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Journal of Physics B Atomic Molecular and Optical Physics

Non-Thomas–Fermi behaviour of a finite-temperature Bose–Einstein condensate in the presence of a thermal cloud

Smain Kouidri, Mohamed Benarous

Published Sep 23, 2011• 6 citations
Publisher

Abstract

We analyse numerically the finite-temperature behaviour of a dilute trapped Bose gas containing a large number of atoms. The generalized Hartree–Fock–Bogoliubov approximation is used to take into account the mutual interactions between the condensate and the thermal cloud. We confront our results with recent experiments and literature and explain in particular the experimentally observed departure from the Thomas–Fermi regime for the condensate radius and the aspect ratio. This clearly illustrates the compression effect of the thermal cloud on the condensate.

DOI
10.1088/0953-4075/44/20/205301

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We analyse numerically the finite-temperature behaviour of a dilute trapped Bose gas containing a large number of atoms. The generalized Hartree–Fock–Bogoliubov approximation is used to take into account the mutual interactions between the condensate and the thermal cloud. We confront our results with recent experiments and literature and explain in particular the experimentally observed departure from the Thomas–Fermi regime for the condensate radius and the aspect ratio. This clearly illustrates the compression effect of the thermal cloud on the condensate.
A simple picture describes the results of recent treatments of partially--condensed, dilute, trapped Bose gases at temperature T > 0. The condensate wave function is nearly identical to that of a T = 0 condensate with the same number of condensate atoms, Ν0.The cloud of non-condensed atoms is described by the statistical mechanics of an ideal Bose gas in the com- bined potentials of the magnetic trap and the cloud-condensate interaction.We provide a physical motivation for this result, show how it emerges in the Hartree-Fock-Bogo liubov-Popov approximation, and explore some of its implications for future experiments.
We derive a description of the spatially inhomogeneous Bose-Einstein condensate, treating the system locally as a homogeneous Bose gas. This approach, similar to the Thomas-Fermi model for the inhomogeneous many-particle fermion system, is well suited to describe the atomic Bose-Einstein condensates that have recently been obtained experimentally through atomic trapping and cooling. In this paper, we confine our attention to the zero-temperature case, although the treatment can be generalized to finite temperatures, as we shall discuss elsewhere. Several features of this approach, which we shall call the Thomas-Fermi-Bogoliubov description, are very attractive. (i) It is simpler than the Hartree-Fock-Bogoliubov technique. We can obtain analytical results in the case of weakly interacting bosons for quantities such as the chemical potential, the local depletion, pairing, pressure, and density of states. (ii) The method provides an estimate for the error due to the inhomogeneity of the Bose-condensed system. This error is a local quantity so that the validity of the description for a given trap and a given number of trapped atoms can be tested as a function of position. We see, for example, that at the edge of the condensate the Thomas-Fermi-Bogoliubov theory always breaks down. (iii) The Thomas-Fermi-Bogoliubov description can be generalized to treat the statistical mechanics of the Bose gas at finite temperatures.
Abstract Using the time-dependent Hartree–Fock–Bogoliubov approach, where the condensate is coupled with the thermal cloud and the anomalous density, we study the equilibrium and the dynamical properties of three-dimensional quantum-degenerate Bose gas at finite temperature. Effects of the anomalous correlations on the condensed fraction and the critical temperature are discussed. In uniform Bose gas, useful expressions for the Bogoliubov excitations spectrum, the first and second sound, the condensate depletion and the superfluid fraction are derived. Our results are tested by comparing the findings computed by quantum Monte Carlo simulations. We present also a systematic investigation of the collective modes of a Bose condensate confined in an external trap. Our predictions are in qualitative agreement with previous experimental and theoretical results. We show in particular that our theory is capable of explaining the so-called anomalous behavior of the m = 0 mode.
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We show that recent treatments of magnetically trapped Bose-Einstein condensates (BECs) at temperature T >0 fit a simple picture: the condensate wavefunction is that of a T = 0 BEC with the appropriate (depleted) number of condensate atoms N 0 , and the surrounding thermal cloud is described by the statistical mechanics of an ideal gas in the combined potentials of the magnetic trap and the cloud-condensate interaction. Even a simple classical description of the cloud reproduces its essential outline, and facilitates easy approximate calculations of BEC properties for T >0.