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

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

2003-09-25

arxiv.org/abs/cond-mat/0309587v1

Physics

Condensed Matter

Soft Condensed Matter

4 pages, 1 eps figure, submitted to PRA

Scientific paper

10.1103/PhysRevA.70.013611

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.

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