Bose-condensed gases in a 1D optical lattice at finite temperatures

We study equilibrium properties of Bose-Condensed gases in a one-dimensional (1D) optical lattice at finite temperatures. We assume that an additional harmonic confinement is highly anisotropic, in which the confinement in the radial directions is much tighter than in the axial direction. We derive a quasi-1D model of the Gross-Pitaeavskii equation and the Bogoliubov equations, and numerically solve these coupled equations to obtain the condensate fraction as a function of the temperature. We also discuss the importance of the radial excitations in the thermodynamic properties at finite temperatures.