The field of atomic quantum gases has seen rapid and sometimes surprising developments since its beginnings in 1995. In this chapter, I summarize, highlight, and comment on selected topics. Introduction Bose-Einstein condensation (BEC) in atomic gases was first observed in 1995, and has changed the face of atomic physics. It is for atoms or matter waves what the laser is for photons: a macroscopically occupied quantum state. It was regarded as an elusive goal until it was discovered in 1995. Although BEC was immediately viewed as a major accomplishment, its impact has far exceeded expectations. Now, twenty years on, there is no question that the field remains exciting. It is impossible to give a review over the developments during those twenty years. Instead, in this chapter, I want to illustrate how often predictions or expectations changed in the pursuit of Bose-Einstein condensation. There were many surprises, and some advances and breakthroughs happened although they were predicted to be impossible. A lesson we can learn from this is that we should always carefully read the fine print when something is proven or assumed impossible, and try to figure out if the assumptions can be circumvented! Since the early history of Bose-Einstein condensation provides several examples for such “impossibility theorems,” I digress into those earlier developments in the first part of this chapter. Early Theoretical Questions Validity of the Prediction of Bose-Einstein Condensation Einstein predicted Bose-Einstein condensation in 1924 in the second of two papers where he generalized Bose's treatment from photons to massive particles [1]. Using statistical arguments introduced by Bose, he found that below a critical temperature, bosonic particles condense in the lowest energy state of the system. In contrast, at very low temperature photons can simply disappear. However, for about a decade, this prediction was not taken at face value. Einstein himself wrote to Ehrenfest, “From a certain temperature on, the molecules ‘condense’ without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it?” [2]. In 1927, George E. Uhlenbeck concluded that the predicted BEC phase transition was an artifact of the replacement of the summation over states by an integral and wrote that no “splitting into two phases” would occur [3].
The field of atomic quantum gases has seen rapid and sometimes surprising developments since its beginnings in 1995. In this chapter, I summarize, highlight, and comment on selected topics. Introduction Bose-Einstein condensation (BEC) in atomic gases was first observed in 1995, and has changed the face of atomic physics. It is for atoms or matter waves what the laser is for photons: a macroscopically occupied quantum state. It was regarded as an elusive goal until it was discovered in 1995. Although BEC was immediately viewed as a major accomplishment, its impact has far exceeded expectations. Now, twenty years on, there is no question that the field remains exciting. It is impossible to give a review over the developments during those twenty years. Instead, in this chapter, I want to illustrate how often predictions or expectations changed in the pursuit of Bose-Einstein condensation. There were many surprises, and some advances and breakthroughs happened although they were predicted to be impossible. A lesson we can learn from this is that we should always carefully read the fine print when something is proven or assumed impossible, and try to figure out if the assumptions can be circumvented! Since the early history of Bose-Einstein condensation provides several examples for such “impossibility theorems,” I digress into those earlier developments in the first part of this chapter. Early Theoretical Questions Validity of the Prediction of Bose-Einstein Condensation Einstein predicted Bose-Einstein condensation in 1924 in the second of two papers where he generalized Bose's treatment from photons to massive particles [1]. Using statistical arguments introduced by Bose, he found that below a critical temperature, bosonic particles condense in the lowest energy state of the system. In contrast, at very low temperature photons can simply disappear. However, for about a decade, this prediction was not taken at face value. Einstein himself wrote to Ehrenfest, “From a certain temperature on, the molecules ‘condense’ without attractive forces; that is, they accumulate at zero velocity. The theory is pretty, but is there some truth in it?” [2]. In 1927, George E. Uhlenbeck concluded that the predicted BEC phase transition was an artifact of the replacement of the summation over states by an integral and wrote that no “splitting into two phases” would occur [3].
