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Bose-Einstein condensation in the alkali gases: Some fundamental concepts

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TLDR
In this paper, the authors present a tutorial review of some ideas that are basic to our current understanding of Bose-Einstein condensation in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species.
Abstract
The author presents a tutorial review of some ideas that are basic to our current understanding of the phenomenon of Bose-Einstein condensation (BEC) in the dilute atomic alkali gases, with special emphasis on the case of two or more coexisting hyperfine species. Topics covered include the definition of and conditions for BEC in an interacting system, the replacement of the true interatomic potential by a zero-range pseudopotential, the time-independent and time-dependent Gross-Pitaevskii equations, superfluidity and rotational properties, the Josephson effect and related phenomena, and the Bogoliubov approximation.

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Many-Body Physics with Ultracold Gases

TL;DR: In this article, a review of recent experimental and theoretical progress concerning many-body phenomena in dilute, ultracold gases is presented, focusing on effects beyond standard weakcoupling descriptions, such as the Mott-Hubbard transition in optical lattices, strongly interacting gases in one and two dimensions, or lowest-Landau-level physics in quasi-two-dimensional gases in fast rotation.
Journal ArticleDOI

Maximally-localized Wannier Functions: Theory and Applications

TL;DR: In this paper, the authors present a survey of the use of Wannier functions in the context of electronic-structure theory, including their applications in analyzing the nature of chemical bonding, or as a local probe of phenomena related to electric polarization and orbital magnetization.
Journal ArticleDOI

Theory of ultracold atomic Fermi gases

TL;DR: In this article, the physics of quantum degenerate atomic Fermi gases in uniform as well as in harmonically trapped configurations is reviewed from a theoretical perspective, focusing on the effect of interactions that bring the gas into a superfluid phase at low temperature.
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Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond

TL;DR: In this article, the authors review recent developments in the physics of ultracold atomic and molecular gases in optical lattices and show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics.
References
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Book

Quantum Mechanics

Book

Optical Coherence and Quantum Optics

Leonard Mandel, +1 more
TL;DR: In this article, the authors present a systematic account of optical coherence theory within the framework of classical optics, as applied to such topics as radiation from sources of different states of coherence, foundations of radiometry, effects of source coherence on the spectra of radiated fields, and scattering of partially coherent light by random media.

Bose-Einstein condensation in dilute gases

TL;DR: In this paper, a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists is provided.
Journal ArticleDOI

Bose-Einstein Condensation in Dilute Gases

TL;DR: In this paper, a unified introduction to the physics of ultracold atomic Bose and Fermi gases for advanced undergraduate and graduate students, as well as experimentalists and theorists is provided.
Book

Statistical Mechanics, 2nd Edition

Kerson Huang
TL;DR: In this article, a clear, concise introduction to the theory of microscopic bodies is given, where the modern theory of critical phenomena is treated, including a self-contained description of thermodynamics and the classical kinetic theory of gases.
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