Interacting bosons in an optical lattice

Details Interacting bosons in an optical lattice Interacting bosons in an optical lattice

2007-07-13

arxiv.org/abs/0707.1979v1

Ann. Phys. (Berlin) 17, pp. 48 (2008)

Physics

Condensed Matter

Other Condensed Matter

58 pages, 14 figures

Scientific paper

10.1002/andp.200710311

Several models of a strongly interacting Bose gas in an optical lattice are studied within the functional-integral approach. The one-dimensional Bose gas is briefly discussed. Then the Bose-Einstein condensate and the Mott insulator of a three-dimensional Bose gas are described in mean-field approximation, and the corresponding phase diagrams are evaluated. Other characteristic quantities, like the spectrum of quasiparticle excitations and the static structure factor, are obtained from Gaussian fluctuations around the mean-field solutions. We discuss the role of quantum and thermal fluctuations, and determine the behavior of physical quantities in terms of density and temperature of the Bose gas. In particular, we study the dilute limit, where the mean-field equation becomes the Gross-Pitaevskii equation. This allows us to extend the Gross-Pitaevskii equation to the dense regime by introducing renormalized parameters in the latter.

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