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Physics World

Bose-Einstein condensation

C. G. Townsend, Wolfgang Ketterle, S. Stringari

Published Mar 1, 1997• 2,623 citations
Publisher

Abstract

In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for “bosons” – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.

DOI
10.1088/2058-7058/10/3/21

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In 1924 the Indian physicist Satyendra Nath Bose sent Einstein a paper in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein generalized Bose's theory to an ideal gas of identical atoms or molecules for which the number of particles is conserved and, in the same year, predicted that at sufficiently low temperatures the particles would become locked together in the lowest quantum state of the system. We now know that this phenomenon, called Bose-Einstein condensation (BEC), only happens for “bosons” – particles with a total spin that is an integer multiple of h, the Planck constant divided by 2π.
In 1924 the Indian physicist Satyendra Nath Bose sent a paper to Einstein in which he derived the Planck law for black-body radiation by treating the photons as a gas of identical particles. Einstein arranged for Bose's paper to be translated into German and published. He also extended Bose's calculations to particles with mass and showed that, at sufficiently low temperatures, they would all condense into the same quantum ground state. And for the next 70 years physicists struggled to make a Bose-Einstein condensate – which is sometimes called the fifth state of matter – in the laboratory.
The subject of this chapter is not only inextricably linked to the wave-like nature of matter, but is also one of the most spectacular affirmations of matter’s wave-like nature. The story began in 1924, when the East Indian physicist S. Nath-Bose proposed a completely new proof of Planck’s law for blackbody radiation by considering thermal radiation as a gas of identical particles. That same year, Bose sent his work for publication; however, to his disappointment, it was rejected. He decided to send his proposal to Einstein, asking him to advocate for its publication in a German scientific journal if he thought he had some value. Indeed, after studying the work carefully, Einstein translated it into German and forwarded it for publication using his undisputed prestige.
About seven decades ago Satyendra Nath Bose and Albert Einstein predicted that a gas of noninteracting integer-spin particles would condense into a macroscopic quantum state when cooled below a critical temperature. Of course Bose–Einstein condensation (BEC) has long since been seen in superfluid He4 and superconductors, but the condensing systems in these examples are far from being noninteracting gases; relatively strong interactions between the condensing particles greatly complicate the theoretical analysis and the experimental behavior. For more than 15 years groups have been cooling and compressing clouds of atoms on a quest to produce and observe a Bose–Einstein condensate in a nearideal gas. They pushed their devices to the limit, seeking to traverse 15 orders of magnitude of phase-space density, and as each technique proved insufficient they developed ingenious variations to create ever colder and denser states.
Bose-Einstein condensation is a macroscopic quantum phenomenon that was first predicted by Albert Einstein in the 1920s, at a time when quantum theory was still developing and was being applied to microscopic systems, such as individual particles and atoms. Einstein applied the new concept of Bose statistics to an ideal gas of identical atoms that were at thermal equilibrium and trapped in a box. He predicted that at sufficiently low temperatures the particles would accumulate in the lowest quantum state in the box, giving rise to a new state of matter with many unusual properties.
Satyendra Nath (S.N.) Bose is one of the great Indian scientists. His remarkable work on the black body radiation or derivation of Planck’s law led to quantum statistics, in particular, the statistics of photon. Albert Einstein applied Bose’s idea to a gas made of atoms and predicted a new state of matter now called Bose-Einstein condensate. It took 70 years to observe the predicted condensation phenomenon in the laboratory. With a brief introduction to the formative period of Professor Bose, this research survey begins with the founding works on quantum statistics and, subsequently, provides a brief account of the series of events terminating in the experimental realization of Bose-Einstein condensation. We also provide two simple examples to visualize the role of synthetic spin-orbit coupling in a quasi-one-dimensional condensate with attractive atom-atom interaction.
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.