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arXiv:cond-mat/0501248 · Physical Review A

Evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries

Sadhan K. Adhikari

Published May 12, 2005• 11 citations
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Abstract

Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.

DOI
10.1103/physreva.71.053603

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Based on the time-dependent Gross-Pitaevskii equation we study the evolution of a collapsing and exploding Bose-Einstein condensate in different trap symmetries to see the effect of confinement on collapse and subsequent explosion, which can be verified in future experiments. We make a prediction for the evolution of the shape of the condensate and the number of atoms in it for different trap symmetries (cigar to pancake) as well as in the presence of an optical lattice potential. We also make a prediction for the jet formation in different cases when the collapse is suddenly terminated by changing the scattering length to zero via a Feshbach resonance. In addition to the usual global collapse to the center of the condensate, in the presence of an optical-lattice potential one could also have in certain cases independent collapse of parts of the condensate to local centers, which could be verified in experiments.
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 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.
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.
Using the time-dependent mean-field Gross-Pitaevskii equation we study the dynamics of small repulsive Bose-Einstein condensed vortex states of 85Rb{}^{85}\mathrm{Rb}85Rb atoms in a cylindrical trap with low angular momentum $\ensuremath{\Elzxh}L$ per atom (L< 6),(L<~6),(L< 6), when the atomic interaction is suddenly turned attractive by manipulating the external magnetic field near a Feshbach resonance. Consequently, the condensate collapses and ejects atoms via explosion and a remnant condensate with a smaller number of atoms emerges that survives for a long time. Details of this collapse and explosion are compared critically with a similar experiment performed with zero angular momentum (L=0)(L=0)(L=0) by Donley et al. [Nature (London) 412, 295 (2001)]. A suggestion for a future experiment with the vortex state is made.
We solve the Gross-Pitaevskii equation numerically for the collapse induced by a switch from positive to negative scattering lengths. We compare our results with experiments performed with Bose-Einstein condensates of 85Rb,{}^{85}\mathrm{Rb},85Rb, in which the scattering length was controlled using a Feshbach resonance. Building on previous theoretical work we identify quantitative differences between the predictions of mean-field theory and the results of the experiments. In addition to the previously reported difference between the predicted and observed critical atom number for collapse, we also find that the predicted collapse times systematically exceed those observed experimentally.
We investigate the collapse of a trapped dipolar Bose-Einstein condensate. This is performed by numerical simulations of the Gross-Pitaevskii equation and the novel application of the Thomas-Fermi hydrodynamic equations to collapse. We observe regimes of both global collapse, where the system evolves to a highly elongated or flattened state depending on the sign of the dipolar interaction, and local collapse, which arises due to dynamically unstable phonon modes and leads to a periodic arrangement of density shells, disks, or stripes. In the adiabatic regime, where ground states are followed, collapse can occur globally or locally, while in the nonadiabatic regime, where collapse is initiated suddenly, local collapse commonly occurs. We analyze the dependence on the dipolar interactions and trap geometry, the length and time scales for collapse, and relate our findings to recent experiments.