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arXiv:cond-mat/0204538 · Physical Review A

Dynamic depletion in a Bose-Einstein condensate via a sudden increase of the scattering length

C. K. Law, P. T. Leung, M.-C. Chu

Published Sep 16, 2002• 6 citations
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Abstract

We examine the time-dependent quantum depletion of a trapped Bose-Einstein condensate arising from a rapid increase of the scattering length. Our solution indicates that a significant buildup of incoherent atoms can occur within a characteristic time that is short compared with the harmonic trap period. We discuss how the depletion density and the characteristic time depend on the physical parameters of the condensate.

DOI
10.1103/physreva.66.033605

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arXiv:cond-mat/9611207•Physical Review A•May 1, 1997•8 citations
We examine the time-dependent quantum depletion of a trapped Bose-Einstein condensate arising from a rapid increase of the scattering length. Our solution indicates that a significant buildup of incoherent atoms can occur within a characteristic time that is short compared with the harmonic trap period. We discuss how the depletion density and the characteristic time depend on the physical parameters of the condensate.
We discuss the response of a Bose-Einstein condensate to a change in the scattering length, which is experimentally realized by tuning the magnetic field near a Feshbach resonance. In particular, we consider the collapse of the condensate induced by a sudden change in the scattering length from a large positive to a small negative value. We also consider the condensate dynamics that results from a single pulse in the magnetic field, due to which the scattering length is rapidly increased from zero to a large value and then after some time rapidly decreased again to its initial value. We focus primarily on the consequences of the quantum evaporation process on the dynamics of the Bose-Einstein condensate, but also discuss the effects of atom-molecule coherence.
We discuss Bose-Einstein condensation in a trapped atomic gas and analyze how the sign of the scattering length a and the ratio \ensuremath{\eta} of the interaction between particles to the level spacing in the trap influence the behavior of the condensate wave function ${\ensuremath{\psi}}_{0}$. We find that for a<0a<0a<0 and $\ensuremath{\eta}\ensuremath{\ll}1$ it is possible to form a metastable Bose condensate, with a long characteristic lifetime with respect to contraction and transitions of particles to excited trap states. For $\ensuremath{\eta}\ensuremath{\gg}1$ a negative scattering length prevents the formation of the condensate. If a>0a>0a>0, then an increase of density is accompanied by the evolution of ${\ensuremath{\psi}}_{0}$ to a comparatively wide quasihomogeneous distribution.
We reinvestigate the dynamics of the grow and collapse of Bose-Einstein condensates in a system of trapped ultracold atoms with negative scattering lengths, and found a new behavior in the long time scale evolution: the number of atoms can go far beyond the static stability limit. The condensed state is described by the solution of the time-dependent nonlinear Schr\"odinger equation, in a model that includes atomic feeding and three-body dissipation. Our results for the model show that, by changing the feeding parameter and when a substantial depletion of the ground-state exists, a chaotic behavior is found. We consider a criterion proposed by Deissler and Kaneko [Phys. Lett. A 119, 397 (1987)] to diagnose spatiotemporal chaos.
Quantum evolution of a collective mode of a Bose-Einstein condensate containing a finite number N of particles can demonstrate the phenomena of collapses and revivals. The characteristic collapse time depends on the scattering length, the initial amplitude of the mode, and N. The corresponding time values have been derived analytically under certain approximations and numerically for the parabolic atomic trap. The revival of the mode amplitude at a time of several seconds, as direct evidence of the effect, can occur if the normal component is significantly suppressed.