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arXiv:cond-mat/0109463 · Physical Review A

Quantum effects on dynamics of instabilities in Bose-Einstein condensates

Vladimir Yurovsky

Published Feb 6, 2002• 57 citations
arXivHTMLPDF

Abstract

Dynamics of fluctuations in unstable Bose-Einstein condensates is analyzed by the solution of approximate operator equations. In the case of a condensate with a negative scattering length the present treatment describes a delay of collapse, in agreement with recent experiments. In the case of a collision of two condensate wave packets it is shown that quantum effects lead to a Bose enhancement of elastic-scattering losses. In both cases the noncondensate atoms are formed as entangled pairs in squeezed states.

DOI
10.1103/physreva.65.033605

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Dynamics of fluctuations in unstable Bose-Einstein condensates is analyzed by the solution of approximate operator equations. In the case of a condensate with a negative scattering length the present treatment describes a delay of collapse, in agreement with recent experiments. In the case of a collision of two condensate wave packets it is shown that quantum effects lead to a Bose enhancement of elastic-scattering losses. In both cases the noncondensate atoms are formed as entangled pairs in squeezed states.
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Superfluid suppression of the elastic scattering loss in atomic Bose condensed systems can be significant when the ratio of the relative velocity of the wave packets to the critical velocity is $\ensuremath{\sim}1.$ We show how to incorporate the effect of such losses and their suppression into the time-dependent dynamics of two colliding condensate wave packets. We illustrate the magnitude of the effect through three-dimensional simulations of the collision dynamics of an ∣F=2,MF=2〉|F=2,{M}_{F}=2〉∣F=2,MF​=2〉 with an ∣F=2,MF=1〉87Rb|F=2,{M}_{F}=1〉{}^{87}\mathrm{Rb}∣F=2,MF​=1〉87Rb condensate in a harmonic trap, as studied in a recent experiment [Maddaloni et al., Phys. Rev. Lett. 85, 2413 (2000)]. These calculations show that the effect of elastic scattering and its suppression should be seen in the oscillatory center-of-mass amplitude of the MF=1{M}_{F}=1MF​=1 wave packet for suitable experimental conditions.
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We consider the dynamics of a quantum degenerate trapped gas of 7Li{}^{7}\mathrm{Li}7Li atoms. Because the atoms have a negative sss-wave scattering length, a Bose condensate of 7Li{}^{7}\mathrm{Li}7Li becomes mechanically unstable when the number of condensate atoms approaches a maximum value. We calculate the dynamics of the collapse that occurs when the unstable point is reached. In addition, we use the quantum Boltzmann equation to investigate the nonequilibrium kinetics of the atomic distribution during and after evaporative cooling. The condensate is found to undergo many cycles of growth and collapse before a stationary state is reached.
Bragg diffraction of atoms by light waves can create high momentum components in a Bose-Einstein condensate. Collisions between atoms from two distinct momentum wave packets cause elastic scattering that can remove a significant fraction of atoms from the wave packets and cause the formation of a spherical shell of scattered atoms. We develop a slowly varying envelope technique that includes the effects of this loss on the condensate dynamics described by the Gross-Pitaevski equation. Three-dimensional numerical calculations are presented for two experimental situations: passage of a moving daughter condensate through a nonmoving parent condensate, and four-wave mixing of matter waves.
Bragg diffraction divides a Bose-Einstein condensate into two overlapping components, moving with respect to each other with high momentum. Elastic collisions between atoms from distinct wave packets can significantly deplete the condensate. Recently, Zi\ifmmode \acute{n}\else \'{n}\fi{} et al. [Phys. Rev. Lett. 94, 200401 (2005)] introduced a model of two counterpropagating atomic Gaussian wave packets incorporating the dynamics of the incoherent scattering processes. Here we study the properties of this model in detail, including the nature of the transition from spontaneous to stimulated scattering. Within the first-order approximation, we derive analytical expressions for the density matrix and anomalous density that provide excellent insight into correlation properties of scattered atoms.