Bose-Einstein Condensation and the Atom Laser

WHEN ATOMS BEHAVE AS WAVES: BOSE-EINSTEIN CONDENSATION AND THE ATOM LASER Nobel Lecture, December 8, 2001 by WOLFGANG KETTERLE* Department of Physics, MIT-Harvard Center for Ultracold Atoms, and Re- search Laboratory of Electronics, Massachusetts Institute of Technology, Cam- bridge, Massachusetts, 02139, USA. INTRODUCTION The lure of lower temperatures has attracted physicists for the past century, and with each advance towards absolute zero, new and rich physics has emerged. Laypeople may wonder why “freezing cold” is not cold enough. But imagine how many aspects of nature we would miss if we lived on the surface of the sun. Without inventing refrigerators, we would only know gaseous mat- ter and never observe liquids or solids, and miss the beauty of snowflakes. Cooling to normal earthly temperatures reveals these dramatically different states of matter, but this is only the beginning: many more states appear with further cooling. The approach into the kelvin range was rewarded with the discovery of superconductivity in 1911 and of superfluidity in helium-4 in 1938. Cooling into the millikelvin regime revealed the superfluidity of helium-3 in 1972. The advent of laser cooling in the 1980s opened up a new approach to ultralow temperature physics. Microkelvin samples of dilute atom clouds were generated and used for precision measurements and studies of ultracold collisions. Nanokelvin temperatures were necessary to ex- plore quantum-degenerate gases, such as Bose-Einstein condensates first realized in 1995. Each of these achievements in cooling has been a major ad- vance, and recognized with a Nobel prize. This paper describes the discovery and study of Bose-Einstein condensates (BEC) in atomic gases from my personal perspective. Since 1995, this field has grown explosively, drawing researchers from the communities of atomic physics, quantum optics, and condensed matter physics. The trapped ultra- cold vapor has emerged as a new quantum system that is unique in the preci- sion and flexibility with which it can be controlled and manipulated. At least thirty groups have now created condensates, and the publication rate on Bose-Einstein condensation has soared following the discovery of the gaseous condensates in 1995 (see Fig. 1). 118 * URL: http://cua.mit.edu/ketterle_group/ The phenomenon 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 spectrum [2]. When a gas of bosonic atoms is cooled below a critical temperature Tc , a large fraction of the atoms condenses in the lowest quantum state. Atoms at temperature T and with mass m can be regarded as quantum-mechanical wavepackets that have a spatial extent on the order of a thermal de Broglie wavelength λdB = (2π�2/mkBT) 1/2. The value of λdB is the position uncertainty associated with the thermal momentum distribution and increases with decreasing tempera- ture. When atoms are cooled to the point where λdB is comparable to the in- teratomic separation, the atomic wavepackets “overlap” and the gas starts to become a “quantum soup” of indistinguishable particles. Bosonic atoms un- dergo a quantum-mechanical phase transition and form a Bose-Einstein con- densate (Fig. 2), a cloud of atoms all occupying the same quantum mechan- ical state at a precise temperature (which, for an ideal gas, is related to the peak atomic density n by nλd 3 B = 2.612). If the atoms are fermions, cooling gradually brings the gas closer to being a “Fermi sea” in which exactly one atom occupies each low-energy state. Creating a BEC is thus simple in principle: make a gas extremely cold until the atomic wave packets start to overlap! However, in most cases quantum de- generacy would simply be pre-empted by the more familiar transitions to a liquid or solid. This more conventional condensation into a liquid and solid can only be avoided at extremely low densities, about a hundred thousandth the density of normal air. Under those conditions, the formation time of mo- lecules or clusters by three-body collisions (which is proportional to the in- verse density squared) is stretched to seconds or minutes. Since the rate of bi- nary elastic collisions drops only proportional to the density, these collisions are much more frequent. Therefore, thermal equilibrium of the translation- 119 Figure 1. Annual number of published papers, which have the words “Bose” and “Einstein” in their title, abstracts or keywords. The data were obtained by searching the ISI (Institute for Scientific Information) database. al degree of freedom of the atomic gas is reached much faster than chemical equilibrium, and quantum degeneracy can be achieved in an effectively metastable gas phase. However, such ultralow density lowers the temperature requirement for quantum degeneracy into the nano- to microkelvin range. The achievement of Bose-Einstein condensation required first the identifi- cation of an atomic