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arXiv:cond-mat/0307344 · Journal of Physics B Atomic Molecular and Optical Physics

Three-dimensional simulation of jet formation in collapsing condensates

Weizhu Bao, D Jaksch, Peter A. Markowich

Published Dec 17, 2003• 50 citations
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Abstract

We numerically study the behaviour of collapsing and exploding condensates using the parameters of the experiments by Donley et al (2001 Nature 412 295). Our studies are based on a full three-dimensional numerical solution of the Gross–Pitaevskii equation (GPE) including three-body loss. We determine the three-body loss rate from the number of remnant condensate atoms and collapse times, and obtain only one possible value which fits with the experimental results. We then study the formation of jet atoms by interrupting the collapse, and find very good agreement with the experiment. Furthermore, we investigate the sensitivity of the jets to the initial conditions. According to our analysis, the dynamics of the burst atoms is not described by the GPE with three-body loss incorporated.

DOI
10.1088/0953-4075/37/2/003

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We numerically study the behaviour of collapsing and exploding condensates using the parameters of the experiments by Donley et al (2001 Nature 412 295). Our studies are based on a full three-dimensional numerical solution of the Gross–Pitaevskii equation (GPE) including three-body loss. We determine the three-body loss rate from the number of remnant condensate atoms and collapse times, and obtain only one possible value which fits with the experimental results. We then study the formation of jet atoms by interrupting the collapse, and find very good agreement with the experiment. Furthermore, we investigate the sensitivity of the jets to the initial conditions. According to our analysis, the dynamics of the burst atoms is not described by the GPE with three-body loss incorporated.
The dynamics of collapsing and exploding Bose-Einstein condensates caused by a sudden switch of interactions from repulsive to attractive are studied by numerically integrating the Gross-Pitaevskii equation with atomic loss for an axially symmetric trap. We investigate the decay rate of condensates and the phenomena of bursts and jets of atoms, and compare our results with those of the experiments performed by E. A. Donley et al. [Nature (London) 412, 295 (2001)]. Our study suggests that the condensate decay and the burst production is due to local intermittent implosions in the condensate, and that atomic clouds of bursts and jets are coherent. We also predict nonlinear pattern formation caused by the density instability of attractive condensates.
We perform a systematic numerical study, based on the time-dependent Gross-Pitaevskii equation, of jet formation in collapsing and exploding Bose-Einstein condensates as in the experiment by Donley et al [2001 Nature 412 295]. In the actual experiment, via a Feshbach resonance, the scattering length of atomic interaction was suddenly changed from positive to negative on a pre-formed condensate. Consequently, the condensate collapsed and ejected atoms via explosion. On a disruption of collapse by suddenly changing the scattering length to zero a radial jet of atoms was formed in the experiment. We present a satisfactory account of jet formation under the experimental conditions as well as make predictions beyond experimental conditions which can be verified in future experiments.
We present a consistent picture of the recent JILA experiments on the collapse of a Bose-Einstein condensate (BEC) [E. A. Donley, et al., Nature 412, 295 (2001)] based on a generalized Gross-Pitaevskii equation that incorporates the effect of a three-body loss. The questions we address in this paper are: (1) Why does a BEC survive, albeit partially, after the collapse? (2) Why does the number of the remnant BEC atoms observed at JILA exceed the critical value? (3) What is the origin of the atom burst? (4) What is the origin of the atom jet and is it coherent? We review our predictions on pattern formation in the course of collapse and on the split instability of vortices that can test our collapsing theory.
We perform numerical simulations based on the time-dependent mean-field Gross-Pitaevskii equation to understand some aspects of a recent experiment by Donley et al. [Nature (London) 412, 295 (2001)] on the dynamics of collapsing and exploding Bose-Einstein condensates of 85Rb{}^{85}\mathrm{Rb}85Rb atoms. These authors manipulated the atomic interaction by an external magnetic field via a Feshbach resonance, thus changing the repulsive condensate into an attractive one, and vice versa. In the actual experiment they suddenly changed the scattering length of atomic interaction from a positive to a large negative value on a preformed condensate in an axially symmetric trap. Consequently, the condensate collapsed and ejected atoms via explosion. We find that the present mean-field analysis can explain some aspects of the dynamics of the collapsing and exploding Bose-Einstein condensates.
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We investigate the collapse dynamics of a dipolar condensate of 52Cr atoms when the s-wave scattering length characterizing the contact interaction is reduced below a critical value. A complex dynamics, involving an anisotropic, d-wave symmetric explosion of the condensate, is observed. The atom number decreases abruptly during the collapse. We find good agreement between our experimental results and those of a numerical simulation of the three-dimensional Gross-Pitaevskii equation, including contact and dipolar interactions as well as three-body losses. The simulation indicates that the collapse induces the formation of two vortex rings with opposite circulations.