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arXiv:2510.03378 · Natural Science Review

A century of the Bose–Einstein condensation concept and half a century of the JINR experiments for observation of condensate in superfluid 4He (He II)

Valentin Anatol'evich Zagrebnov

Published Nov 7, 2025• 0 citations
arXivHTMLPDF

Abstract

This short review is devoted to the celebration of two major events in quantum physics. The first one is the birth of the concept of Bose–Einstein condensation (1925) and the second is the experimental proof that it does exist and appears in liquid 4He simultaneously with superfluidity below the λ-point (1975).Both of these events are tightly related to the Bogoliubov theory of superfluidity (1947). The existence of condensate in the system of interacting bosons is the key ansatz of this theory. Therefore, the experiments started at JINR-Dubna in 1975 confirmed this prediction of the Bogoliubov theory that superfluidity of liquid 4He (He II) should emerge at the same time as the Bose–Einstein condensation. Corrected: 13 November 2025 (the captions to Figures 1 and 2 were changed)26 November 2025 (changes were made in formulas (53) and (55))

DOI
10.54546/naturalscirev.100504

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The nature of superfluidity and Bose-Einstein condensation: From liquid 4He to dilute ultracold atomic gases (Review Article)

S. I. Vilchynskyy, A. I. Yakimenko, Karyna Isaieva +1 more

We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.

Low Temperature Physics•Sep 1, 2013•14 citations

New light on the intriguing history of superfluidity in liquid4He

Allan Griffin

Surprisingly, it was 30 years after the first liquefaction of (4)He in 1908 that the discovery that liquid (4)He is not just a 'cold' liquid was made. Below T = 2.18 K, it is a 'quantum' liquid which exhibits spectacular macroscopic quantum behaviour that can be seen with the naked eye. Since the observation of superfluidity in liquid (4)He is one of the greatest discoveries in modern physics, we present a day-to-day chronology of the tangled events which preceded the seminal discovery of zero viscosity in 1938 by Kapitza in Moscow and by Allen and Misener in Cambridge. On the theory side, London argued in 1938 that the microscopic basis for this new superfluid phase was the forgotten phenomenon of Bose-Einstein condensation (BEC) first suggested by Einstein in 1925. In 1941, Landau developed a very successful theory of superfluid (4)He, but it was not anchored in a microscopic theory of interacting atoms. It took another 20 years for theorists to unify the two seemingly different theories of Landau and London. Experiments on trapped superfluid atomic gases since 1995 have shone new light on superfluid (4)He. In the mid-1930s, London had emphasized that superconductivity in metals and superfluidity in liquid (4)He were similar. Experiments on trapped two-component Fermi gases in the last five years have shown that a Bose condensate is indeed the basis of both of these superfluid phases. This confirms the now famous Bardeen-Cooper-Schrieffer-BEC crossover scenario developed for superfluidity by Leggett and Nozières in the early 1980s but largely ignored until a few years ago. The study of superfluid (4)He will increasingly overlap with strongly interacting dilute quantum gases, perhaps opening up a new era of research on this most amazing liquid.

Journal of Physics Condensed Matter•Mar 31, 2009•26 citations

Superfluidity with and without a Condensate in Interacting Bose Fluids

Anna Minguzzi, N. H. March, Monica Tosi

Motivated by recent experiments on alkali gases in atom traps, a largely pedagogical account is given of the implications of the existence of a single-particle Bose-Einstein condensate for the phenomenon of superfluidity. The first conclusion is that, for alkalis in traps at the lowest temperatures, Bose-Einstein condensation coexists with superfluidity. Both experimental evidence and basic microscopic theory are reviewed in this context, with superfluidity in finite systems, quantized vortices and the threshold for breakdown of superfluidity all being referred to. The contrast between liquid 4He below the λ point and the alkali atom gases is then emphasized. Both exhibit superfluidity, but the manifestations of a Bose-Einstein condensate are quite different. For the atomic vapours, near to 100% of the atoms are condensed at the lowest temperatures, whereas from (i) neutron scattering and (ii) computer simulations in liquid 4He present evidence is that 7% is the condensate fraction. This leads finally into a brief discussion of superfluidity without a condensate, with specific reference to the two-dimensional Bose Coulomb gas. The main conclusion is that Bose-Einstein condensation and superfluidity are distinct consequences of deeper topological properties of the many-body wavefunction.

