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Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice

Statistical Mechanics 2008-09-23 v1 Other Condensed Matter Mathematical Physics math.MP

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 \cite{ALSSY} 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\lambda. For small λ\lambda and temperature Bose-Einstein condensation (BEC) is proved to occur, while at large λ\lambda 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.

Keywords

Cite

@article{arxiv.cond-mat/0412034,
  title  = {Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice},
  author = {M. Aizenman and E. H. Lieb and R. Seiringer and J. P. Solovej and J. Yngvason},
  journal= {arXiv preprint arXiv:cond-mat/0412034},
  year   = {2008}
}

Comments

To appear in the proceedings of QMath9, Giens, France, Sept. 12--16, 2004