht absorptio n i mages, but t hey were quite dis- torted since the optical plug bea m, which we couldn’t s witch off, pushed at o ms a p art d uri n g t h e b allisti c e x p a nsi o n ( Fi g. 5 ). Still, t h e s u d d e n a p p e ar- a nce of dark s pots mea nt gro u ps of ato ms wit h very s mall relative velocity. For t he next fe w hours, we c haracterized t he appeara nce of t hose spots, but t he n decided that further progress required an acousto-optical modulator to s witc h off t he optical plug. Bet wee n 4:00 a nd 5:30 i n t he early mor ni ng, we i nstalle d o ptics a n d rf electro nics a n d were fi nally able to s witc h off t he argo n io n laser bea m d uri ng ballistic ex pa nsio n. Fiftee n mi n utes later, we observe d t he bi modal distributio ns t hat are no w t he hall mark of B E C. T he lab book of t his nig ht captured t he excite me nt of t he mo me nt (Fig. 6). T hose first measure me nts were do ne by i magi ng t he ato ms i n t he lo wer hy- per fi ne ( F = 1) state. For t he next r u n, w hic h took place a fe w days later, we prepared optical pu mping and i maging on the cycling F = 2 tra nsiti o n, a n d obtai ne d a m uc h better sig nal-to- noise ratio i n o ur i mages. T he occ urre nce of B E C was very dra matic (Fig. 7). Our a ni mated re nderi ng of t he data obtai ned in that run (done by Dallin Durfee) beca me well kno wn (see [92]). We had obtained condensates with 500,000 ato ms, 200 ti mes more than in Boulder, wit h a cooli ng cycle (of o nly ni ne seco nds) 40 ti mes s horter. Our paper was quickly writte n a nd sub mitted o nly t wo weeks after t he experi me nt.

Fi g ure 5. Ti me-of- flig ht absorptio n i mages of so me of t he first co nde nsates produced at MI T in the night of Septe mber 29, 1995. After t he mag netic quadrupole trap was s witc hed off, t he ato m cloud expa nd- e d b allisti c ally. H o w ev er, si n c e t h e o pti c al plug (i ndicated by black circles) could n ot b e t ur n e d off at t h e s a m e ti m e, it dis- torted t he expa ndi ng cloud. Still, as t he te mperature was lo wered fro m top to bot- to m, a distinctly sharp shado w appeared marki ng t he prese nce of a co nde nsate.

1 3 2 Fi g ure 6. One page of the lab book during the night of Septe mber 29, 1995, when B E C was first o bs er v e d at MI T. T h e h a n d writi n g is by Kl a asj a n v a n Dr ut e n. At 5: 5 0 a. m., w e h a d i nst all e d a n e w aco usto-o ptical mo d ulator to s witc h-off t he o ptical pl ug ( Ar io n laser bea m). Fiftee n mi n utes la- ter, we had t he first de fi nitive evide nce for B E C i n sodiu m.

In my wildest drea ms I had not assu med that the step fro m evaporative cooling to B E C would be so fast. Figure 8 sho ws ho w dra matic the progress was after laser a nd evaporative cooli ng were co mbi ned. Wit hi n less t ha n t wo years, t he nu mber of alkali ato ms i n a si ngle qua ntu m state was i ncreased by about t welve orders of mag nitude – a true si ngularity de mo nstrati ng t hat a p hase tra nsiti o n was ac hieve d!

1 3 3 Fi g ure 7. Observatio n of Bose- Ei nstei n co nde nsatio n by absorptio n i magi ng. S ho w n is absorptio n vs. t wo spatial di me nsio ns. T he Bose- Ei nstei n co nde nsate is c haracterized by its slo w expa nsio n observed after 6 ms ti me-of- flight. The left picture sho ws an expanding cloud cooled to just above t he tra nsitio n poi nt; middle: just after t he co nde nsate appeared; rig ht: after furt her evaporative cooli ng has left a n al most pure co nde nsate. T he total nu mber of ato ms at t he p hase tr a nsiti o n is a b o ut 7 1 0 5 , t he te m perat ure at t he tra nsiti o n p oi nt is 2 µ K.

MI T wit h its l o n g tr a diti o n i n at o mi c p hysi cs w as a s p e ci al pl a c e t o p urs u e the B E C work. The essential step was the co mbination of laser cooling and evaporative cooli ng. My next-door neig hbors i n Buildi ng 26 at MI T have bee n Dave Pritc hard, a pio neer i n laser cooli ng w ho co nceived t he mag neto-optical trap, and Dan Kleppner, who together with Harald Hess and To m Greytak co nceive d a n d realize d eva porative cooli ng (see Fig. 9). I feel privilege d for

Fi g ure 8. Progress i n evaporative cooli ng of alkali ato ms up to 1996. T he nu mber of ato ms i n t he lo west q ua nt u m state is pro portio nal to t he p hase-s pace de nsity, a n d has to excee d a critical n u m- - 3 ber of 2.612 to ac hieve Bose- Ei nstei n co nde nsatio n. For N 0 < 1 0 , t he i ncrease i n p hase-s pace de nsity d ue to eva poratio n is plotte d. For t he Rice res ult of J uly 1995 see ref. [79] a n d t he erra- t u m [ 9 3 ].

