When Eric Cornell and Carl Wieman made the first Bose–Einstein condensate from a gas of cold rubidium-87 atoms in 1995, I was excited and impressed. Conceptually, BECs are simple enough to have been included in my undergraduate quantum mechanics course. But making one—what a feat!
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.
As was shown by Einstein in 1924, Bose-Einstein statistics gives rise to a phase transition in which a macroscopic part of a gaseous state condenses into a phase with ground state properties, offering a unique view on the behavior of matter at zero temperature. From the very start the nature of Bose-Einstein condensation (BEC) has provoked statements concerning its relation with respect to superconductivity in electron gases (Einstein 1925) and the superfluidity of liquid helium (London 1938), but this connection is not easily grasped experimentally. Remarkably, although the concept of BEC appears routinely in very different contexts, ranging from excitons in semiconductors to nuclear matter, it had never been observed in its pure form, i.e., in a gaseous phase, until in 1995 BEC in ultracold Rb vapor was reported by Cornell and Wieman. Bose-Einstein condensation is probably the most exciting phenomenon currently under experimental investigation in ultracold atomic gases. In the tutorial the physics will be addressed which is at the roots of the current interest of BEC in atomic gases.
The phenomenon of Bose-Einstein condensation (BEC), first predicted by Einstein 70 years ago, has finally been observed in the laboratory. In this elusive state of matter the concept of individual particles ceases to have meaning: the atoms condense into the same quantum state and act as a single entity that displays quantum mechanical behaviour on a macroscopic scale. The condensate was observed when Eric Cornell, Carl Wieman and colleagues at the Joint Institute for Laboratory Astrophysics in Boulder, Colorado, cooled a dilute gas of rubidium atoms, confined in a magnetic trap, to a temperature of just a few nanoKelvin (M H Anderson et al. 1995 Science 269 198).
Introduction Bose–Einstein condensation (BEC) is one of the most intriguing phenomena in physics. The basic idea goes back to the 1920s, when Einstein made predictions for the behavior of atoms at sufficiently low temperatures and high densities. However, it took seven decades for experimental physicists to realize this phase under the low-density conditions envisioned by Einstein. In the intermediate period there were many experiments in which aspects of BEC played important roles. Therefore, phenomena such as superfluidity and superconductivity were connected to BEC long before its 1995 realization in ultra-cold, low-density atomic vapors. Since BEC can be discussed with very many different backgrounds and applications in mind, the subject can sometimes be overwhelming for interested students. There is a very good reason why a chapter on BEC does not belong in this book. In all the other chapters here, the processes described involve one or at most two atoms, and the interactions that play a role are between the particles that constitute the atom, namely between the nucleus (or nuclei) and their electrons. The interactions are described quantum mechanically by their Hamiltonian that can always be written exactly in non-relativistic terms, and in some cases can even be solved exactly. This makes atoms and molecules a branch of physics where comparisons between theory and experiments become very meaningful since theoretical predictions are often confirmed to very high accuracy. In BEC, it is the interactions among many atoms that are the key for understanding the phenomenon. Although in principle one could write a Hamiltonian for a Bose condensed gas, its large number of particles makes this not very practical. The starting point for the description of a BEC is in the area of many-body physics that belongs to the expertise of condensed-matter physicists. The interactions between ~10 23 electrons in a solid state with a lattice formed by ~10 23 ions resemble the kind of interactions in a BEC much more closely than the simple fewbody interactions in an atom or molecule. Thus all the theoretical models that have been described up to now are not applicable for the contents of this chapter.
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.
I will discuss the work of the JILA/University of Colorado group on the creation and study of Bose–Einstein condensation (BEC) in a gas of very cold rubidium atoms. Over the years, a large number of students and postdocs have contributed to this work, with Eric Cornell and myself as the coleaders of the project. The data reported in this paper were obtained by Mike Anderson, Eric Burt, Jason Ensher, Rich Ghrist, Deborah Jin, Mike Matthews and Chris Myatt. Theoretical contributions have been provided by Murray Holland, Jinx Cooper, Brett Esry and Chris Greene. In the first part of this paper, I will briefly discuss how we create and observe BEC; in the second portion, I will discuss some of the work on BEC that has been carried out at JILA in the past year.