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The dynamics of collapsing Bose-Einstein condensates.

Douglas Grimm

Published Jan 1, 2002• 0 citations
Publisher

Abstract

This project aims to study the behavior of a cloud of Rubidium-85 atoms under an attractive interaction potential when used to create a Bose-Einstein condensate. Efforts to describe the dynamics of an attractive condensate using only the Gross-Pitaevskii equation have been unable to describe all of the features of such a system, and so the mathematical approach used is a perturbative method of corrections to the Gross-Pitaevskii equation. A system of analytical equations to describe a condensate is derived herein, which is then arranged into a form suitable for numerical solution. The actual calculation is not performed, but details of the computational procedure are provided, as well as an analysis of the difficulties inherent in the calculation.

DOI
10.25911/5d7a28a76fb1a

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This project aims to study the behavior of a cloud of Rubidium-85 atoms under an attractive interaction potential when used to create a Bose-Einstein condensate. Efforts to describe the dynamics of an attractive condensate using only the Gross-Pitaevskii equation have been unable to describe all of the features of such a system, and so the mathematical approach used is a perturbative method of corrections to the Gross-Pitaevskii equation. A system of analytical equations to describe a condensate is derived herein, which is then arranged into a form suitable for numerical solution. The actual calculation is not performed, but details of the computational procedure are provided, as well as an analysis of the difficulties inherent in the calculation.
A variational technique is applied to solve the time-dependent nonlinear Schr\"odinger equation (Gross-Pitaevskii equation) with the goal to model the dynamics of dilute ultracold atom clouds in the Bose-Einstein condensed phase. We derive analytical predictions for the collapse, equilibrium widths, and evolution laws of the condensate parameters and find them to be in very good agreement with our numerical simulations of the nonlinear Schr\"odinger equation. It is found that not only the number of particles, but also both the initial width of the condensate and the effect of different perturbations to the condensate may play a crucial role in the collapse dynamics. The results are applicable when the shape of the condensate is sufficiently simple.
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 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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