1 3 4 t he o p port u nity to co mbi ne t heir work a n d take it to t he next level. It is har d to overesti mate the roles which Dave Pritchard and Dan Kleppner have playe d for mo der n ato mic p hysics. T he fa mily tree of ato mic p hysicists (Fig. 10) s ho ws so me of t he re markable p hysicists t hat were trai ne d a n d i ns pire d by t h e m. Looki ng back, it see ms t hat ma ny tec h niques suc h as t he Dark SP O T, co m- pressed M O T [94], t he T OP trap a nd t he optically plugged trap were critical for first de mo nstrati ng B E C, but by no mea ns i ndispe nsable. T his is best il- lustrated by t he experi me nt at Rice w hic h used o nly Doppler cooli ng to load t he mag netic trap – a tec h nique w hic h had bee n developed i n t he 1980s. T he collisio n rate was slo w, b ut a n excelle nt vac u u m ma de a very slo w eva poratio n pr o c ess p ossi bl e [ 7 9 ]. S o i n hi n dsi g ht, B E C i n al k ali g as es di d n ot r e q uir e m a- jor i n novatio ns i n cooli ng a nd trappi ng. It merely required e noug h opti mis m to risk a fe w years i n t he atte mpt to co mbi ne laser a nd evaporative cooli ng. S uc h a n atte m pt nee de d a fe w years of very foc use d work as it i nvolve d t he i n- tegratio n of several tec h nologies t hat were not sta n dar d i n t he fiel d, i ncl u d- ing ultrahigh vacuu m, sensitive C C D ca meras and i mage processing, high- curre nt po wer supplies for mag netic traps, a nd flexible co mputer co ntrol of a multi-step cooli ng a nd detectio n process. Figure 11 co mpares a state-of- t he-art laser cooli ng experi me nt i n 1993 to a B E C experi me nt i n 2001 usi ng the sa me vacuu m apparatus in the sa me laboratory at MI T. A lot of co mpo- ne nts have bee n added, a nd I co nti nue to be i mpressed by my collaborators, who no w handle experi ments far more co mplex than I did so me five years a g o.

Fi g ure 9. MI T faculty i n ultralo w-te mperature ato mic p hysics. Da n Klepp ner, W. K., To m Greytak a nd Dave Pritc hard look at t he latest sodiu m B E C apparatus.

1 3 5 Fi g ure 1 0. F a mily tr e e of at o mi c p hysi cists. P e o pl e wit h n a m e i n it ali cs ar e N o b el l a ur e at es.

T he clo verle af tr a p After our first observatio n of B E C, we made t he rig ht decisio n for t he wro ng reaso n. We expected ma ny ot her groups to quickly upgrade t heir laser cool- i ng experi me nts to mag netic trappi ng a nd evaporative cooli ng, a nd to joi n i n duri ng t he next fe w mo nt hs. Nobody expected t hat it would take al most t wo years before the next groups succeeded in reaching B E C (the groups of Dan Heinzen, Lene Hau, Mark Kasevich and Gerhard Re mpe follo wed in 1997). I was co ncer ned t hat our plugged trap would put us at a disadva ntage si nce t he trapping potential strongly depended on the shape and align ment of the laser foc us. So we deci de d to i nstall t he cloverleaf tra p i nstea d a n d disco n- ti nue our plugged trap after o nly t wo experi me ntal B E C “ru ns”. Si nce we did n’t wa nt to break t he vacuu m, we i nstalled t he ne w trap i n a n u nfavorable geo metry. T he mag net coils for t he plugged trap were orie nted vertically in re-entrant flanges and when we replaced the m with cloverleaf c oils, t he weakly c o n fi ni ng axis of t he I offe- Pritc har d tra p was vertical. I n s uc h a geo metry, t he gravitatio nal sag would reduce t he ef ficie ncy of rf i nduced evaporatio n si nce ato ms would o nly evaporate at t he botto m of t he cloud [8, 95]. But before breaki ng t he vacuu m a nd reorie nti ng t he coils, we wa nted to see t he li mitatio n. Arou nd Dece mber 1995, w he n we were just starti ng to look at the efficiency of evaporation, we lost the vacuu m once again due to a cracked cera mic part i n a n electric feedt hroug h a nd decided to reorie nt t he whole experi ment, with the weakly confining axis of the trap no w aligned horizo ntally. Si nce t hat ti me, no w more t ha n six years, t he mac hi ne has bee n u nder vacuu m. T his is i n s harp co ntrast to t he co nditio ns i n 1995, w he n we had to open the cha mber, pu mp do wn and bake out every couple of months. Finally, we had learned fro m our previous mistakes and developed a very syste matic procedure for pu mp do wns and bakeouts. I still re me mber t he nig ht of Marc h 13, 1996, w he n t he experi me nt was up and running, and Klaasjan van Druten and I had fine-tuned the bias field of

1 3 6 Fi g ure 1 1. Co mparison of a laser cooling and B E C experi ment. The upper photograph sho ws the a ut hor i n 1993 worki ng o n t he Dark S P O T tra p. I n t he follo wi ng years, t his laser cooli ng ex peri- ment was upgraded to a BE C experi ment. The lo wer photograph sho ws the sa me apparatus in 2001 after many additional co mponents have been added. t he mag netic tra p, so t hat t he s witc h-over to t he ne w mag netic tra p was fi nal- ly co mpleted. It was already after mid nig ht, too late to start so me serious work, when Klaasjan asked half jokingly why don’t we just try to get B E C. Without kno wing what our te mperatures and densities were, without having ever measured t he trap freque ncies, we played arou nd wit h t he rf s weep t hat deter mi nes t he cooli ng trajectory, a nd a co nde nsate s ho wed up arou nd 2:10 a. m. We were relieved si nce we had n’t produced co nde nsates for al most half a year, b ut also t he ease at w hic h we got t he co n de nsate i n a ne w tra p tol d us o ur set u p was rob ust a n d t hat we were rea dy to s witc h fro m e ngi neeri ng cool- i ng sc he mes a n d tra ps to t he st u dy of t he co n de nsate. T he cloverleaf tra p a n d ot her wi ndi ng patter ns for t he Ioffe-Pritc hard co n figuratio n are no w used by al most all B E C experi ments. Figure 12 sho ws the experi mental setup during t h os e d ays. W hy had n’t we co nsidered t his trap earlier a nd avoided t he detours wit h the quadrupole trap, Majorana flops and plugging the hole? First, the q ua dr u pole tra p was si m pler to b uil d, a n d it allo we d us to p urs ue eva porative

