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Europhysics Letters (EPL)

Observation of interaction dynamics in finite-temperature Bose condensed atom clouds

B. D. Busch, Chien Liu, Zachary Dutton, C. H Behroozi, Lene Vestergaard Hau

Published Sep 1, 2000• 8 citations
Publisher

Abstract

We present measurements of finite-temperature atom clouds cooled below the transition temperature for Bose-Einstein condensation. We study the dynamics of the interface region between the Bose condensed and noncondensed components of the atom clouds, where the time-dependent density profile is highly sensitive to interactions between the two components. We observe directly the effects of repulsion from the condensate on the dynamics of noncondensed atoms. The measurements are compared to calculations based on Hartree-Fock-Bogoliubov mean-field theory. We infer a value for the spatial second-order correlation function for noncondensed atoms of g 0,NC (2) ( r = 0) = 1.8 ± 0.3.

DOI
10.1209/epl/i2000-00363-0

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We present measurements of finite-temperature atom clouds cooled below the transition temperature for Bose-Einstein condensation. We study the dynamics of the interface region between the Bose condensed and noncondensed components of the atom clouds, where the time-dependent density profile is highly sensitive to interactions between the two components. We observe directly the effects of repulsion from the condensate on the dynamics of noncondensed atoms. The measurements are compared to calculations based on Hartree-Fock-Bogoliubov mean-field theory. We infer a value for the spatial second-order correlation function for noncondensed atoms of g 0,NC (2) ( r = 0) = 1.8 ± 0.3.
We present a detailed study of the temperature dependence of the condensate and noncondensate density profiles of a Bose-condensed gas in a parabolic trap. These quantities are calculated self-consistently using the Hartree-Fock-Bogoliubov equations within the Popov approximation. Below the Bose-Einstein transition the excitation frequencies have a relatively weak temperature dependence even though the condensate is strongly depleted. As the condensate density goes to zero through the transition, the excitation frequencies are strongly affected and approach the frequencies of a noninteracting trapped gas in the high temperature limit.
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We study the effects of quantum and thermal fluctuations on Bose-Bose mixtures at finite temperature employing the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory. The theory governs self-consistently the motion of the condensates, the noncondensates, and of the anomalous components on an equal footing. The finite temperature criterion for the phase separation is established. We numerically analyze the temperature dependence of different densities for both miscible and immiscible mixtures. We show that the degree of the overlap between the two condensates and the thermal clouds is lowered and the relative motion of the centers of mass of the condensed and thermal components is strongly damped due to the presence of the pair anomalous fluctuations. Our results are compared with previous theoretical and experimental findings. On the other hand, starting from our TDHFB equations, we develop a random-phase theory for the elementary excitations in a homogeneous mixture. We find that the normal and anomalous fluctuations may lead to enhance the excitations and the thermodynamics of the system.
In contrast with Chapter 2, in this chapter we include the dynamics of the thermal cloud. As noted in Chapter 1, we treat the noncondensate atoms using the simplest microscopic model approximation that captures the important physics. In particular, we consider only temperatures high enough ( T ≥ 0.4 T BEC ) that the noncondensate atoms can be described by a particle-like Hartree–Fock (HF) spectrum. To extend the analysis to very low temperatures is in principle straightforward (see Chapter 7). However, the details are more complicated since the excitations of the thermal cloud take on a collective aspect (i.e. a Bogoliubov-type quasiparticle spectrum must be used). In trapped Bose gases, the HF single-particle spectrum gives a good approximation down to much lower temperatures than in the case of uniform Bose gases, as first emphasized by Giorgini et al . (1997). In Section 3.1, we derive a generalized form of the Gross–Pitaevskii equation for the Bose order parameter Φ( r , t ) that is valid at finite temperatures. It involves terms that are coupled to the noncondensate component (the thermal cloud) and thus its solution in general requires one to know the equations of motion for the dynamics of the noncondensate atoms. In Section 3.2 we restrict ourselves to finite temperatures high enough that the noncondensate atoms can be described by a quantum kinetic equation for the single-particle distribution function f ( p, r , t ). A detailed microscopic derivation of this kind of kinetic equation is given in Chapters 6 and 7 using the Kadanoff–Baym Green's function formalism. A characteristic feature of a Bose-condensed gas is that the kinetic equation governing f ( p, r , t ) involves a collision integral C 12 [ f , Φ] describing collisions between condensate and noncondensate atoms.
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.