Physics and Chemistry of Liquids•Aug 1, 2003•3 citations

The first BEC conference in Levico in 1993

Allan Griffin

In opening the Levico BEC 2003 meeting, the directors thought it would be useful to say a little about the first BEC workshop held in the same hotel, in the same lecture room, almost exactly ten years ago. I want to give you a personal view of what led up to the historic BEC 93 workshop at Levico and contrast the situation then with the fantastic developments which have occurred over the last decade. BEC 93 was organized by Griffin, Snoke, Stringari, Laloe and Baym. The purpose of the workshop was to bring together people working in different fields of physics but with a common interest in the phenomenon of Bose–Einstein condensation. It is useful to briefly recall the history of BEC studies before the BEC 93 workshop, to understand why it was organized. In 1938 Fritz London suggested that the mysterious phase transition which occurred in liquid 4 He at T = 2.17 K might be related to the formation of a Bose–Einstein condensate (BEC) of 4 He atoms, a phenomenon first predicted by Einstein in 1925 in an ideal gas. After Tisza suggested that the spectacular superfluid effects discovered in 1938 were related to the motion of the Bose condensate, BEC became a hot topic in the years before World War II. In 1941, Landau developed a very successful two-fluid theory of superfluid 4 He, based on the relatively new concept of elementary excitations of a many-body system to describe the 'normal fluid' component. The Landau picture was spectacularly successful in explaining various thermodynamic and transport properties, albeit in a phenomenological manner. However, Landau's magnificent theory made no use of the concept of BEC, or even the fact that the 4 He atoms obeyed Bose statistics. Interest in BEC faded from low temperature conferences in the period 1945–1955, in spite of Bogoliubov's seminal work in 1947 showing that a dilute weakly interacting Bose gas still exhibited BEC. Quite separate from the study of BEC in superfluid 4 He, interest in finding a BEC in a dilute, weakly interacting Bose gas started to develop in the early 1960s. The first system was optically excited excitons in semiconductors (electron-hole pairs, with zero total spin, played the role of the bosons). However, the short lifetime of the excitons in most semiconductors frustrated the early experiments. A second major effort developed in the 1980s with attempts to produce an atomic BEC in spin-polarized hydrogen gas. The initial experiments were very promising, but various problems ultimately stopped people from ever producing (until 1998) high enough densities needed for BEC. However, this work revived interest in the theory of a dilute, weakly interacting Bose gas, and also led to several workshops on 'spin-polarized' quantum gases in the 1980s in which BEC was a major topic. The preceding summary sets the stage for why BEC 93 was organized, namely, to bring together people (both theorists and experimentalists!) interested in BEC in quite different systems, for encouragement as well as stimulation. The topic was largely ignored in the large international low temperature conferences. The organizers were mainly from the condensed matter and low temperature physics communities. Fortunately Franck Laloe was involved, and he was aware of the attempts to produce a BEC in trapped alkali gases using the novel technique of laser-cooling. The titles of the review talks given at BEC 93 show that the popular Bose systems in 1993 were liquid 4 He, excitons, spin-polarized hydrogen and small Cooper pairs in high-temperature superconductors. Work on laser-cooled alkali gases was reviewed by Yvan Castin, but people seemed pessimistic at the time about producing a stable BEC in these very dilute systems in the near future. We also had several excellent talks about Bose condensates involving mesons, as well as Cooper pairing in nuclei. The main reason for this was that crucial financial support for BEC 93 came from the newly formed ECT* Institute in Trento, thanks to Stringari. As a result, several theorists interested in condensates in nuclear and high energy physics were incorporated into the schedule of BEC 93. To my surprise, their talks, relating to Bose condensates in fairly exotic settings, fitted in very well with the other speakers. It was decided to hold BEC 93 in Levico-Terme at the Grand Hotel Bellavista. Stringari scouted many hotels in the area around Trento and Sandro clearly chose wisely, since we returned ten years later for Levico BEC 2003. Because of the interdisciplinary quality of the BEC 93 workshop and the slightly controversial nature of BEC in real systems, however, we found it very difficult to obtain funding for BEC 93. Many of the funding agencies turned down requests for funding so the BEC 93 workshop was funded by the ECT*, a small grant from CNRS in France, a payment from Cambridge University Press (in lieu of royalties for the conference proceedings) and registration fees. We were therefore overjoyed when we received some late applications from people who said they would pay the full registration