1 3 7 Fig ure 1 2. Experi me ntal setup for cooling sodiu m ato ms to Bose- Einstein condensation around 1996. The ato ms are trapped and cooled in the center of the U H V cha mber. The ato mic bea m oven and the Zee man slo wer are to the left (outside the photo). The cloverleaf magnetic trap was mo u nte d horizo ntally i n re-e ntra nt fla nges. O nly t he lea ds for t he c ur- re nt a n d water cooli ng are visible. The diagonal flange above acco m- modated a B N C feedthrough for radio frequency fields which were used to control the evaporative cooling. The lens and the mirror above the cha mber were used to observe t he co nde nsate by disper- siv e or a bs or pti o n i m a gi n g.

c o oli n g f ast er. S e c o n d, w e i niti ally f av or e d t h e q u a dr u p ol e tr a p b as e d o n a n a nalysis w hic h s ho ws t hat co n fi ne me nt by a li near pote ntial is muc h stro nger than by the quadratic potential of the Ioffe-Pritchard configuration [10]. H o wever, a very el o ngate d I offe- Pritc har d tra p pr ovi des effectively li near c o n- fi ne me nt i n t he t wo ra dial directio ns, a n d it was o nly i n 1995 t hat I realize d t hat it wo ul d be easy to a diabatically defor m t he ro u n d laser-coole d clo u d to suc h a n elo ngated s hape. The next weeks were exciting and dra matic: we i mple mented dispersive i magi ng a nd sa w for t he first ti me t he co nde nsate i n t he trap. We could take i mages non-destructively and recorded t wo sequential i mages of the sa me co nde nsate. After year-lo ng co ncer ns of ho w fragile a nd se nsitive t he co n- densate would be once created, it was an over whel ming experience to ob- serve t he co n de nsate wit ho ut destroyi ng it. Fig ure 13 s ho ws a s patial i mage of a co n de nsate; it was take n i n no n- destr uctive dis persive i magi ng. We first i m- ple mented dispersive i maging using the dark-ground technique [96], but soon upgraded to phase-contrast i maging, which was the technique used to recor d t he fig ure. I n t he first week of A pril 1996, t here was a works ho p o n “ Collective effects i n ultracold ato mic gases” i n Les Houc hes, Fra nce, w here most of t he leadi ng groups were represented. It was the first such meeting after the su m mer of

1 3 8 Fig ure 1 3. P hase co ntrast i mages of trapped Bose gases across the BE C phase transition. At high te mpera- ture, above the B E C transition te m- perature, t he de nsity pro file of t he gas is s mooth. As the te mperature drops belo w the BE C phase transi- ti o n, a hi g h- d e nsity c or e of at o ms a p- pears i n t he ce nter of t he distrib u- tion. This is the Bose-Einstein condensate. Lo wering the te mpera- ture further, the condensate nu mber gro ws and the ther mal wings of the distrib utio n beco me s horter. Fi nally, the te mperature drops to the point w here a p ure co n de nsate wit h no dis- cernible ther mal fraction re mains. Each i mage sho ws an equilibrated gas obtained in one co mplete trap- pi n g a n d c o oli n g cy cl e. T h e a xi al a n d radial freque ncies are about 17 a nd 2 3 0 Hz, r es p e ctiv ely.

1995, and it was not without strong e motions that I reported our results. Since no other experi mental group had made major progress in BE C over the last fe w months, it was our work which provided opti mis m for further rapid develop me nts.

I nterfere nce bet wee n t wo co nde nsates After we got B E C i n t he cloverleaf trap, bot h t he mac hi ne a nd t he group were i n overdrive. After years of buildi ng a nd i mprovi ng, freque nt failures a nd fr ustratio n, it was like a p hase tra nsitio n to a sit uatio n w here al most every- t hi ng worked. Wit hi n t hree mo nt hs after getti ng a co nde nsate i n t he clover- leaf trap we had writte n t hree papers o n t he ne w trap a nd t he p hase tra nsi- tion [91], on non-destructive i maging [96], and on collective excitations [97]. Klaasja n va n Drute n left t he group, s hortly after C hristop her To w nse nd had joi ned us as a postdoc. As t he next major goal, we decided to study t he coherence of the condensate. With our optical plug, we had already devel- o pe d t he tool to s plit a co n de nsate i nto t wo halves a n d ho pe d to observe t heir i nterfere nce, w hic h would be a clear sig nature of t he lo ng-ra nge spatial co- h er e n c e. Around the sa me ti me, the idea ca me up to extract ato ms fro m the con- de nsate usi ng rf-i n d uce d s pi n fli ps – t he rf o ut p ut co u pler. So me t heorists re- garded an output coupler as an open question in the context of the ato m laser. I suggested to my group t hat we could si mply pulse o n t he radio fre- quency source that was already used during evaporation, and couple ato ms

