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International Journal of Modern Physics B

FINITE TEMPERATURE FIELD THEORY OF BOSE-EINSTEIN CONDENSATES

David A. W. Hutchinson

Published May 10, 2001• 0 citations
Publisher

Abstract

The field theory treatments of Base condensed systems developed forty years ago have received renewed attention within the context of inhomogeneous systems since the realisation of Base-Einstein condensation in dilute trapped alkali gases in 1995. These experiments allow quantitative tests of the theories used to describe them and hence provide a unique laboratory in which to evaluate and develop these field theoretical methods to an unprecedented degree. Various examples are discussed to illuminate these developments.

DOI
10.1142/s021797920100615x

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The field theory treatments of Base condensed systems developed forty years ago have received renewed attention within the context of inhomogeneous systems since the realisation of Base-Einstein condensation in dilute trapped alkali gases in 1995. These experiments allow quantitative tests of the theories used to describe them and hence provide a unique laboratory in which to evaluate and develop these field theoretical methods to an unprecedented degree. Various examples are discussed to illuminate these developments.
Bose–Einstein condensation was predicted in 1925 [Ein24, Ein25] but, except for its indirect manifestation in the superfluidity of He 4 [Lon38, Kap38, AllMis38], it remained a purely theoretical construct until 1995, when condensation in alkali gases was achieved in the laboratory [CorWie02, Ket02]. Since then, a great deal of the theoretical work in the previous 70 years has been put to the experimental test, while new avenues have been opening up, such as the superfluid-insulator or Mott transition [FWGF89, GMEHB02, CaHuRe06], the BEC-BCS cross-over [Leg06, Reg04] and the Tonks gas regime [Gir60, Par04]. Because of the great experimental control over the relevant parameters and the deep understanding of the fundamental physics, BECs have become a field of choice to perform experiments of interest not just in atomic and molecular physics, but also in quantum optics, condensed matter physics, quantum critical dynamics, even field theory, gravitation, cosmology and black hole physics [CoEnWi99, PetSmi02, Sou02, BonSen04, ParZha93, ParZha95, UnrSch07, BaLiVi05]. Moreover, cold Bose gases on optical lattices have been proposed as a possible implementation of a quantum information processing (QIP) device [JakZo104], boosting new interest in these systems. As introductions and reviews on this fast evolving subject abound, it is perhaps more fitting for us to focus on certain aspects of the nonequilibrium field theory of BEC, specifically [And04] the application of quantum field theoretic methods described in this book to the description of nonequilibrium evolution of condensed gases in magneto-optical traps [ChCoPh95].
For sufficiently low temperatures, a Bose gas experiences a transition into a Bose-Einstein condensate, characterized by a macroscopic occupation of the ground state of the system. The development of efficient cooling and trapping techniques for neutral atoms led in 1995, to the first observation of BEC in dilute alkali gases in 87Rb [1]. This remarkable achievement has been followed by BEC experiments in various other elements. The BEC has become during the last years, one of the most active and fruitful research areas of modern atomic physics, constituting an interdisciplinary field, which links atomic physics with various other research areas, like quantum optics, condensed-matter physics, and very especially nonlinear physics.
The 1995 observation of Bose–Einstein condensation in dilute atomic vapours spawned the field of ultracold, degenerate quantum gases. Unprecedented developments in experimental design and precision control have led to quantum gases becoming the preferred playground for designer quantum many-body systems. This self-contained volume provides a broad overview of the principal theoretical techniques applied to non-equilibrium and finite temperature quantum gases. Covering Bose–Einstein condensates, degenerate Fermi gases, and the more recently realised exciton–polariton condensates, it fills a gap by linking between different methods with origins in condensed matter physics, quantum field theory, quantum optics, atomic physics, and statistical mechanics. Thematically organised chapters on different methodologies, contributed by key researchers using a unified notation, provide the first integrated view of the relative merits of individual approaches, aided by pertinent introductory chapters and the guidance of editorial notes. Both graduate students and established researchers wishing to understand the state of the art will greatly benefit from this comprehensive and up-to-date review of non-equilibrium and finite temperature techniques in the exciting and expanding field of quantum gases and liquids.
For many years, 4^44He typified Bose-Einstein superfluids, but recent advances in dilute ultra-cold alkali-metal gases have provided new neutral superfluids that are particularly tractable because the system is dilute. This chapter starts with a brief review of the physics of superfluid 4^44He, followed by the basic ideas of Bose-Einstein condensation (BEC), first for an ideal Bose gas and then considering the effect of interparticle interactions, including time-dependent phenomena. Extensions to more exotic condensates include magnetic dipolar gases, mixtures of two components, and spinor condensates that require a focused infrared laser for trapping of all the various hyperfine magnetic states in a particular hyperfine FFF manifold of mFm_FmF​ states. With an applied rotation, the trapped BECs nucleate quantized vortices. Recent theory and experiment have shown that laser coupling fields can mimic the effect of rotation. The resulting synthetic gauge fields have produced vortices in a nonrotating condensate.