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

Abstract

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

Dimensional crossover of a boson gas in multilayers

“…where N a is the number of bosons contained inside a volume a 3 . Clearly, the first term in (11) is the number of particles N 0 (T ) in the condensed state while the second term is the number of bosons N e in excited states. For T > T c , N 0 (T ) is negligible compared with N while for T < T c it becomes a sizeable fraction of N .…”

“…These systems with planar symmetry have been described in [8,9] and several periodic potentials have been used such as the sinusoidal [10] and the biparabolic [11] with good results only in the low particle energy limit, or in the tight-binding approximation [12]. However, to analyze structural effects like particle trapping between the planes or quasi-2D behavior when plane separation is of the order of half the thermal wavelength, it is necessary to consider a much wider temperature region in which a large number of energy bands needs to be included in the calculation of the system thermodynamic properties.…”

“…Non-relativistic composite bosons in layered structures are found as molecular electron pairs in cuprate superconductors [1], alkaline atoms in optical lattices [2], excitons in multilayered semiconductors [3], exciton polaritons in microcavities [4] or simply as atoms of helium four adsorbed on graphite [5] or any another substrate [6,7]. These systems with planar symmetry have been described in [8,9] and several periodic potentials have been used such as the sinusoidal [10] and the biparabolic [11] with good results only in the low particle energy limit, or in the tight-binding approximation [12]. However, to analyze structural effects like particle trapping between the planes or quasi-2D behavior when plane separation is of the order of half the thermal wavelength, it is necessary to consider a much wider temperature region in which a large number of energy bands needs to be included in the calculation of the system thermodynamic properties.…”

Suppression of the critical temperature for superfluidity near the Mott transition

“…Recently, the question of whether a purely normal cloud could also give rise to such narrow peaks has been raised theoretically, thus ques-tioning the interpretation of this interference pattern as a signature for the appearance of a superfluid component [28,31]. So far, this question could not be settled due to a lack of an accurate thermometry method in the optical lattice potential [32,33]. Here, the direct comparison of the experimental data and the simulations allows to determine a temperature for the ultracold lattice gas.…”

Critical temperature of a Bose gas in an optical lattice

“…with ζ(α) ≡ ζ α (1), as in [6] (also see [19]). A better approximation to g 0 (K) is to use the quadratic shape approximation, g 0 (K) = 6K(W − K)/W 3 a d for 0 < K < W and zero otherwise [20], as shown in Fig.…”