1 3 9 o ut of t he co n de nsate by fli p pi ng t heir s pi n to a no n-tra p pe d state (Fig. 14). T he experi me nt worked t he first ti me we tried it (but t he qua ntitative work took a while [98]). I have never regarded the output coupler as one of our major acco mplish ments because it was so si mple, but it had i mpact on the co m munity and nobody has ever since regarded outcoupling as a proble m! I n J uly 1996, we ha d t he first res ults o n t he rf o ut p ut co u pler, a n d also sa w first fri nges w he n t wo co n de nsates were se parate d wit h a s heet of gree n lig ht a n d overla p pe d i n ballistic ex pa nsio n. I was i n A ustralia for vacatio n a n d for t he I Q E C co nfere nce i n Syd ney. By e- mail a nd telep ho ne I discussed wit h my group the ne w results. The fringes were most pronounced when the conden- sates were accelerate d i nto eac h ot her by re movi ng t he lig ht s heet s hortly be- fore s witc hi ng off t he mag netic trap. We co ncluded t hat so me of t he fri nges may be relate d to so u n d a n d ot her collective effects t hat occ ur w he n t wo co n- de nsates at fairly hig h de nsity “t o uc h” eac h ot her. I prese nte d t h ose res ults at t he Sy d ney meeti ng o nly to ill ustrate we were able to do ex peri me nts wit h t wo co nde nsates, but no w we had to sort out w hat was happe ni ng. It took us four more mo nt hs u ntil we observed clea n i nterfere nce bet wee n t wo co n de nsates. W he n t wo co n de nsates t hat were i nitially se parate d by a dis- t a n c e d i nterfere a n d t he i nterfere nce patter n is recor de d after a ti me t of b al- listic ex pa nsio n, t he n t he fri nge s paci ng is t he de Broglie wavele ngt h h / m v as-

Fig ure 1 4. The MI T ato m laser operating at 200 Hz. Pulses of co here nt sodiu m ato ms are coupled out fro m a Bose- Einstein condensate confined in a magnetic trap (field of vie w 2.5 5. 0 m m 2 ). Every 5 ms, a s h ort rf p ulse tra nsferre d a fracti o n of t hese ato ms i nto a n u nco n fi ned qua ntu m state. T hese ato ms were accelerated do w n ward by gravi- ty a nd spread out due to repulsive i nteractio ns. The ato m pulses were observed by absorption i maging. Each pulse contained bet ween 10 5 a n d 1 0 6 at o ms.

1 4 0 s ociate d wit h t he relative vel ocity v = d/t . For our geo metry with t wo con- de nsates abo ut 100 µ m i n le ngt h, we esti mate d t hat we wo ul d nee d at least 60 ms of ti me- of- flig ht t o o bserve fri nges wit h a 10 µ m p eri o d, cl os e t o t h e r es o- lution of our i maging syste m. Unfortunately, due to gravity, the ato ms dropped out of t he field of vie w of our wi ndo ws after 40 ms. So we tried to gain a longer expansion ti me in a fountain geo metry where we magnetically launched the ato ms and observed the m when they fell back through the ob- servatio n regio n after more t ha n 100 ms [99], but t he clouds were distorted. We also tried to co mpe nsate gravity by a vertical mag netic field gradie nt. So me ti me later I lear nt about ne w calculatio ns by t he t heory group at t he Max- Pla nck I nstit ute i n Garc hi ng, s ho wi ng t hat t he effective se paratio n of t wo elo ngated co nde nsates is s maller t ha n t heir ce nter-of- mass separatio n [100]. T his mea nt t hat we co ul d observe i nterfere nce fri nges after o nly 40 ms, j ust before t he ato ms fell o ut of t he observatio n regio n. We i m me diately ha d a dis- cussion in the group and decided to stop working on fountains and “anti- gr avity” a n d si m ply l et t h e at o ms f all by 8 m m d uri n g 4 0 ms. We made so me a mbiguous observations where we sa w lo w-contrast fringes toget her wit h so me optical i nterfere nce patter ns of t he probe lig ht, but t he breakthrough ca me on Nove mber 21, 1996, when we observed striking inter- fere nce patter ns (Fig. 15). I still re me mber t he sit uatio n late t hat nig ht w he n we wondered ho w could we prove beyond all doubt that these were matter- wave i nterfere nce patter ns a nd not so me for m of self-diffractio n of a co n- densate confined by a light sheet and then released. We ca me up with the idea of eli minating one of the condensates in the last mo ment by focusing resonant yello w light on it. Whi msically, this laser bea m was dubbed the “ fla me t hro wer”. If t he fri nges were self- diffractio n d ue to t he s har p e dge i n

Fi g ure 1 5. I nterfere nce patter n of t wo expa ndi ng co nde nsates observed after 40 ms ti me-of- flig ht. T he widt h of t he absorptio n i mage is 1.1 m m. T he i nterfere nce fri nges have a spaci ng of 15 µ m a nd are stro ng evide nce for t he lo ng-ra nge co here nce of Bose- Ei nstei n co nde nsates.