The study of Bose-Einstein condensation has undergone a remarkable expansion during the last twenty years. Observations of this phenomenon have been reported in a number of diverse atomic, optical, and condensed matter systems, facilitated by remarkable experimental advances. The synergy of experimental and theoretical work in this broad research area is unique, leading to the establishment of Bose-Einstein condensation as a universal interdisciplinary area of modern physics. This chapter reviews the broad expansion of Bose-Einstein condensation physics in the past two decades. Introduction The field of Bose-Einstein condensation (BEC) has undergone an explosive expansion during the past twenty years. Newcomers to this field are now often introduced to this as a universal phenomenon, which nonetheless exhibits diverse (and sometimes strikingly different) manifestations. Despite such differences, the common underlying theme creates a unique identity across many different energy and length scales. The study of BEC as a universal phenomenon was highlighted in a focused conference in 1993, leading to the publication of the well-known “green book” [1], which surveyed the breadth of the field of condensate physics at that time. The success of the conference led to a second meeting in 1995, at which Eric Cornell and Carl Wieman announced the achievement of Bose-Einstein condensation of ultracold 87 Rb atoms in a harmonic trap. That work began an explosion of new research in the field of cold atoms, which has continued to this day, and this very success inevitably led many of those studying cold atoms to pay less attention to other types of condensates. Wolfgang Ketterle gives a historical overview of this exciting period of time in Chapter 3. Recently, various scientific meetings have worked to re-establish the physical connections across different BEC systems, and in 2013 a workshop was held with the focused goal of improving communications across disciplines. This present book is an outgrowth of that meeting. The Situation Before the Revolution Because of the great success of the cold atom BEC and other BEC systems in the past twenty years, it may be hard for young scientists to understand the climate of BEC research in the early 1990s. At that time, there was only one known example of BEC, namely liquid helium-4, and there was a small but vocal minority of scientists who questioned whether BEC was established even in that system.
The experimental realization in 1995 of Bose–Einstein condensation in dilute atomic gases marked the beginning of a very rapid development in the study of quantum gases. The initial experiments were performed on vapours of rubidium, sodium, and lithium. So far, the atoms 1 H, 7 Li, 23 Na, 39 K, 41 K, 52 Cr, 85 Rb, 87 Rb, 133 Cs, 170 Yb, 174 Yb and 4 He * (the helium atom in an excited state) have been demonstrated to undergo Bose–Einstein condensation. In related developments, atomic Fermi gases have been cooled to well below the degeneracy temperature, and a superfluid state with correlated pairs of fermions has been observed. Also molecules consisting of pairs of fermionic atoms such as 6 Li or 40 K have been observed to undergo Bose–Einstein condensation. Atoms have been put into optical lattices, thereby allowing the study of many-body systems that are realizations of models used in condensed matter physics. Although the gases are very dilute, the atoms can be made to interact strongly, thus providing new challenges for the description of strongly correlated many-body systems. In a period of less than ten years the study of dilute quantum gases has changed from an esoteric topic to an integral part of contemporary physics, with strong ties to molecular, atomic, subatomic and condensed matter physics. The dilute quantum gases differ from ordinary gases, liquids and solids in a number of ways, as we shall now illustrate by giving values of physical quantities.
Bose Einstein Condensate (BEC) is the fifth state of matter in condensed matter physics. It is the most impressive example of quantum behaviour on a macroscopic scale but the most difficult state to observe. When low-density boson gas is cooled to a temperature nearly absolute zero, then BEC is formed. In this condition, the bosons have almost no free energy to move relative to each other. They clump together, come into the lowest quantum state, and behave as a single atom. Then microscopic quantum mechanical phenomena work on a macroscopic scale. This chapter summarizes the history and the developments regarding BEC with a brief discussion of the key scientists in this field. In the next section, the summary of the all chapters is given.
A Bose-Einstein condensate (BEC), the first of which was shown experimentally 22 years ago, isn’t your garden variety state of matter. It formed at a fraction above absolute zero and only in atoms that act like bosons, one of two types of fundamental particles. Bosons don’t follow the Pauli exclusion principle, which prohibits two particles from existing in the same quantum state. When bosonic atoms are cooled to form a condensate, they can lose their individuality. They behave like one big collective superatom, analogous to how photons become indistinguishable in a laser beam. But it’s even weirder than that.
