arXiv:cond-mat/0207308 · Physical Review A

Bose-Einstein condensate collapse: A comparison between theory and experiment

Craig M. Savage, Nicholas P. Robins, J. J. Hope

Published Jan 28, 2003• 67 citations

Abstract

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 ${}^{85}\mathrm{Rb},$ 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.

DOI: 10.1103/physreva.67.014304

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arXiv:cond-mat/0207308 · Physical Review A

Bose-Einstein condensate collapse: A comparison between theory and experiment

Craig M. Savage, Nicholas P. Robins, J. J. Hope

Published Jan 28, 2003• 67 citations

arXiv HTML PDF

Abstract

{}^{85}\mathrm{Rb},

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.

DOI: 10.1103/physreva.67.014304

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Mean-field description of collapsing and exploding Bose-Einstein condensates

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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 ${}^{85}\mathrm{Rb}$ 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.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 ${}^{85}\mathrm{Rb}$ 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 study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two, or three of the scattering lengths ${a}_{\mathrm{ij}}$ for scattering of boson i with j, $i,j=1,2,$ are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.We study the collapse in a coupled Bose-Einstein condensate of two types of bosons 1 and 2 under the action of a trap using the time-dependent Gross-Pitaevskii equation. The system may undergo collapse when one, two, or three of the scattering lengths ${a}_{\mathrm{ij}}$ for scattering of boson i with j, $i,j=1,2,$ are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.

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{}^{85}\mathrm{Rb},

{}^{85}\mathrm{Rb}

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.

{}^{85}

Rb condensates with attractive interactions and find quantitative agreement with the predictions of the Gross-Pitaevskii equation. The collapse data and measurements of the decay of atoms from our condensates allow us to put new limits on the value of the

{}^{85}

Rb three-body loss coefficient

{K}_{3}

at small positive and negative scattering lengths.

We analyze quantum field models of the bosenova experiment, in which

^{85}\mathrm{Rb}

Bose-Einstein condensates were made to collapse by switching their atomic interactions from repulsive to attractive. Specifically, we couple the lowest order quantum field correlation functions to the Gross-Pitaevskii function, and solve the resulting dynamical system numerically. Comparing the computed collapse times with the experimental measurements, we find that the calculated times are much larger than the measured values. The addition of quantum field corrections does not noticeably improve the agreement compared to a pure Gross-Pitaevskii theory.

{a}_{\mathrm{ij}}

for scattering of boson i with j,

i,j=1,2,

are negative representing an attractive interaction. Depending on the parameters of the problem a single or both components of the condensate may experience collapse.