1 4 1 the confine ment, they would re main; if they were true interference they would vanish. This was like a double-slit experi ment in optics where you cover o ne of t he slits. It took a fe w ho urs to alig n t he ne w laser bea m, a n d we veri fied i n p hase-co ntrast i magi ng t hat we were able to selectively eli mi nate o ne of t he t wo co n de nsates. We had a s witch in our control panel which toggled bet ween condensate eli mi natio n o n a nd off. T he n we we nt back a nd alig ned t he setup for t he ob- servation of interference. When we toggled the s witch we had to wait for about half a minute until a ne w condensate was produced. This was the mo- me nt of tr ut h. If t he fri nges a p peare d wit ho ut a seco n d co n de nsate, t he n na- ture would have fooled us for t he w hole nig ht – but t hey disappeared a nd a n e nor mo us te nsio n disa p peare d, as well. It was alrea dy early t he next mor ni ng, wit h people arrivi ng to work. I walked to Da n Klepp ner’s of fice a nd told hi m there was so mething he should see. So he shared the mo ment with us where we toggle d t he s witc h o n alter nati ng cooli ng cycles a n d corres po n di ngly, t he interference pattern disappeared and reappeared. Interference bet ween t wo li g ht b e a ms is q uit e a si g ht, b ut wit h at o ms it is m or e dr a m ati c. D estr u ctiv e i n- terference means that ato ms plus ato ms add up to vacuu m! T he evide nce for i nterfere nce was so co mpelli ng t hat we sub mitted our pa- per based solely o n t he data of o ne experi me ntal ru n [101]. T his ru n is me m- orable to me for a not her reaso n: it was to be t he last ti me I playe d a major role i n prepari ng a nd ru n ni ng a n experi me nt. Duri ng t he nig ht, I had put i n t he o ptics for t he “ fla me t hro wer”. U p to t he n, I was fa miliar wit h every piece of equip me nt i n t he lab a nd never t houg ht t his could c ha nge quickly, but it was like a not her p hase tra nsitio n. Ha ns-Joac hi m Mies ner ha d j ust arrive d, t he first postdoc who stayed for more than a year, and he soon took over much responsibility for organizing the lab. There were more de mands on my ti me to write papers a nd give talks, t he group gre w wit h t he additio n of t wo more graduate stude nts (S hi n I nouye a nd C hris Kukle wicz), a nd we had i nte nsi fied our efforts to build a second B E C experi ment. All this coincided in a fe w mo nt hs. After ear ni ng my P h D i n 1986, I spe nt eleve n more years i n t he lab d uri ng t hree post doc positio ns a n d as a n assista nt professor, b ut no w bega n to pl ay a n a dvis or y r ol e. T he papers o n t he rf output coupler [98] a nd t he i nterfere nce [101] of t wo condensates appeared in the sa me week in January 1997. Together they de mo nstrated t he ability to create multiple pulses of co here nt ato ms, a nd have bee n regarded as t he realizatio n of a n ato m laser. T he period starti ng with the early drea ms of pursuing B E C and ending with the observation of t he co here nce of t he co nde nsate was re markable. It was full of speculatio n, drea ms, u nk no w n p hysics, failures a nd successes, passio n, excite me nt, a nd frustratio n. T his period fused toget her a tea m of very differe nt people w ho had one co m mon deno minator: the passion for experi mental physics. It was a u nique experie nce for me to work wit h t hese outsta ndi ng people (Fig. 16).

1 4 2 Al e x M arti n

Kl a a sj a n C hrist o p h er van Druten To wnsend W. K. K e n D a vi s

Mi c h a el J off e

Hans-Joachi m Mi es n er

Dan Sta mper- Kurn Marc Me wes Dave Pritchard Michael Andre ws D alli n D urf e e The tea m 1992 - 1996 Fi g ure 1 6. Tea m p hoto. T his p hoto was take n i n early 1996 i n fro nt of t he MI T do me. T he bottle of cha mpagne was e mptied to celebrate B E C in the cloverleaf trap. Na mes and photos of other collaborators during the period 1992–1996 have been added.

T HE MAGIC OF MATTER WAVES Ma ny studies of B E Cs have bee n perfor med over t he last several years. T he progress u ntil 1998 is nicely su m marized i n t he Vare n na su m mer sc hool pro- ceedi ngs [102]. T he studies t hat were most exciti ng for me displayed macro- scopic quantu m mechanics, the wavelike properties of matter on a macro- scopic scale. These were also pheno mena that no ordinary gas would sho w, a nd illustrated dra matically t hat a ne w for m of matter had bee n created. T he i nterfere nce of t wo co nde nsates prese nted above (Fig. 15) is o ne suc h exa m- pl e. I n t h e f oll o wi n g, I w a nt t o dis c uss t h e a m pli fi c ati o n of at o ms a n d t h e o b- servati o n of lattices of q ua ntize d v ortices. T hese t wo exa m ples are re prese ntative of t he t wo areas i nto w hic h researc h on gaseous B E C can be divided: in the first ( which could be labelled “ The ato mic condensate as a coherent gas” or “ Ato m lasers”), one would like to h av e as littl e i nt er a cti o n as p ossi bl e – al m ost li k e t h e p h ot o ns i n a l as er. T h e experi me nts are preferably do ne at lo w de nsities. T he Bose- Ei nstei n co nde n- sate serves as a n i nte nse source of ultracold co here nt ato ms for experi me nts i n ato m optics, i n precisio n studies or for exploratio ns of basic aspects of quantu m mechanics. The second area could be labelled “ B E C as a ne w quan- tu m fluid” or “ B E C as a ma ny-body syste m”. T he focus here is o n t he i nterac- tio ns bet wee n t he ato ms t hat are most pro nou nced at hig h de nsities. T he co-

1 4 3 here nt a mpli ficatio n of ato ms is a n exa mple of ato m optics wit h co nde nsates, a n d t he st u dy of vortices a d dresses t he s u per fl ui d pro perties of t he gas.

A m pli fic atio n of ato ms i n a Bose- Ei nstei n co n de ns ate Since ato ms are de Broglie waves, there are many analogies bet ween ato ms a nd lig ht, w hic h co nsists of electro mag netic waves. T his is exploited i n t he fiel d of ato m o ptics w here ato ms are re flecte d, diffracte d a n d i nterfere usi ng various ato m-optical ele ments [103]. One i mportant question was whether t hese a nalogies ca n be exte nded to t he optical laser, w hic h is based o n t he a mplification of light. When our group de monstrated a rudi mentary ato m laser i n 1997 we had solved t he proble m of outcoupli ng (or extracti ng) ato ms fro m the BE C and of verifying their coherence. The ato mic a mplification process happened during the for mation of the Bose-Einstein condensate [104], which is quite different fro m the way light is a mplified in passing t hroug h a n active mediu m. It was o nly i n 1999 t hat our group ma naged to ob- serve t he a mpli ficatio n of ato ms passi ng t hroug h a not her cloud of ato ms serv- ing as the active mediu m [105] (si multaneously with the group in Tokyo [ 1 0 6 ] ). A mplifyi ng ato ms is more subtle t ha n a mplifyi ng electro mag netic waves be- cause ato ms can only change their quantu m state and cannot be created. T herefore, eve n if o ne could a mplify gold ato ms, o ne would not realize t he drea ms of medieval alche my. An ato m a mplifier converts ato ms fro m the ac- tive mediu m i nto a n ato mic wave t hat is exactly i n t he sa me qua ntu m state as t h e i n p ut w av e ( Fi g. 1 7 ). T he ato m a mpli fier requires a reservoir, or a n active mediu m, of ultracold