fee. One of these was Eric Cornell, a young AMO physicist from 'someplace' called JILA in Boulder, Colorado. We gladly accepted his money and his participation. The opening session of BEC 93 in the Grand Hotel Bellavista was a very historic occasion, since almost all the people in the world interested in BEC were present. The excellent review talks and energetic discussions quickly made us realize that the workshop was going to be a success. People heard about the search for BEC in systems quite different from what they were familiar with. It probably was the first time that the CMP and AMO communities were in the same room together. Eric Cornell later told me that it was the first meeting where he met a lot of well known CMP theorists, and heard them arguing about the role of interactions, broken symmetry and order parameters, Goldstone modes, phase rigidity, etc. It dawned on Eric that the physics of a Bose condensate had not been completely settled in Einstein's 1925 paper! One of the star invited speakers was Nozières but at the last moment, he could not attend because of family reasons. However, he gave a lecture a month later at the 60th birthday party for Cohen-Tannoudji in Paris, based on his planned talk for BEC 93. I convinced him that his lecture 'belonged' to BEC 93 so he wrote it up for the BEC book we were preparing. His insightful article became one of the most quoted articles in the book, and many of his phrases (fragmentation of the condensate, phase locking, enemies of Bose–Einstein condensation, etc.) have entered our language. At the conference dinner, we gave out small prizes to some of the best speakers and participants who had made a significant contribution. One of the themes of BEC 93 was to pin down what an unambiguous signature of a Bose condensate was, and the term 'smoking gun' became very popular in discussions. Shlyapnikov received the coveted 'Smoking Gun' award, the prize being a package of cigarettes. The 'Prix d'Or' (1000 Lire), for giving the most convincing evidence for a Bose condensate, was awarded to Wolfe for his group's work on exciton gases. Some years later, in 1999, further work by his group at Urbana showed that an unexpected rapid exciton decay process had not been included in the original data analysis. As a result, the exciton densities had been over-estimated and they had not crossed into the BEC region. Shortly after, I received a letter from Wolfe telling me about the new results, and also the original 1000 Lire banknote he had received as a prize at BEC 93. It made me proud having colleagues like this. Brown, who argued that kaon condensates played a crucial role in the collapse of large stars, received the very special 'Smoking Universe' award. He gave the most impressive 'thank you' speech, worthy of the Academy Awards. At the end of BEC 93, we had an open discussion about whether we should organize another BEC workshop two years later, in 1995. Many people felt that, while BEC 93 had been very stimulating, there probably would not be enough progress to have another BEC meeting 'so soon', but a committee was set up to monitor developments. Walraven took the initiative to organize BEC 95, which was held in Mt St Odile near Strasbourg in France, in June 1995. As luck would have it, a few weeks before BEC 95 convened, rumours circulated that the JILA group at Boulder had clear evidence for a Bose condensate in a trapped gas of 87 Rb atoms. When Eric arrived in Mt St Odile from a meeting in Capri and presented the JILA data 'hot off the press', we all gave him a standing ovation. The earth had moved and BEC was about to move to centre stage. Another piece of luck was that our BEC 93 book ( Bose–Einstein Condensation 1995 ed A Griffin, D W Snoke and S Stringari (Cambridge: Cambridge University Press)) finally appeared in March 1995. The discovery of BEC in atomic gases a few months later made the book a modest 'bestseller' and it was quickly re-issued as a paperback (almost unheard of for this type of conference proceedings). Several people later congratulated us on producing such an excellent book on BEC so quickly after the discovery in June 1995! The BEC book (often called the 'Green Book') did fill a vacuum in the early days, providing carefully written reviews about many aspects of BEC. Several of the articles were well ahead of their time, such as the discussion of the BCS–BEC crossover in Fermi gases by Randeria. We are only now seeing a lot of references to his review article, as the search for BCS pairing in trapped Fermi gases has developed over the last year. Probably over half of all publications in the area of BEC and ultracold quantum gases since 1995 have made one or more references to the Green Book. Beginning with BEC 95, these biennial meetings have now become a regular affair, generously financed and sponsored by the European Science Foundation (ESF). BEC 99, 2001 and 2003 have all been held in San Feliu de Guixols, in Spain. Since BEC 95, these workshops have been dominated by people working on trapped atomic gases, for obvious reasons. However, it is nice to see that work has picked up recently in the search