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arXiv:cond-mat/0205369 · Physical Review A

Many-particle entanglement in two-component Bose-Einstein condensates

Andrea Micheli, Dieter Jaksch, J. I. Cirac, P. Zoller

Published Jan 23, 2003• 264 citations
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Abstract

We investigate schemes to dynamically create many-particle entangled states of a two-component Bose-Einstein condensate in a very short time proportional to $1/N,$ where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for $N>~50.$ We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections.

DOI
10.1103/physreva.67.013607

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We investigate schemes to dynamically create many-particle entangled states of a two-component Bose-Einstein condensate in a very short time proportional to 1/N,1/N,1/N, where N is the number of condensate particles. For small N we compare exact numerical calculations with analytical semiclassical estimates and find very good agreement for N> 50.N>~50.N> 50. We also estimate the effect of decoherence on our scheme, study possible scenarios for measuring the entangled states, and investigate experimental imperfections.
Based on the exact solution of the time-dependent Schrödinger equation for two-species Bose–Einstein condensates (BECs) consisting of two hyperfine states of the atoms coupled by a tuned adiabatic and time-varying Raman coupling, we obtain analytically the entanglement dynamics of the system with various initial states, particularly the SU(2) coherent state, for both of cases with and without the nonlinear interactions. It is shown that the effect of nonlinear interaction on the entanglement appears only in a longer time period depending on the BEC parameters.
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We investigate the time evolution of the entanglement entropy of coupled single-mode Bose-Einstein condensates in a double-well potential at T=0T=0T=0 temperature by combining numerical results with analytical approximations. We find that the coherent oscillations of the condensates result in entropy oscillations on the top of a linear entropy generation at short time scales. Due to dephasing, the entropy eventually saturates to a stationary value, in spite of the lack of equilibration. We show that this long-time limit of the entropy reflects the semiclassical dynamics of the system, revealing the self-trapping phase transition of the condensates at large interaction strength by a sudden entropy jump. We compare the stationary limit of the entropy to the prediction of a classical microcanonical ensemble and find surprisingly good agreement in spite of the nonequilibrium state of the system. Our predictions should be experimentally observable on a Bose-Einstein condensate in a double-well potential or on a two-component condensate with interstate coupling.