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Physical Review A

Quasiparticle instabilities in multicomponent atomic condensates

Elena V. Goldstein, Pierre Meystre

Published Apr 1, 1997• 145 citations
Publisher

Abstract

We extend the Hartree-Bogoliubov theory to the case of a multicomponent Bose condensate and determine the resulting quasiparticle frequency spectrum. We show that interferences resulting from cross coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.

DOI
10.1103/physreva.55.2935

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We extend the Hartree-Bogoliubov theory to the case of a multicomponent Bose condensate and determine the resulting quasiparticle frequency spectrum. We show that interferences resulting from cross coupling between the condensate components can lead to a reversal of the sign of the effective two-body interaction and to the onset of spatial instabilities.
We propose and analyze a way in which effective multicomponent condensates can be created inside high-QQQ multimode cavities. In contrast to the situation involving several atomic species or levels, the coupling between the various components of the dressed condensates is linear. We predict analytically and confirm numerically the onset of instabilities in the quasiparticle excitation spectrum.
We analyze the mean-field equilibrium states of a homogeneous Bose-Einstein condensate of boson particles in different internal states, possibly in the presence of an internal Josephson interaction, and we describe the quantum fluctuations by constructing an explicit form of the Bogoliubov transformation that characterizes the quasiparticle excitations of the system. The derivation of the Bogoliubov transformation is based on a simple geometrical picture which leads to a convenient parametrization of the transformation. Our calculations of physical properties, such as depletions and phonon velocities, as well as our discussion of stability, indicate the sense and the extent to which the internal Josephson interaction controls the many-body physics of multicomponent phase coherent matter.
Abstract We report the effects of anisotropy in the confining potential on two component Bose–Einstein condensates (TBECs) through the properties of the low energy quasiparticle excitations. Starting from generalized Gross–Pitaevskii equation, we obtain the Bogoliubov–de Gennes equation for TBECs using the Hartree–Fock–Bogoliubov theory. Based on this theory, we present the influence of radial anisotropy on TBECs in the immiscible or the phase-separated domain. In particular, the TBECs of 85 Rb– 87 Rb and 133 Cs– 87 Rb TBECs are chosen as specific examples of the two possible interface geometries, shell-structured and side by side, in the immiscible domain. We also show that the dispersion relation for the TBEC shell-structured interface has two branches, and anisotropy modifies the energy scale and structure of the two branches.
We analyze a Bose-Einstein condensate (BEC) mixed with a superfluid two-component Fermi gas in the whole BCS-BEC crossover. Using a quasiparticle random-phase approximation combined with Beliaev theory to describe the Fermi superfluid and the BEC, respectively, we show that the single-particle and collective excitations of the Fermi gas give rise to an induced interaction between the bosons, which varies strongly with momentum and frequency. It diverges at the sound mode of the Fermi superfluid, resulting in a sharp avoided crossing feature and a corresponding sign change of the interaction energy shift in the excitation spectrum of the BEC. In addition, the excitation of quasiparticles in the Fermi superfluid leads to damping of the excitations in the BEC. Besides studying induced interactions themselves, we can use these prominent effects to systematically probe the strongly interacting Fermi gas.
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.