for BEC in exciton gases (especially in quantum wells), and the study of trapped Fermi gases has stimulated new connections with people working in nuclear physics as well as highly correlated electron systems. So one can see that the exciting interdisciplinary atmosphere of BEC 93 may return in the near future. The papers given at Levico BEC 2003 already show strong evidence of this trend. In their 2001 Nobel Prize lectures, Cornell, Wieman and Ketterle all emphasized how 'surprised' they were on how rich BEC physics turned out to be. Initially, they expected that these atomic condensates would be small and somewhat delicate, certainly only of minor interest to the larger physics community. In fact, as we all know, interest in ultracold gases has exploded since 1995 like a 'Bosenova' and, like the universe, there is no sign of this expansion stopping. It is rapidly producing a whole new field of research which is an amalgamation of AMO and CMP physics. This in turn is producing a major re-organization of all major physics departments, in terms of the hiring of new faculty and resource allocations. International conferences in more traditional research areas in CMP and AMO have been trying to incorporate this growing subject, but it is probably time to start a new 'International Conference on Ultracold Quantum Gases' which is open to all. Of course, the young physicists who have organized and are the main speakers at Levico BEC 2003 illustrate this on-going revolution. I predict that Bose matter waves, atomic optics and, more generally, phenomena in ultracold quantum gases, will be the basis for all really new technology in the 21st century. I say this with confidence, since I don't see any real competition from developing technologies based on electrons (discovered about 1900) and laser beams (discovered about 1960). As with these older technologies, it will take decades to see how cold quantum gases can be used, in ways that we cannot even imagine today. A crucial reason for the exciting future of ultracold gases is based on the fact that it involves a creative interaction between two major areas of physics, CMP and AMO. Each has their own well developed paradigms for thinking about physics, and this difference surfaces in dealing with cold quantum gases. This creates a certain tension but ultimately it is the basis of a new creativity. Many CMP theorists who had previously worked in the area of quantum fluids and superconductors have entered this new field. This is shown by the recent publication of two excellent books on cold quantum gases (Pethick C and Smith H 2002 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press); Pitaevskii L and Stringari S 2003 Bose–Einstein Condensation (Oxford: Oxford University Press)), both by CMP theorists. This is easy to understand since trapped atomic gases (Bose or Fermi) are beautiful examples of interacting, highly coherent, quantum many-body systems, precisely the subject that CMP theorists have been struggling to understand since the 1950s. The new concepts and techniques needed to understand such many-body systems were developed and fought over in the period 1955–1965, when it was realized that there was more to the quantum theory of matter than solving Schrödinger's wave equation. A major contribution was made by the Landau school in Moscow. This battle of ideas was focused on the attempts to understand both superconductivity and superfluid 4 He. While the BCS theory of superconductivity in metals which appeared in 1957 clearly had the right physics to explain the key properties of superconductors, it still took some time for most theorists to really understand the BCS theory at a deeper level, in terms of broken symmetry, order parameters and Goldstone modes. The BCS theory gave CMP physics a simple microscopic model for superfluidity in a real system, in terms of the coherent motion of Cooper pairs. Very quickly, the close analogy was made between Bogoliubov's theory of a Bose-condensed gas and the BCS theory of superconductors. Strangely enough, however, it was only in the 1980s that pioneering work by Leggett, Nozières and others re-emphasized that one should think of the BCS theory as a Bose condensate of Cooper pairs. This led to an understanding of the BCS–BEC crossover, and also that the Bogoliubov theory of a weakly interacting Bose-condensed gas was 'buried' in the full BCS theory. It is fitting that, in 2003, this BCS–BEC crossover is becoming a central topic in the field of ultracold atoms. I say this because it represents a beautiful synthesis of both AMO physics (the formation of diatomic molecules using Feshbach resonances) and CMP physics (many-body effects giving rise to Cooper pairs) in a novel setting. As Levico BEC 2003 and the articles published in this special section show, we can expect more exciting advances of this kind in the near future. Acknowledgments I would like to thank the organizers of the Levico BEC 2003 workshop for inviting me to participate as a senior lecturer and also to commemorate the tenth anniversary of the first BEC workshop held in Levico-Terme. My research is funded by NSERC of Canada.

