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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Cited by in corpus (24)
- Basics of Bose-Einstein Condensation
- 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
- Characterization of Mott-insulating and superfluid phases in the one-dimensional Bose--Hubbard model
- Scheme of thinking quantum systems
- Dynamical Mean Field Theory for the Bose-Hubbard Model
- Theory of Cold Atoms: Basics of Quantum Statistics
- Bose-Einstein condensation temperature of weakly interacting atoms
- Difference in Bose-Einstein condensation of conserved and unconserved particles
- Instability of insulating states in optical lattices due to collective phonon excitations
- Mode interference in quantum joint probabilities for multimode Bose-condensed systems
- Quasiequilibrium Mixture of Itinerant and Localized Bose Atoms in Optical Lattice
- Mesoscopic disorder in double-well optical lattices
- Double-Well Optical Lattices with Atomic Vibrations and Mesoscopic Disorder
- Destiny of optical lattices with strong intersite interactions
- Optical lattice with heterogeneous atomic density
- Mid-range order in trapped quasi-condensates of bosonic atoms
- Stability of normal quantum-fluid mixtures
- Phonon instability of insulating states in optical lattices
- Sensitive linear response of an electron-hole superfluid in a periodic potential
- Unified theory of quantum crystals and optical lattices with Bose-Einstein condensate
- Stability of the Mott phase in excitonic double layers