Bose-Einstein Condensation as a Quantum Phase Transition in an Optical Lattice
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 . For small and temperature Bose-Einstein condensation (BEC) is proved to occur, while at large 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