This velocity-distribution data for a gas of rubidium atoms confirmed the discovery of the Bose–Einstein condensate in 1995. In these three snapshots in time, atoms—cooled to near absolute zero—condensed from less dense areas on the left (red, yellow, and green) to very dense areas at the center and the right (blue and white). Image courtesy of NIST/JILA/CU-Boulder.
“In a very good analogy, one can view a BEC as a bell, which begins to ring spontaneously when it is cooled below a certain temperature,” writes physicist Nick Proukakis at the Joint Quantum Centre Durham–Newcastle in the United Kingdom, in Universal Themes of Bose–Einstein Condensation , a forthcoming collection of research essays on progress in BECs (1). That behavior provides physicists with an extraordinary opportunity: to study bizarre quantum effects on a large scale, instead of having to probe individual particles.
For the last two decades, physicists have treated BECs something like Play-Doh. They poke it, smash it, tickle it with lasers, and trap it in magnetic fields. They mix condensates together to see what happens, and use it to slow down light (2). They have observed strange behaviors that would have been impossible to predict even two decades ago: solids that flow …
Bose-Einstein condensation is a unique phase transition in that it is not driven by interparticle interactions, but can theoretically occur in an ideal gas, purely as a consequence of quantum statistics. This chapter addresses the question, ‘ How is this ideal Bose gas condensation modified in the presence of interactions between the particles?’ This seemingly simple question turns out to be surprisingly difficult to answer. Here we outline the theoretical background to this question and discuss some recent measurements on ultracold atomic Bose gases that have sought to provide some answers. Introduction Unlike the vast majority of phase transitions, Bose-Einstein condensation (BEC) is not driven by interparticle interactions but can theoretically occur in an ideal (noninteracting) gas, purely as a consequence of quantum statistics. However, in reality, interactions are needed for a Bose gas to remain close to thermal equilibrium. It is thus interesting to discuss if something close to ideal gas BEC can be observed in a real system and what happens in the vicinity of the BEC transition in the presence of interparticle interactions. These simple questions have not been easy to answer, either theoretically or experimentally. The theoretical foundations for studying the effect of interactions on Bose condensed systems were laid over half a century ago by Bogoliubov [1], Penrose and Onsager [2], and Belieav [3], among others. These works initially focused on zerotemperature properties and were extended to nonzero temperature in the pioneering papers of Lee, Huang, and Yang [4, 5, 6, 7]. At that time, the main experimental system was liquid He-4 in which the inter-particle interactions are strong, making connections with theory difficult. The realisation in 1995 of BEC in weakly interacting ultracold atomic gases [8, 9] thus opened up the possibility to experimentally revisit some of these long-discussed questions. This was further aided by, among other advances, the use of Feshbach resonances to tune the interaction strength in atomic gases [10, 11]. Thus, in the last twenty years the study of ultracold Bose gases has been very successful (see Chapter 3 for an insightful account of selected topics and surprising developments over this exciting period). However, the fact that, until recently, ultracold atoms were confined using harmonic potentials has hindered the study of the BEC transition itself.
Bose–Einstein condensation (BEC) in cold atomic gases was first achieved experimentally in 1995. Since then there has been a surge of activity in this field, with ingenious experiments putting forth more and more astonishing results about the behaviour of matter at very cold temperatures. The theoretical investigation of BEC goes back much further, and even predates the modern formulation of quantum mechanics. It was investigated in two papers by Einstein in 1924 and 1925, respectively, following up on a work by Bose on the derivation of Planck's radiation law. Einstein's result, in its modern formulation, can be found in any textbook on quantum statistical mechanics, and was concerned with ideal, i.e., non-interacting gases. The understanding of BEC in the presence of interparticle interactions poses a formidable challenge to mathematical physics. Some progress has been made in the last ten years or so, and the purpose of this chapter is to explain part of what was achieved and how it is related to the actual experiments on cold gases.