Fig ure 1 7. A m pli ficatio n of lig ht a n d ato ms: I n t he o ptical laser, lig ht is a m pli fie d by passi ng it through an excited inverted mediu m. In the MI T ato m a mplifier, an input matter wave is sent t hroug h a Bose- Ei nstei n co nde nsate illu mi nated by laser lig ht. Boso nic sti mulatio n by t he i nput ato ms ca uses lig ht to be scattere d by t he co n de nsate exactly at t he a ngle at w hic h a recoili ng co n- de nsate ato m joi ns t he i nput matter wave a nd aug me nts it.

1 4 4 ato ms t hat have a very narro w spread of velocities a nd ca n be tra nsferred to t he ato mic bea m. A natural c hoice for t he reservoir was a Bose- Ei nstei n co n- de nsate. O ne also needs a coupli ng mec ha nis m t hat tra nsfers ato ms fro m t he reservoir at rest to an input mode while conserving energy and mo mentu m. T his tra nsfer of ato ms was acco m plis he d by scatteri ng laser lig ht. T he recoil of t he scatteri ng process accelerate d so me ato ms to exactly matc h t he veloci- ty of t he i nput ato ms (Fig. 18). Not o nly were t he ato ms a mpli fied, but were i n exactly t he sa me motio nal state as t he i n p ut ato ms, i.e., t hey ha d t he sa me quantu m- mechanical phase. This was verified by interfering the a mplified output wit h a copy of t he i nput wave a nd observi ng p hase co here nce. This direct observation of ato m a mplification in the su m mer of 1999 was preceded by a surprisi ng occurre nce late o ne nig ht i n October 1998 w he n we discovered a ne w for m of superradia nce [107]. We were studyi ng Bragg spec- troscopy [108] a nd illu mi nated a B E C wit h t wo laser bea ms. I had no role i n the running of the experi ment and was working in my office, when around midnight the students ca me fro m the lab and told me that they sa w ato ms shooting out fro m the condensate with a velocity co mponent perpendicular to t he directio n of t he laser bea ms. We expected ato ms to receive recoil mo- me ntu m o nly alo ng t he laser bea ms, a nd all motio n perpe ndicular to it to be diffuse due to t he ra ndo m directio n of spo nta neous Rayleig h scatteri ng. The whole lab started to discuss what was going on. With a running ma- c hi ne, everyt hi ng could be tried out i m mediately. T he first ideas were mu n- da ne: let’s illu mi nate t he co nde nsate wit h o nly o ne laser bea m a nd see w hat happen (the directional bea ms re mained). We scrutinized the experi mental setup for bouncing laser bea ms or bea ms which had not been co mpletely

Fi g ure 1 8. Observation of ato m a mplification. Ato m a mplification is probed by sending an input bea m through the ato m a mplifier which is a Bose- Einstein condensate ( B E C) illu minated with laser lig ht. O n t he left side, t he i nput bea m has passed t hroug h t he co nde nsate wit hout a mpli fi- catio n. So me 20 ms later, a s hado w picture is take n of t he co nde nsate a nd t he i nput ato ms. W he n t he a m pli ficatio n process was activate d by ill u mi nati ng t he co n de nsate wit h laser lig ht, t he o ut p ut p uls e c o nt ai n e d m a ny m or e at o ms t h a n t h e i n p ut p uls e – ty pi c al a m pli fi c ati o n f a ct ors w er e b e- t w e e n 1 0 a n d 1 0 0. T h e fi el d of vi e w is 1. 9 2. 6 m m 2 .

1 4 5 s witc hed off, but we fou nd not hi ng. I ncreasi ngly, we co nsidered t hat t he ob- served pheno menon was genuine and not due to so me experi mental artifact. K no wi ng t hat t he co nde nsate was pe ncil-s haped, t he idea of laser e missio n alo ng t he lo ng co nde nsate axis ca me up, a nd t his was already very close. We decided to stop t he ge neral discussio n a nd co nti nue taki ng data; t he mac hi ne was r u n ni ng well a n d we wa nte d to take a dva ntage of it. So so me st u de nts, i n- cluding Shin Inouye and Ananth Chikkatur, characterized the pheno menon, w hile Da n Sta mper- Kur n a nd I we nt to a black board a nd tried to figure out w hat was goi ng o n. Wit hi n t he next ho ur, we develo pe d t he correct se mi-clas- sical descri ptio n of s u perra dia nce i n a co n de nsate. I n t he lab, t he pre dicte d stro ng depe nde nce o n laser polarizatio n was veri fied. A fe w mo nt hs later we realized ho w we could use the superradiant a mplification mechanis m to build a phase-coherent ato m a mplifier. Ho wever, the labs were undergoing co m- plete re novatio n at t his poi nt a n d we ha d to wait u ntil t he mac hi ne was r u n- ning again before the phase-coherent a mplification was i mple mented. The de monstration of an ato m a mplifier added a ne w ele ment to ato m op- tics. I n a d ditio n to passive ele me nts like bea m s plitters, le nses a n d mirrors, t here is no w a n active ato m-optical ele me nt. Co here nt matter wave a mpli fiers may i mprove the perfor mance of ato m interfero meters by making up for losses i nside t he device or by a mplifyi ng t he output sig nal. Ato m i nterfero- meters are alrea dy use d as precise gravity a n d r otati o n se ns ors.

