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In current experiments with cold quantum gases in periodic potentials,interference fringe contrast is typically the easiest signal in which to lookfor effects of non-trivial many-body dynamics. In order better to calibratesuch measurements, we analyse the background effect of thermal decoherence asit occurs in the absence of dynamical interparticle interactions. We study theeffect of optical lattice potentials, as experimentally applied, on thecondensed fraction of a non-interacting Bose gas in local thermal equilibriumat finite temperatures. We show that the experimentally observed decrease ofthe condensate fraction in the presence of the lattice can be attributed, up toa threshold lattice height, purely to ideal gas thermodynamics; conversely weconfirm that sharper decreases in first-order coherence observed in strongerlattices are indeed attributable to many-body physics. Our results also suggestthat the fringe visibility 'kinks' observed in F.Gerbier et al., Phys. Rev.Lett. 95, 050404 (2005) may be explained in terms of the competition betweenincreasing lattice strength and increasing mean gas density, as the gaussianprofile of the red-detuned lattice lasers also increases the effective strengthof the harmonic trap.

Finite temperature coherence of the ideal Bose gas in an optical lattice