Occupation number and fluctuations in the finite-temperature Bose-Hubbard model

Abstract

We study the occupation numbers and number fluctuations of ultra-cold atoms in deep optical lattices for finite temperatures within the Bose-Hubbard model. Simple analytical expressions for the mean occupation number and number fluctuations are obtained in the weak-hopping regime using an interpolation between results from different perturbation approaches in the Mott-insulator and superfluid phases. These analytical results are compared to exact one dimensional numerical calculations using a finite temperature variant of the Density-Matrix Renormalisation Group (DMRG) method and found to have a high degree of accuracy. We also find very good agreement in the crossover ``thermal'' region. With the present approach the magnitude of number fluctuations under realistic experimental conditions can be estimated and the properties of the finite temperature phase diagram can be studied.

4 pages, 1 eps figure, submitted to PRA

References in corpus (4)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Coherent transport of neutral atoms in spin-dependent optical lattice potentials
• Defect-Suppressed Atomic Crystals in an Optical Lattice
• Ultracold atoms in optical lattices

Cited by in corpus (15)

• Cold Bosons in Optical Lattices
• Boson Mott insulators at finite temperatures
• Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition
• Phase Diagram for Ultracold Bosons in Optical Lattices and Superlattices
• Exact number conserving phase-space dynamics of the M-site Bose-Hubbard model
• Excitation spectra of strongly correlated lattice bosons and polaritons
• The one-dimensional Bose-Fermi-Hubbard model in the heavy-fermion limit
• Finite Drude weight for 1D low temperature conductors
• Finite-temperature effects on the number fluctuation of ultracold atoms across the Superfluid to Mott-insulator transition
• Finite-temperature effects on the superfluid Bose-Einstein condensation of confined ultracold atoms in three-dimensional optical lattices
• Slave particle approach to the finite temperature properties of ultracold Bose gases in optical lattices
• Stochastic Simulation of a finite-temperature one-dimensional Bose-Gas: from Bogoliubov to Tonks-Girardeau regime
• Quasiequilibrium Mixture of Itinerant and Localized Bose Atoms in Optical Lattice
• Coherence, Transport, and Chaos in 1D Bose-Hubbard Model: Disorder vs. Stark Potential
• Finite-temperature quantum rotor approach for ultracold bosons in optical lattices