Bose-Einstein condensation as a quantum phase transition in an optical lattice

M. Aizenman, E. H. Lieb, R. Seiringer, J. P. Solovej, J. Yngvason

Research output: Chapter in Book/Report/Conference proceedingChapter

5 Scopus citations

Abstract

One of the most remarkable recent developments in the study of ultracold Bose gases is the observation of a reversible transition from a Bose Einstein condensate to a state composed of localized atoms as the strength of a periodic, optical trapping potential is varied. In [1] a model of this phenomenon has been analyzed rigorously. The gas is a hard core lattice gas and the optical lattice is modeled by a periodic potential of strength λ. For small λ and temperature Bose- Einstein condensation (BEC) is proved to occur, while at large λ BEC disappears, even in the ground state, which is a Mott-insulator state with a characteristic gap. The inter-particle interaction is essential for this effect. This contribution gives a pedagogical survey of these results.

Original languageEnglish (US)
Title of host publicationMathematical Physics of Quantum Mechanics
Subtitle of host publicationSelected and Refereed Lectures from QMath9
EditorsJoachim Asch, Alain Joye
Pages199-215
Number of pages17
DOIs
StatePublished - 2006

Publication series

NameLecture Notes in Physics
Volume690
ISSN (Print)0075-8450

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy (miscellaneous)

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    Aizenman, M., Lieb, E. H., Seiringer, R., Solovej, J. P., & Yngvason, J. (2006). Bose-Einstein condensation as a quantum phase transition in an optical lattice. In J. Asch, & A. Joye (Eds.), Mathematical Physics of Quantum Mechanics: Selected and Refereed Lectures from QMath9 (pp. 199-215). (Lecture Notes in Physics; Vol. 690). https://doi.org/10.1007/3-540-34273-7_16