Observatio n of Vortex Lattices i n Bose- Ei nstei n Co nde nsates Quantu m mechanics and the wave nature of matter have subtle manifesta- tions when particles have angular mo mentu m or, more generally, when quan- tu m syste ms are rotating. When a quantu m- mechanical particle moves in a circle t he circ u mfere nce of t he orbit has to be a n i nteger m ulti ple of t he de Broglie wavele ngt h. T his qua ntizatio n rule leads to t he Bo hr model a nd t he discrete e nergy levels of t he hy droge n ato m. For a rotati ng s u per fl ui d, it lea ds to qua ntized vortices [109]. If o ne spi ns a nor mal liquid i n a bucket, t he fl ui d will fi nally rotate as a rigi d bo dy w here t he velocity s moot hly i ncreases fro m t he ce nter to t he e dge (Fig. 19, left). Ho wever, t his s moot h variatio n is i mpossible for particles i n a si ngle qua ntu m state. To ful fill t he above- me n- tio ned qua ntizatio n rule, t he flo w field has to develop si ngular regio ns w here the nu mber of de Broglie wavelengths on a closed path ju mps up by one. One possibility would be a radially sy m metric flo w field wit h co nce ntric ri ngs. Bet wee n adjace nt ri ngs, t he nu mber of de Broglie wavele ngt hs o n a circu m- fere nce would c ha nge by o ne. H o w ev er, t h e e n er g eti c ally m ost f av or a bl e c o n fi g ur ati o n is a c hi ev e d w h e n t h e si n g ul ariti es i n t h e v el o city fi el d ar e n ot distri b ut e d o n cyli n dri c al s h ells, b ut o n li nes. T his c orres p o n ds t o a n array of v ortices. I n c o ntrast t o classical vortices suc h as i n tor nados or i n a flus hi ng toilet, t he vortices i n a Bose- Einstein condensate are quantized: when an ato m goes around the vortex core, its quantu m mechanical phase changes by exactly 2 π . Suc h qua ntized vortices play a key role i n super fluidity a nd superco nductivity. I n superco n- d uctors, mag netic fl ux li nes arra nge t he mselves i n reg ular lattices t hat have

1 4 6 Fig ure 1 9. Co mparison of the flo w fields of rotating nor mal liquids and super fluids. A nor mal fluid u ndergoes rigid body rotatio n, w hereas a super fluid develops a n array of qua ntized vortices.

bee n directly i mage d. I n s u per fl ui ds, previo us direct observatio ns of vortices ha d bee n li mite d to s mall arrays ( u p to eleve n vortices), bot h i n liq ui d 4 H e [110] a nd i n rotati ng gaseous Bose- Ei nstei n co nde nsates ( B E C) by a group i n P aris [ 1 1 1 ]. In 2001, our group observed the for mation of highly-ordered vortex lat- tices in a rotating Bose-condensed gas [112]. They were produced by spin- ni ng laser bea ms arou nd t he co nde nsate, t hus setti ng it i nto rotatio n. T he condensate then exhibited a re markable manifestation of quantu m mechan- ics at a macrosco pic level. T he rotati ng gas clo u d was ri d dle d wit h more t ha n o ne hu ndred vortices. Si nce t he vortex cores were s maller t ha n t he optical resol utio n, t he gas was allo we d to ballistically ex pa n d after t he mag netic tra p was s witc he d off. T his mag ni fie d t he s patial str uct ures t we nty-fol d. A s ha do w pict ure of t hese clo u ds s ho we d little brig ht s pots w here t he lig ht pe netrate d t hroug h t he e mpty vortex cores like troug h tu n nels (Fig. 20 s ho ws a negative i m a g e ). A striki ng feat ure of t he o bserve d v ortex lattices is t he extre me reg ularity, fr e e of a ny m aj or dist orti o ns, ev e n n e ar t h e b o u n d ar y. S u c h “ A bri k os ov” l at- tices were first predicted for qua ntized mag netic flux li nes i n type-II super- conductors. Ho wever, nature is not al ways perfect: so me of the i mages s ho we d distortio ns or defects of t he vortex lattices; t wo exa m ples are s ho w n i n Fig. 21. T he p hysics of vortices is very ric h. S ubseq ue nt work by my gro u p a n d ot hers has starte d to a d dress t he dy na mics a n d no n-eq uilibri u m pro perties of vortex structures. Ho w are vortices for med? Ho w do t hey decay? Are t he vor- tices straig ht or be nt? Suc h experi me nts ca n be directly co mpared wit h first- pri n ci pl e c al c ul ati o ns, w hi c h ar e p ossi bl e f or s u c h a dil ut e syst e m. T his i nt er- play bet ween theory and experi ment may lead to a better understanding of super fluidity and macroscopic quantu m pheno mena.

1 4 7 Fig ure 2 0. Observatio n of vortex lattices i n rotati ng Bose- Ei nstei n co nde nsates. T he exa mples s ho w n co ntai n ( A) 16 ( B) 32 ( C) 80 a nd ( D) 130 vortices as t he speed of rotatio n was i ncreased. T h e v orti c es h av e “ cr yst alliz e d” i n a tri a n g ul ar p att er n. T h e di a m et er of t h e cl o u d i n ( D ) w as 1 m m after ballistic expa nsio n, w hic h represe nts a mag ni ficatio n of t we nty. ( Repri nted wit h per- missio n fro m ref. [112]. Copyrig ht 2001 A merica n Associatio n for t he Adva nce me nt of Scie nce.)