system which would stay gaseous all the way to the BEC transition, and second, the development of cooling and trapping techniques to reach the required regime of temperature and density. Even around 1990, it was not certain that nature would provide us with such a system. Indeed, many people doubted that BEC could ever be achieved, and it was regarded as an elusive goal. Many believed that pursuing BEC would result in new and interesting physics, but whenever one would come close, some new pheno- menon or technical limitation would show up. A news article in 1994 quoted Steve Chu: “I am betting on nature to hide Bose condensation from us. The last 15 years she’s been doing a great job” [3]. In brief, the conditions for BEC in alkali gases are reached by combining two cooling methods. Laser cooling is used to precool the gas. The principle of laser cooling is that scattered photons are on average blue-shifted with re- spect to the incident laser beam. As a result, the scattered light carries away more energy than has been absorbed by the atoms, resulting in net cooling. Blue-shifts are caused by Doppler shifts or ac Stark shifts. The different laser cooling schemes are described in the 1997 Nobel lectures in physics [4–6]. After the precooling, the atoms are cold enough to be confined in a magne- tic trap. Wall-free confinement is necessary, otherwise the atoms would stick to the surface of the container. It is noteworthy that similar magnetic con- finement is also used for plasmas which are too hot for any material con- tainer. After magnetically trapping the atoms, forced evaporative cooling is applied as the second cooling stage [7–9]. In this scheme, the trap depth is reduced, allowing the most energetic atoms to escape while the remainder rethermalize at steadily lower temperatures. Most BEC experiments reach quantum degeneracy between 500 nK and 2 µK, at densities between 1014 and 1015 cm-3. The largest condensates are of 100 million atoms for sodium, and a billion for hydrogen; the smallest are just a few hundred atoms. Depending on the magnetic trap, the shape of the condensate is either approximately round, with a diameter of 10 to 50 µm, or cigar-shaped with about 15 µm in diameter and 300 µm in length. The full cooling cycle that produces a con- densate may take from a few seconds to as long as several minutes. After this short overview, I want to provide the historical context for the search for BEC and then describe the developments which led to the obser- vation of BEC in sodium at MIT. Finally, some examples will illustrate the 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 comprehensive review papers [8, 10–12]. 120 BEC AND CONDENSED-MATTER PHYSICS Bose-Einstein condensation is one of the most intriguing phenomena pre- dicted by quantum statistical mechanics. The history of the theory of BEC is very interesting, and is nicely described in the biographies of Einstein [13] and London [14] and reviewed by Griffin [15]. For instance, Einstein made his predictions before quantum theory had been fully developed, and before the differences between bosons and fermions had been revealed [16]. After Einstein, important contributions were made by, most notably, London, Landau, Tisza, Bogoliubov, Penrose, Onsager, Feynman, Lee, Yang, Huang, Beliaev and Pitaevskii. An important issue has always been the relationship be- tween BEC and superfluidity in liquid helium, an issue that was highly con- troversial between London and Landau (see ref. [14]). Works by Bogoliubov, Beliaev, Griffin and others showed that Bose-Einstein condensation gives the microscopic picture behind Landau’s “quantum hydrodynamics.” BEC is closely related to superconductivity, which can be described as being due to Bose-Einstein condensation of Cooper pairs. Thus Bose-Einstein condensa- tion is at the heart of several macroscopic quantum phenomena. BEC is unique in that it is a purely quantum-statistical phase transition, i.e., it occurs even in the absence of interactions. Einstein described the transition as condensation “without attractive forces” [16]. This makes BEC an impor- tant paradigm of statistical mechanics, which has been discussed in a variety of contexts in condensed-matter, nuclear, particle and astrophysics [17]. On the other hand, real-life particles will always interact, and even the weakly- interacting Bose gas behaves qualitatively differently from the ideal Bose gas 121 Figure 2. Criterion for Bose- Einstein condensation. At high temperatures, a weakly interact- ing gas can be treated as a sys- tem of “billiard balls.” In a sim- plified quantum description, the atoms can be regarded as wavepackets with an extension of their de Broglie wavelength λdB. At the BEC transition tem- perature, λdB becomes compar- able to the distance between atoms, and a Bose condensate forms. As the temperature ap- proaches zero, the thermal cloud disappears, leaving