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arXiv:cond-mat/0011526 · Physical Review A

Coupled Bose-Einstein condensate: Collapse for attractive interaction

Sadhan K. Adhikari

Published Mar 20, 2001• 50 citations
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Abstract

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.

DOI
10.1103/physreva.63.043611

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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 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.
We present a numerical study of the coupled time-dependent Gross-Pitaevskii equation, which describes the Bose-Einstein condensate of several types of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. The same approach is used to study both stationary and time-evolution problems. We consider up to four types of atoms in the study of stationary problems. We consider the time-evolution problems where the frequencies of the traps or the atomic scattering lengths are suddenly changed in a stable preformed condensate. We also study the effect of periodically varying these frequencies or scattering lengths on a preformed condensate. These changes introduce oscillations in the condensate, which are studied in detail. Good convergence is obtained in all cases studied.
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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)].
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We study the mechanisms of collapse of the condensate wave function in the Gross-Pitaevskii theory with attractive interparticle interaction. We reformulate the Gross-Pitaevskii equation as Newton's equations for a flux of particles, and introduce the collapsing fraction of particles. We assume that this collapsing fraction is expelled from the condensate due to dissipation. Using this hypothesis we analyze the dependence of the collapse behavior on the initial conditions. We find that, for a properly chosen negative scattering length, the remnant fraction of atoms becomes larger when the initial aspect ratio of the condensate is increased.