Journal of Physics B Atomic Molecular and Optical Physics•Mar 24, 2004•2 citations

A Brief History of Our Understanding of BEC: From Bose to Beliaev

Allan Griffin

We review how our current ideas about BEC developed in the early period 1925-1965, which had the specific goal of understanding superfluid $^4$He. This history is presented by commenting on the key contributions made by Einstein, Fritz London, Tisza, Landau, Bogoliubov, Oliver Penrose and Feynman. We emphasize the emergence of the concept of a macroscopic wavefunction describing the condensate. Starting with the fundamental work of Beliaev in 1957, the period 1957-1965 was a golden era for theoretical studies of interacting Bose-condensed gases. This work provided a sound conceptual basis for understanding the properties of trapped atomic gases which were discovered thirty years later.

•Jan 13, 1999•18 citations

Superfluidity of Bose—Einstein condensates in ultracold atomic gases

Qi-Zhong Zhu, Biao Wu

Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose–Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose–Einstein condensate (BEC), offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin–orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spin–orbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross–Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.

arXiv:1501.04153•Chinese Physics B•Apr 30, 2015•14 citations
This short review is devoted to the celebration of two major events in quantum physics. The first one is the birth of the concept of Bose–Einstein condensation (1925) and the second is the experimental proof that it does exist and appears in liquid 4He simultaneously with superfluidity below the λ-point (1975).Both of these events are tightly related to the Bogoliubov theory of superfluidity (1947). The existence of condensate in the system of interacting bosons is the key ansatz of this theory. Therefore, the experiments started at JINR-Dubna in 1975 confirmed this prediction of the Bogoliubov theory that superfluidity of liquid 4He (He II) should emerge at the same time as the Bose–Einstein condensation. Corrected: 13 November 2025 (the captions to Figures 1 and 2 were changed)26 November 2025 (changes were made in formulas (53) and (55))
We present a brief overview of crucial historical stages in creation of superfluidity theory and of the current state of the microscopic theory of superfluid 4He. We pay special attention to the role of Bose-Einstein condensates (BECs) in understanding of physical mechanisms of superfluidity and identification of quantum mechanical structure of 4He superfluid component below λ-point, in particular—the possibility that at least two types of condensates may appear and coexist simultaneously in superfluid 4He. In this context we discuss the properties of the binary mixtures of BECs and types of excitations, which may appear due to intercomponent interaction in such binary mixtures of condensates. We also discuss current status of investigations of persistent currents in toroidal optical traps and present an outlook of our recent findings on this subject.
Surprisingly, it was 30 years after the first liquefaction of (4)He in 1908 that the discovery that liquid (4)He is not just a 'cold' liquid was made. Below T = 2.18 K, it is a 'quantum' liquid which exhibits spectacular macroscopic quantum behaviour that can be seen with the naked eye. Since the observation of superfluidity in liquid (4)He is one of the greatest discoveries in modern physics, we present a day-to-day chronology of the tangled events which preceded the seminal discovery of zero viscosity in 1938 by Kapitza in Moscow and by Allen and Misener in Cambridge. On the theory side, London argued in 1938 that the microscopic basis for this new superfluid phase was the forgotten phenomenon of Bose-Einstein condensation (BEC) first suggested by Einstein in 1925. In 1941, Landau developed a very successful theory of superfluid (4)He, but it was not anchored in a microscopic theory of interacting atoms. It took another 20 years for theorists to unify the two seemingly different theories of Landau and London. Experiments on trapped superfluid atomic gases since 1995 have shone new light on superfluid (4)He. In the mid-1930s, London had emphasized that superconductivity in metals and superfluidity in liquid (4)He were similar. Experiments on trapped two-component Fermi gases in the last five years have shown that a Bose condensate is indeed the basis of both of these superfluid phases. This confirms the now famous Bardeen-Cooper-Schrieffer-BEC crossover scenario developed for superfluidity by Leggett and Nozières in the early 1980s but largely ignored until a few years ago. The study of superfluid (4)He will increasingly overlap with strongly interacting dilute quantum gases, perhaps opening up a new era of research on this most amazing liquid.
Motivated by recent experiments on alkali gases in atom traps, a largely pedagogical account is given of the implications of the existence of a single-particle Bose-Einstein condensate for the phenomenon of superfluidity. The first conclusion is that, for alkalis in traps at the lowest temperatures, Bose-Einstein condensation coexists with superfluidity. Both experimental evidence and basic microscopic theory are reviewed in this context, with superfluidity in finite systems, quantized vortices and the threshold for breakdown of superfluidity all being referred to. The contrast between liquid 4He below the λ point and the alkali atom gases is then emphasized. Both exhibit superfluidity, but the manifestations of a Bose-Einstein condensate are quite different. For the atomic vapours, near to 100% of the atoms are condensed at the lowest temperatures, whereas from (i) neutron scattering and (ii) computer simulations in liquid 4He present evidence is that 7% is the condensate fraction. This leads finally into a brief discussion of superfluidity without a condensate, with specific reference to the two-dimensional Bose Coulomb gas. The main conclusion is that Bose-Einstein condensation and superfluidity are distinct consequences of deeper topological properties of the many-body wavefunction.