a pure Bose condensate. [18]. It was believed for quite some time that interactions would always lead to “ordinary” condensation (into a solid) before Bose-Einstein condensation would happen. Liquid helium was the only counter-example, where the light mass and concomitant large zero-point kinetic energy prevents solidification even at zero kelvin. Erwin Schrödinger wrote in 1952 in a textbook on ther- modynamics about BEC: “The densities are so high and the temperatures so low – those required to exhibit a noticeable departure [from classical stati- stics] – that the van der Waals corrections are bound to coalesce with the pos- sible effects of degeneration, and there is little prospect of ever being able to separate the two kinds of effect” [19]. What he didn’t consider were dilute sys- tems in a metastable gaseous phase! The quest to realize BEC in a dilute, weakly interacting gas was pursued in at least three different directions: liquid helium, excitons and atomic gases. Experimental [20, 21] and theoretical work [22] showed that the onset of su- perfluidity for liquid helium in Vycor has features of dilute-gas Bose-Einstein condensation. At sufficiently low coverage, the helium adsorbed on the po- rous sponge-like glass behaved like a dilute three-dimensional gas. However, the interpretation of these results is not unambiguous [23]. Excitons, which consist of weakly-bound electron-hole pairs, are composite bosons. The physics of excitons in semiconductors is very rich and includes the formation of an electron-hole liquid and biexcitons. As nicely discussed in refs. [24, 25], there are systems where excitons form a weakly interacting gas. However, the initial evidence for Bose-Einstein condensation in Cu2O [26] was retracted [27]. Recent work in coupled quantum-well structures is very promising [28]. When excitons strongly interact with light in a cavity, they form polaritons. In such polariton systems, stimulated scattering and non- equilibrium condensates have been observed recently [29–31]. SPIN-POLARIZED HYDROGEN Dilute atomic gases are distinguished from the condensed-matter systems dis- cussed above by the absence of strong interactions. Interactions at the densi- ty of a liquid or a solid considerably modify and complicate the nature of the phase transition. Hecht[32], and Stwalley and Nosanow [33] used the quan- tum theory of corresponding states to conclude that spin-polarized hydrogen would remain gaseous down to zero temperature and should be a good can- didate to realize Bose-Einstein condensation in a dilute atomic gas. These suggestions triggered several experimental efforts, most notably by Silvera and Walraven in Amsterdam, by Greytak and Kleppner at MIT, and by others at Moscow, Turku, British Columbia, Cornell, Harvard, and Kyoto. The stabi- lization of a spin-polarized hydrogen gas [34, 35] created great excitement about the prospects of exploring quantum-degenerate gases. Experiments were first done by filling cryogenic cells with the spin-polarized gas and by compressing it, and since 1985, by magnetic trapping and evaporative cooling. BEC was finally accomplished in 1998 by Kleppner, Greytak and col- laborators [36]. See refs. [9, 37–39] and in particular ref. [40] for a full ac- 122 count of the pursuit of Bose-Einstein condensation in atomic hydrogen. Evi- dence for a phase transition in two dimensions was reported in 1998 [41]. The work in alkali atoms is based on the work in spin-polarized hydrogen in several respects: • Studies of spin-polarized hydrogen showed that systems can remain in a metastable gaseous state close to BEC conditions. The challenge was then to find the window in density and temperature where this metastability is suf- ficient to realize BEC. • Many aspects of BEC in an inhomogeneous potential [42–44], and the the- ory of cold collision processes (see e.g. [45]) developed in the 1980s for hy- drogen could be applied directly to the alkali systems. • The technique of evaporative cooling was developed first for hydrogen [7, 46] and then used for alkali atoms. LASER COOLING Laser cooling opened a new route to ultralow temperature physics. Laser cooling experiments, with room temperature vacuum chambers and easy op- tical access, look very different from cryogenic cells with multi-layer thermal shielding around them. Also, the number of atomic species that can be studi- ed at ultralow temperatures was greatly extended from helium and hydrogen to all of the alkali atoms, metastable rare gases, several earth-alkali atoms, and others (the list of laser-cooled atomic species is still growing). A full account of the relevant laser cooling techniques and their development is given in refs. [47–49] and in the 1997 Nobel lectures of Chu, Cohen-Tannoudji and Phillips [4–6]. Some papers and proposals written in the early and mid 1980s, before and during the developments of the basic cooling and trapping