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arXiv:cond-mat/0112292

The Damping of the Bose-Condensate Oscillations in a Trap at Zero Temperature

Yu. Kagan, Leonid A. Maksimov

Published Dec 16, 2001• 1 citation
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Abstract

We discuss an existence of the damping for the radial condensate oscillations in a cylindric trap at zero temperature. The damping is a result of the parametric resonance leading to energy transfer from the coherent condensate oscillations to the longitudinal sound waves within a finite frequency interval. The parametric resonance is due to the oscillations of the sound velocity. The triggering amplitudes at zero temperature are associated with the zero-point oscillations.

DOI
10.48550/arxiv.cond-mat/0112292

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We discuss an existence of the damping for the radial condensate oscillations in a cylindric trap at zero temperature. The damping is a result of the parametric resonance leading to energy transfer from the coherent condensate oscillations to the longitudinal sound waves within a finite frequency interval. The parametric resonance is due to the oscillations of the sound velocity. The triggering amplitudes at zero temperature are associated with the zero-point oscillations.
A general system of nonlinear equations describing the nondissipative evolution of an oscillating Bose condensate is presented. The relaxation of the transverse oscillations of the condensate in a trap of cylindrical symmetry is considered. The evolution is due to the parametric resonance coupling the transverse mode with the longitudinal ones. Nonlinear rescattering in the subsystem of discrete longitudinal modes leads to the suppression of back energy recovery, generating the nondissipative nonmonotonic relaxation of the transverse oscillations of the condensate.
Using the explicit numerical solution of the axially symmetric Gross–Pitaevskii equation, we study the oscillation of the Bose–Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a. When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC. 1.
Using the explicit numerical solution of the axially symmetric Gross–Pitaevskii equation, we study the oscillation of the Bose–Einstein condensate (BEC) induced by a periodic variation in the atomic scattering length a . When the frequency of oscillation of a is an even multiple of the radial or axial trap frequency, respectively, the radial or axial oscillation of the condensate exhibits resonance with a novel feature. In this nonlinear problem without damping, at resonance in the steady state the amplitude of oscillation passes through a maximum and minimum. Such a growth and decay cycle of the amplitude may keep on repeating. Similar behaviour is also observed in a rotating BEC.
Whole excitation spectrum is calculated within the Popov approximation of the Bogoliubov theory for a cylindrical symmetric Bose-Einstein gas trapped radially by a harmonic potential. The full dispersion relation and its temperature dependence of the zero sound mode propagating along the axial direction are evaluated in a self-consistent manner. The sound velocity is shown to depend not only on the peak density, but also on the axial area density. Recent sound velocity experiment on Na atom gas is discussed in light of the present theory.
Collective excitations of a dilute Bose gas were probed above and below the Bose-Einstein condensation temperature. The temperature dependencies of the frequency and damping rates of condensate oscillations indicate significant interactions between the condensate and the thermal cloud. Hydrodynamic oscillations of the thermal cloud were observed, constituting first sound. An antisymmetric dipolar oscillation of the thermal cloud and the condensate was studied, representing the bulk flow of a superfluid through the normal fluid. The excitations were observed in situ using non-destructive imaging techniques.