Thermodynamics of noninteracting bosonic gases in cubic optical lattices versus ideal homogeneous Bose gases

TL;DR

This paper analyzes the thermodynamic behavior of noninteracting bosonic gases in cubic optical lattices, revealing weak temperature dependence and near-linear power laws in the condensed phase, with results useful for experiments and theoretical models.

Contribution

It provides explicit thermodynamic expressions and numerical analysis for bosonic gases in optical lattices, highlighting differences from homogeneous gases and effects of filling factors.

Findings

Entropy and energy depend weakly on temperature in the normal phase.

In the condensed phase, thermodynamic quantities show nearly linear power dependence on reduced temperature.

The specific heat discontinuity decreases with increasing filling factor, approximately inversely proportional to it.

Abstract

We have studied thermodynamic properties of noninteracting gases in periodic lattice potential at arbitrary integer fillings and compared them with that of ideal homogeneous gases. Deriving explicit expressions for thermodynamic quantities and performing exact numerical calculations we have found that the dependence of e.g. entropy and energy on the temperature in the normal phase is rather weak. In the Bose condensed phase their power dependence on the reduced temperature is nearly linear, which is in contrast to that of ideal homogeneous gases. We evaluated the discontinuity in the slope of the specific heat which turned out to be approximately the same as that of the ideal homogeneous Bose gas for filling factor $\nu=1$. With increasing $\nu$ it decreases as the inverse of $\nu$. These results may serve as a checkpoint for various experiments on optical lattices as well as theoretical studies of weakly interacting Bose systems in periodic potentials being a starting point for perturbative calculations.