In opening the Levico BEC 2003 meeting, the directors thought it would be useful to say a little about the first BEC workshop held in the same hotel, in the same lecture room, almost exactly ten years ago. I want to give you a personal view of what led up to the historic BEC 93 workshop at Levico and contrast the situation then with the fantastic developments which have occurred over the last decade. BEC 93 was organized by Griffin, Snoke, Stringari, Laloe and Baym. The purpose of the workshop was to bring together people working in different fields of physics but with a common interest in the phenomenon of Bose–Einstein condensation. It is useful to briefly recall the history of BEC studies before the BEC 93 workshop, to understand why it was organized. In 1938 Fritz London suggested that the mysterious phase transition which occurred in liquid 4 He at T = 2.17 K might be related to the formation of a Bose–Einstein condensate (BEC) of 4 He atoms, a phenomenon first predicted by Einstein in 1925 in an ideal gas. After Tisza suggested that the spectacular superfluid effects discovered in 1938 were related to the motion of the Bose condensate, BEC became a hot topic in the years before World War II. In 1941, Landau developed a very successful two-fluid theory of superfluid 4 He, based on the relatively new concept of elementary excitations of a many-body system to describe the 'normal fluid' component. The Landau picture was spectacularly successful in explaining various thermodynamic and transport properties, albeit in a phenomenological manner. However, Landau's magnificent theory made no use of the concept of BEC, or even the fact that the 4 He atoms obeyed Bose statistics. Interest in BEC faded from low temperature conferences in the period 1945–1955, in spite of Bogoliubov's seminal work in 1947 showing that a dilute weakly interacting Bose gas still exhibited BEC. Quite separate from the study of BEC in superfluid 4 He, interest in finding a BEC in a dilute, weakly interacting Bose gas started to develop in the early 1960s. The first system was optically excited excitons in semiconductors (electron-hole pairs, with zero total spin, played the role of the bosons). However, the short lifetime of the excitons in most semiconductors frustrated the early experiments. A second major effort developed in the 1980s with attempts to produce an atomic BEC in spin-polarized hydrogen gas. The initial experiments were very promising, but various problems ultimately stopped people from ever producing (until 1998) high enough densities needed for BEC. However, this work revived interest in the theory of a dilute, weakly interacting Bose gas, and also led to several workshops on 'spin-polarized' quantum gases in the 1980s in which BEC was a major topic. The preceding summary sets the stage for why BEC 93 was organized, namely, to bring together people (both theorists and experimentalists!) interested in BEC in quite different systems, for encouragement as well as stimulation. The topic was largely ignored in the large international low temperature conferences. The organizers were mainly from the condensed matter and low temperature physics communities. Fortunately Franck Laloe was involved, and he was aware of the attempts to produce a BEC in trapped alkali gases using the novel technique of laser-cooling. The titles of the review talks given at BEC 93 show that the popular Bose systems in 1993 were liquid 4 He, excitons, spin-polarized hydrogen and small Cooper pairs in high-temperature superconductors. Work on laser-cooled alkali gases was reviewed by Yvan Castin, but people seemed pessimistic at the time about producing a stable BEC in these very dilute systems in the near future. We also had several excellent talks about Bose condensates involving mesons, as well as Cooper pairing in nuclei. The main reason for this was that crucial financial support for BEC 93 came from the newly formed ECT* Institute in Trento, thanks to Stringari. As a result, several theorists interested in condensates in nuclear and high energy physics were incorporated into the schedule of BEC 93. To my surprise, their talks, relating to Bose condensates in fairly exotic settings, fitted in very well with the other speakers. It was decided to hold BEC 93 in Levico-Terme at the Grand Hotel Bellavista. Stringari scouted many hotels in the area around Trento and Sandro clearly chose wisely, since we returned ten years later for Levico BEC 2003. Because of the interdisciplinary quality of the BEC 93 workshop and the slightly controversial nature of BEC in real systems, however, we found it very difficult to obtain funding for BEC 93. Many of the funding agencies turned down requests for funding so the BEC 93 workshop was funded by the ECT*, a small grant from CNRS in France, a payment from Cambridge University Press (in lieu of royalties for the conference proceedings) and registration fees. We were therefore overjoyed when we received some late applications from people who said they would pay the full registration fee. One of these was Eric Cornell, a young AMO physicist from 'someplace' called JILA in Boulder, Colorado. We gladly accepted his money and his participation. The opening session of BEC 93 in the Grand Hotel Bellavista was a very historic occasion, since almost all the people in the world interested in BEC were present. The excellent review talks and energetic discussions quickly made us realize that the workshop was going to be a success. People heard about the search for BEC in systems quite different from what they were familiar with. It probably was the first time that the CMP and AMO communities were in the same room together. Eric Cornell later told