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arXiv:1108.2561 · Physical Review A

Collapse and three-body loss in a 85 Rb Bose-Einstein condensate

P. A. Altin, G. R. Dennis, Gordon McDonald, D. Döring, J. E. Debs, J. D. Close, Craig M. Savage, Nicholas P. Robins

Published Sep 26, 2011• 56 citations
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Abstract

Collapsing Bose-Einstein condensates are rich and complex quantum systems for which quantitative explanation by simple models has proved elusive. We present experimental data on the collapse of high-density ${}^{85}$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.

DOI
10.1103/physreva.84.033632

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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 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 aij{a}_{\mathrm{ij}}aij​ for scattering of boson i with j, i,j=1,2,i,j=1,2,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.
Evolution and collapse of a trapped Bose condensate with negative scattering length are predetermined by 3-body recombination of Bose-condensed atoms and by feeding of the condensate from the nonequilibrium thermal cloud. The collapse, starting once the number of condensate atoms reaches the critical value, ceases and turns to expansion when the density becomes so high that the recombination losses dominate over attractive interparticle interaction. As a result, we obtain a sequence of collapses, each of them followed by dynamic oscillations of the condensate. In every collapse the 3-body recombination burns only a part of the Bose-condensed atoms.
We study the collapse of an attractive Bose-Einstein condensate, where an unstable system evolves towards a singularity, by numerically solving the underlying cubic-quintic nonlinear Schrödinger equation. We find good agreement between our simulations and the atom-loss measurements with a K 39 condensate. Our simulations reveal an interplay of weak collapse and the propensity of the system to form a hotspot and we uncover scaling laws that govern this behavior. We also identify promising signatures of the theoretically predicted, but so far experimentally elusive, elastic three-body interactions.
In this paper, we present a theoretical study of a two-component Bose-Einstein condensate composed of ytterbium (Yb) isotopes in a three-dimensional anisotropic harmonic potential. The condensate consists of a mixture of 176Yb^{176}\mathrm{Yb}176Yb atoms which have a negative sss-wave scattering length and 174Yb^{174}\mathrm{Yb}174Yb atoms having a positive sss-wave scattering length. We study the ground-state as well as dynamic properties of this two-component condensate. Due to the attractive interactions between 176Yb^{176}\mathrm{Yb}176Yb atoms, the condensate of 176Yb^{176}\mathrm{Yb}176Yb undergoes a collapse when the particle number exceeds a critical value. The critical number and the collapse dynamics are modified due to the presence of 174Yb^{174}\mathrm{Yb}174Yb atoms. We use coupled two-component Gross-Pitaevskii equations to study the collapse dynamics. The theoretical results obtained are in reasonable agreement with the experimental results of Fukuhara et al. [Phys. Rev. A 79, 021601(R) (2009)].
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.