Interacting bosons in an optical lattice
arXiv:0707.1979 · doi:10.1002/andp.20085200804
Abstract
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.
58 pages, 14 figures
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- Dynamic properties of the one-dimensional Bose-Hubbard model
- Effects of symmetry breaking in finite quantum systems
- Ultracold bosons with short-range interaction in regular optical lattices
- Dipolar and spinor bosonic systems
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- Optical lattice with heterogeneous atomic density
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- Stability of the Mott phase in excitonic double layers