me that it was the first meeting where he met a lot of well known CMP theorists, and heard them arguing about the role of interactions, broken symmetry and order parameters, Goldstone modes, phase rigidity, etc. It dawned on Eric that the physics of a Bose condensate had not been completely settled in Einstein's 1925 paper! One of the star invited speakers was Nozières but at the last moment, he could not attend because of family reasons. However, he gave a lecture a month later at the 60th birthday party for Cohen-Tannoudji in Paris, based on his planned talk for BEC 93. I convinced him that his lecture 'belonged' to BEC 93 so he wrote it up for the BEC book we were preparing. His insightful article became one of the most quoted articles in the book, and many of his phrases (fragmentation of the condensate, phase locking, enemies of Bose–Einstein condensation, etc.) have entered our language. At the conference dinner, we gave out small prizes to some of the best speakers and participants who had made a significant contribution. One of the themes of BEC 93 was to pin down what an unambiguous signature of a Bose condensate was, and the term 'smoking gun' became very popular in discussions. Shlyapnikov received the coveted 'Smoking Gun' award, the prize being a package of cigarettes. The 'Prix d'Or' (1000 Lire), for giving the most convincing evidence for a Bose condensate, was awarded to Wolfe for his group's work on exciton gases. Some years later, in 1999, further work by his group at Urbana showed that an unexpected rapid exciton decay process had not been included in the original data analysis. As a result, the exciton densities had been over-estimated and they had not crossed into the BEC region. Shortly after, I received a letter from Wolfe telling me about the new results, and also the original 1000 Lire banknote he had received as a prize at BEC 93. It made me proud having colleagues like this. Brown, who argued that kaon condensates played a crucial role in the collapse of large stars, received the very special 'Smoking Universe' award. He gave the most impressive 'thank you' speech, worthy of the Academy Awards. At the end of BEC 93, we had an open discussion about whether we should organize another BEC workshop two years later, in 1995. Many people felt that, while BEC 93 had been very stimulating, there probably would not be enough progress to have another BEC meeting 'so soon', but a committee was set up to monitor developments. Walraven took the initiative to organize BEC 95, which was held in Mt St Odile near Strasbourg in France, in June 1995. As luck would have it, a few weeks before BEC 95 convened, rumours circulated that the JILA group at Boulder had clear evidence for a Bose condensate in a trapped gas of 87 Rb atoms. When Eric arrived in Mt St Odile from a meeting in Capri and presented the JILA data 'hot off the press', we all gave him a standing ovation. The earth had moved and BEC was about to move to centre stage. Another piece of luck was that our BEC 93 book ( Bose–Einstein Condensation 1995 ed A Griffin, D W Snoke and S Stringari (Cambridge: Cambridge University Press)) finally appeared in March 1995. The discovery of BEC in atomic gases a few months later made the book a modest 'bestseller' and it was quickly re-issued as a paperback (almost unheard of for this type of conference proceedings). Several people later congratulated us on producing such an excellent book on BEC so quickly after the discovery in June 1995! The BEC book (often called the 'Green Book') did fill a vacuum in the early days, providing carefully written reviews about many aspects of BEC. Several of the articles were well ahead of their time, such as the discussion of the BCS–BEC crossover in Fermi gases by Randeria. We are only now seeing a lot of references to his review article, as the search for BCS pairing in trapped Fermi gases has developed over the last year. Probably over half of all publications in the area of BEC and ultracold quantum gases since 1995 have made one or more references to the Green Book. Beginning with BEC 95, these biennial meetings have now become a regular affair, generously financed and sponsored by the European Science Foundation (ESF). BEC 99, 2001 and 2003 have all been held in San Feliu de Guixols, in Spain. Since BEC 95, these workshops have been dominated by people working on trapped atomic gases, for obvious reasons. However, it is nice to see that work has picked up recently in the search for BEC in exciton gases (especially in quantum wells), and the study of trapped Fermi gases has stimulated new connections with people working in nuclear physics as well as highly correlated electron systems. So one can see that the exciting interdisciplinary atmosphere of BEC 93 may return in the near future. The papers given at Levico BEC 2003 already show strong evidence of this trend. In their 2001 Nobel Prize lectures, Cornell, Wieman and Ketterle all emphasized how 'surprised' they were on how rich BEC physics turned out to be. Initially, they expected that these atomic condensates would be small and somewhat delicate, certainly only of minor interest to the larger physics community. In fact, as we all know, interest in ultracold gases has exploded since 1995 like a 'Bosenova' and, like the universe, there is no sign of this expansion stopping. It is rapidly producing a whole new field of research which is an amalgamation of AMO and CMP physics. This in turn is producing a major re-organization of all major physics departments, in terms of the hiring of new faculty and resource allocations. International conferences in more traditional research areas in CMP and AMO have been trying to incorporate this growing subject, but it is probably time to start a new 'International Conference on Ultracold Quantum Gases' which is open to all. Of course, the young physicists who have organized and are the main speakers at Levico BEC 2003 illustrate this