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.