Fi g ure 2 1. Vortex lattices wit h defects. I n t he left i mage, t he lattice has a disl ocati o n near t he ce n- ter of the condensate. In the right one, there is a defect re miniscent of a grain boundary. ( Reprinted with per mission fro m ref. [112]. Copyright 2001 A merican Association for the Adva nce me nt of Scie nce.)

1 4 8 OUTL O OK T he rapid pace of develop me nts i n ato mic B E C duri ng t he last fe w years has take n t he co m mu nity by surprise. After decades of a n elusive searc h, nobody expected t hat co nde nsates would be so robust a nd relatively easy to ma nipu- late. Furt her, nobody i magi ned t hat suc h a si mple syste m would pose so ma ny c halle nges, not o nly to experi me ntalists, but also to our fu nda me ntal u nder- sta n di ng of p hysics. T he list of f ut ure c halle nges, bot h for t heorists a n d ex- peri me ntalists, is lo ng a n d i ncl u des t he ex ploratio n of s u per fl ui dity a n d sec- ond sound in Bose gases, the physics of correlations and non-classical wavefu nctio ns (p he no me na beyo nd t he Gross-Pitaevskii equatio n), t he study of quantu m-degenerate molecules and Fer mi gases, the develop ment of prac- tical “ hig h- po wer” ato m lasers, a n d t heir a p plicatio n i n ato m o ptics a n d pre- cisio n measure me nts. T hese scie nti fic goals are closely i nter wove n wit h tec h- nological advances to produce new single- or multi-species quantu m- dege nerate syste ms a nd novel ways of ma nipulatio n, suc h as usi ng microtraps a nd ato m c hips. T here is every i ndicatio n for more excite me nt to co me! Work o n B E C at MI T has bee n a tre me ndous tea m effort, a nd I a m grateful to the past and present collaborators who have shared both the excite ment and the hard work: J. R. Abo-Shaeer, M. R. Andre ws, M. Boyd, G. Ca mpbell, A. P. C hi k k at ur, J.- K. C hi n, K. B. D avis, K. Di e c k m a n n, D. S. D urf e e, A. G örlitz, S. G u pt a, T. L. G ust avs o n, Z. H a dzi b a bi c, S. I n o uy e, M. A. J off e, D. Ki el pi ns ki, M. K ö hl, C. E. K u kl e wi cz, A. E. L e a n h ar dt, R. F. L ö w, A. M arti n, M.- O. M e w es, H.-J. Mi es n er, R. O n ofri o, T. Pf a u, D. E. Prit c h ar d, C. R a m a n, D. S c h n e bl e, C. Sc hu nck, Y.-I. S hi n, D. M. Sta mper- Kur n, C. A. Sta n, J. Ste nger, E. Streed, Y. Torii, C. G. To w nse nd, N.J. va n Drute n, J. M. Vogels, K. Xu, M. W. Z wierlei n, and many MI T undergraduate students. Exe mplary ad ministrative support has bee n provided by Carol Costa for more t ha n t welve years. Figure 22 s ho ws the tea m in Nove mber 2001. Special thanks go to Dan Kleppner and To m Greytak for inspiration and constant encourage ment. The author also ac- k no wledges t he fruitful i nteractio ns wit h colleagues all over t he world w ho have co ntrib ute d to t his ric h a n d exciti ng fiel d. So me of t hese colleag ues are depicted i n Fig. 23, w hic h is a group p hoto of t he lecturers at t he Vare n na su m mer sc hool o n B E C i n 1998. I n particular, t he yearlo ng co mpetitio n wit h t he group at Boulder led by Eric Cor nell a nd Carl Wie ma n i nspired t he best fro m me and my tea m and, despite tight co mpetition, there has been ge- nui ne collegiality a nd frie nds hip. I wa nt to t ha nk t he Of fice of Naval Re- searc h, t he Natio nal Scie nce Fou ndatio n, t he Ar my Researc h Of fice, t he Joi nt Services Electronics Progra m, N AS A and the David and Lucile Packard Fou ndatio n for t heir e ncourage me nt a nd fi na ncial support of t his work.

1 4 9 Fig ure 2 2. The author with his tea m in Nove mber 2001. Front ro w, fro m left to right: Z. Ha dzibabic, K. X u, S. G u pta, E. Tsikata, Y.-I. S hi n. Mi d dle ro w: A. P. C hikkat ur, J.- K. C hi n, D. E. Prit c h ar d, W. K., G. C a m p b ell, A. E. L e a n h ar dt, M. B oy d. B a c k r o w: J. R. A b o- S h a e er, D. S c h n e bl e, J. M. V o g els, K. Di e c k m a n n, C. A. St a n, Y. T orii, E. Str e e d.

Fig ure 2 3. Lecturers, se minar speakers and directors at the su m mer school on “ Bose- Einstein Co nde nsatio n i n Ato mic Gases” i n Vare n na, July 7–17, 1998. Fro nt ro w: Jea n Dalibard, Gugliel mo Tino, Fernando Sols, Kris Hel merson. Back ro w: Sandro Stringari, Carl Wie man, Alexander F ett er, Til m a n Essli n g er, M assi m o I n g us ci o, Willi a m P hilli ps, D a ni el H ei nz e n, P et er F e di c h ev, L ev Pit a evs kii, W. K., All a n Grif fi n, K eit h B ur n ett, D a ni el Kl e p p n er, Al ai n As p e ct, E n ni o Ari m o n d o, T heodor Hä nsc h, Eric Cor nell.

1 5 0 REFERE NCES

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