on-going revolution. I predict that Bose matter waves, atomic optics and, more generally, phenomena in ultracold quantum gases, will be the basis for all really new technology in the 21st century. I say this with confidence, since I don't see any real competition from developing technologies based on electrons (discovered about 1900) and laser beams (discovered about 1960). As with these older technologies, it will take decades to see how cold quantum gases can be used, in ways that we cannot even imagine today. A crucial reason for the exciting future of ultracold gases is based on the fact that it involves a creative interaction between two major areas of physics, CMP and AMO. Each has their own well developed paradigms for thinking about physics, and this difference surfaces in dealing with cold quantum gases. This creates a certain tension but ultimately it is the basis of a new creativity. Many CMP theorists who had previously worked in the area of quantum fluids and superconductors have entered this new field. This is shown by the recent publication of two excellent books on cold quantum gases (Pethick C and Smith H 2002 Bose–Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press); Pitaevskii L and Stringari S 2003 Bose–Einstein Condensation (Oxford: Oxford University Press)), both by CMP theorists. This is easy to understand since trapped atomic gases (Bose or Fermi) are beautiful examples of interacting, highly coherent, quantum many-body systems, precisely the subject that CMP theorists have been struggling to understand since the 1950s. The new concepts and techniques needed to understand such many-body systems were developed and fought over in the period 1955–1965, when it was realized that there was more to the quantum theory of matter than solving Schrödinger's wave equation. A major contribution was made by the Landau school in Moscow. This battle of ideas was focused on the attempts to understand both superconductivity and superfluid 4 He. While the BCS theory of superconductivity in metals which appeared in 1957 clearly had the right physics to explain the key properties of superconductors, it still took some time for most theorists to really understand the BCS theory at a deeper level, in terms of broken symmetry, order parameters and Goldstone modes. The BCS theory gave CMP physics a simple microscopic model for superfluidity in a real system, in terms of the coherent motion of Cooper pairs. Very quickly, the close analogy was made between Bogoliubov's theory of a Bose-condensed gas and the BCS theory of superconductors. Strangely enough, however, it was only in the 1980s that pioneering work by Leggett, Nozières and others re-emphasized that one should think of the BCS theory as a Bose condensate of Cooper pairs. This led to an understanding of the BCS–BEC crossover, and also that the Bogoliubov theory of a weakly interacting Bose-condensed gas was 'buried' in the full BCS theory. It is fitting that, in 2003, this BCS–BEC crossover is becoming a central topic in the field of ultracold atoms. I say this because it represents a beautiful synthesis of both AMO physics (the formation of diatomic molecules using Feshbach resonances) and CMP physics (many-body effects giving rise to Cooper pairs) in a novel setting. As Levico BEC 2003 and the articles published in this special section show, we can expect more exciting advances of this kind in the near future. Acknowledgments I would like to thank the organizers of the Levico BEC 2003 workshop for inviting me to participate as a senior lecturer and also to commemorate the tenth anniversary of the first BEC workshop held in Levico-Terme. My research is funded by NSERC of Canada.
We review how our current ideas about BEC developed in the early period 1925-1965, which had the specific goal of understanding superfluid 4^44He. This history is presented by commenting on the key contributions made by Einstein, Fritz London, Tisza, Landau, Bogoliubov, Oliver Penrose and Feynman. We emphasize the emergence of the concept of a macroscopic wavefunction describing the condensate. Starting with the fundamental work of Beliaev in 1957, the period 1957-1965 was a golden era for theoretical studies of interacting Bose-condensed gases. This work provided a sound conceptual basis for understanding the properties of trapped atomic gases which were discovered thirty years later.
Liquid helium 4 had been the only bosonic superfluid available in experiments for a long time. This situation was changed in 1995, when a new superfluid was born with the realization of the Bose–Einstein condensation in ultracold atomic gases. The liquid helium 4 is strongly interacting and has no spin; there is almost no way to change its parameters, such as interaction strength and density. The new superfluid, Bose–Einstein condensate (BEC), offers various advantages over liquid helium. On the one hand, BEC is weakly interacting and has spin degrees of freedom. On the other hand, it is convenient to tune almost all the parameters of a BEC, for example, the kinetic energy by spin–orbit coupling, the density by the external potential, and the interaction by Feshbach resonance. Great efforts have been devoted to studying these new aspects, and the results have greatly enriched our understanding of superfluidity. Here we review these developments by focusing on the stability and critical velocity of various superfluids. The BEC systems considered include a uniform superfluid in free space, a superfluid with its density periodically modulated, a superfluid with artificially engineered spin–orbit coupling, and a superfluid of pure spin current. Due to the weak interaction, these BEC systems can be well described by the mean-field Gross–Pitaevskii theory and their superfluidity, in particular critical velocities, can be examined with the aid of Bogoliubov excitations. Experimental proposals to observe these new aspects of superfluidity are discussed.