techniques, listed quantum degeneracy in a gas as a visionary goal for this new emerging field [50–52]. However, major limitations of laser cooling and trapping were soon identified. Although there is no fundamental low temperature limit, the final temperature provided by polarization gradient cooling – about ten times the recoil energy – was regarded as a practical limit. Sub-recoil laser cooling tech- niques, especially in three dimensions, were harder to implement, and re- quired long cooling times. The number and density of atoms were limited by inelastic, light-induced collisions (leading to trap loss [53, 54]) and by ab- sorption of scattered laser light [55], which results in an outward radiation pressure (weakening the trapping potential and limiting the density). Furthermore, since the lowest temperatures could not be achieved at the highest densities [56–58], most trapping and cooling techniques reached a maximum phase-space density of around nλd 3 B = 10 -5; and a value of 2.612 is needed for BEC. This was the situation when the author joined the field of cold atoms in 1990. It was only more recently that major increases in phase- space density were achieved by laser cooling [59–61], but so far laser cooling by itself has not been able to reach BEC. 123 THE EFFORT AT MIT 1990–1996 Improving laser cooling When I teamed up with Dave Pritchard at MIT in 1990 as a postdoc, the initial goal was to build an intense source of cold atoms to study cold collisions and pure long-range molecules. However, Dave and I frequently talked about the limitations in density and temperature of the current techniques and tried to develop ideas on how to get around them. One limitation of magnetic traps is that they can hold atoms only in weak-field seeking hyperfine states. Therefore, a collision between two trapped atoms can lead to a spinflip, and the Zeeman energy is converted into kinetic energy (dipolar relaxation). This process has been a major limitation to the experiments in atomic hydrogen. First, we asked ourselves if the inclusion of electric and gravitational fields would allow the stable confinement of atoms in their lowest hyperfine states- – but the answer was negative [62]. One loophole was time-dependent mag- netic fields, and building on an earlier proposal [63], I designed an experi- ment to confine sodium atoms with ac magnetic fields which looked feasible. However, we learnt that Eric Cornell at Boulder had developed a similar idea and experimentally implemented it [64] – so we left the idea on the drawing board. It wasn’t the last time that Eric and I would develop similar ideas in- dependently and almost simultaneously! Trapping atoms in the lowest hyperfine state was not necessary to accom- plish BEC. Already in 1986, Pritchard correctly estimated the rate constants of elastic and inelastic collisions for alkali atoms [52]. From these estimates one could easily predict that for alkali atoms, in contrast to hydrogen, the so- called good collisions (elastic collisions necessary for the evaporation pro- cess) would clearly dominate over the so-called bad collisions (inelastic two- and three-body collisions); therefore, evaporative cooling in alkalis would probably not be limited by intrinsic loss and heating processes. However, there was pessimism [65] and skepticism, and the above-mentioned experi- mental [64] and theoretical [62] work on traps for strong-field seeking atoms has to be seen in this context. In those years, there were some suggestions that time-dependent potentials could lead to substantial cooling, but we showed that this was not possible [66]. Real cooling needs an open system which allows entropy to be removed from the system – in laser cooling in the form of scattered photons, in evapo- rative cooling in the form of discarded atoms. Dave and I brainstormed about novel laser cooling schemes. In 1991, at the Varenna summer school, Dave presented a new three-level cooling scheme [67]. Inspired by these ideas, I developed a scheme using Raman transitions. Replacing the six laser beams in optical molasses by counterpropagating beams driving the Doppler-sensi- tive Raman transition, we hoped to realize Doppler molasses with a linewidth that was proportional to the optical pumping rate, and therefore adjustable. We had started setting up radio-frequency (rf) electronics and magnetic shields for Raman cooling when we heard that Mark Kasevich and Steve Chu were working on Raman cooling using laser pulses [68]. For this reason, and also because around the same time we had developed the idea for the Dark 124 SPOT (spontaneous force optical tray; see later in this section), trap, we stopped our work on Raman cooling. Our experimental work in those years focused first on generating a large flux of slow atoms. In my first months at MIT when I overlapped with Kris Helmerson and Min Xiao, we built a sodium vapor cell magneto-optical trap