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arXiv:cond-mat/0003110 · Physical Review A

Momentum distribution of an interacting Bose-Einstein condensed gas at finite temperature

Anna Minguzzi, Patrizia Vignolo, Mario P. Tosi

Published Jul 17, 2000• 10 citations
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Abstract

We use a semiclassical two-fluid model to study the momentum distribution of a Bose-Einstein condensed gas with repulsive interactions inside a harmonic trap at finite temperature, with specific focus on atomic hydrogen. We give particular attention to the average kinetic energy, which is almost entirely associated with the thermal cloud. A nonlinear dependence of the kinetic energy on temperature is displayed, affording a precise way to assess the temperature of the gas. We also show that the kinetic energy increases with the strength of the interactions, reflecting an enhanced rate of depletion of the condensate with increasing temperature.

DOI
10.1103/physreva.62.023604

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We use a semiclassical two-fluid model to study the momentum distribution of a Bose-Einstein condensed gas with repulsive interactions inside a harmonic trap at finite temperature, with specific focus on atomic hydrogen. We give particular attention to the average kinetic energy, which is almost entirely associated with the thermal cloud. A nonlinear dependence of the kinetic energy on temperature is displayed, affording a precise way to assess the temperature of the gas. We also show that the kinetic energy increases with the strength of the interactions, reflecting an enhanced rate of depletion of the condensate with increasing temperature.
We have investigated experimentally the finite-temperature properties of a Bose-Einstein condensed cloud of 87Rb{}^{87}\mathrm{Rb}87Rb atoms in a harmonic trap. Focusing primarily on condensed fraction and expansion energy, we measure unambiguous deviations from ideal-gas thermodynamics and obtain good agreement with a Hartree-Fock description of the mixed cloud. Our results offer clear evidence of the mutual interaction between the condensed and thermal components. To probe the low-temperature region unaccessible to the usual time-of-flight technique, we use coherent Bragg scattering as a filtering technique for the condensate. This allows us to separate spatially the condensed and normal components in time of flight and to measure reliably temperatures as low as 0.2Tc00.2{T}_{c}^{0}0.2Tc0​ and thermal fractions as low as 10%. Finally, we observe evidence for the limitations of the usual image analysis procedure, pointing out to the need for a more elaborate model of the expansion of the mixed cloud.
Present experiments with Bose condensed gases can be largely described by a semi-ideal two-gas model. In this model, the condensate is influenced only by the mean-field repulsion among condensed atoms, while the thermal cloud is considered an ideal gas confined by an effective potential that consists of the external trap and the mean-field repulsion by the condensate. This simple, intuitive model provides explicit analytical expressions for the density distributions of the condensate and the thermal component. It describes the reduction of the condensate fraction relative to that of an ideal gas as a consequence of the positive chemical potential due to interactions in the condensate.
Abstract This chapter describes the main properties of the ideal Bose gas confined by a harmonic potential. It calculates the temperature dependence of the condensate density and identify the value of the critical temperature in terms of the oscillator frequency and the number of atoms. This identification provides an important temperature scale for experiments with ultracold atomic gases. The chapter also discusses the behaviour of the expanding cloud after the release of the trap and how the anisotropy of the gas evolves in time, reflecting the initial anisotropy of the momentum distribution. It finally discusses the possibility of getting Bose–Einstein condensation through adiabatic transformations, working with non-harmonic trapping potentials or with mixtures of two atomic species trapped by different harmonic potentials.
We devote a particular attention to the role played by the repulsive interaction on the chemical potential of condensed atoms, the chemical potential of non-condensed atoms, the anomalous fraction and the heat specific capacity for Bose gas in harmonic trap. First, we point out that the generalized Hartree-Fock Bogoliubov approximations (GHFB) produces a change in the specific temperature via estimation experience, and we discuss these inadequacies. We calculate a behavior of condensate density in Thomas Fermi approximation, where the thermal cloud is not negligible. Finally, we compare our results with various recent numerical estimates and experience.
Because of experimental interest in the effects of particle interactions in Bose condensates, such as a dilute atomic vapour of 87Rb, we have worked out the momentum distribution in an N-Boson many-body assembly at T = 0, for which both confinement and interbosonic interactions are modelled as purely harmonic. The half-width of the Gaussian momentum distribution is displayed as a function of N and of the strength and sign of the harmonic interactions. The bosonic kinetic energy is finally treated.