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Modern Physics Letters B

ENTANGLEMENT DYNAMICS OF FLUCTUATIONS IN TWO-MODE BOSE–EINSTEIN CONDENSATES

P. L. Shu, L. C. Wang, X. X. Yi

Published Sep 17, 2010• 0 citations
Publisher

Abstract

The entanglement dynamics of fluctuations in two weakly coupled Bose–Einstein condensates (BECs) is studied in this paper. By calculating the time evolution of entanglement between two fluctuations of condensates in a double-well potential, we show that the nonlinear tunneling transition can be reflected in the entanglement dynamics of fluctuations in BECs. This complements the study on the entanglement dynamics of BECs based on the mean-field approximation.

DOI
10.1142/s0217984910024924

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The entanglement dynamics of fluctuations in two weakly coupled Bose–Einstein condensates (BECs) is studied in this paper. By calculating the time evolution of entanglement between two fluctuations of condensates in a double-well potential, we show that the nonlinear tunneling transition can be reflected in the entanglement dynamics of fluctuations in BECs. This complements the study on the entanglement dynamics of BECs based on the mean-field approximation.
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Coherence dynamics of two-species Bose–Einstein condensates in double wells is investigated in the mean-field approximation. We show that the system can exhibit decoherence phenomena even without the condensate–environment coupling and the variation tendency of the degree of coherence depends not only on the parameters of the system but also the initial states. We also investigate the time evolution of the degree of coherence for a Rosen–Zener form of tunnelling strength, and propose a method to get a condensate system with a certain degree of coherence through a time-dependent tunnelling strength.
The dynamics of the Bose–Einstein condensate (BEC) in a double-well potential is often investigated under the mean-field theory (MFT). This works successfully for large particle numbers with dynamical stability. But for dynamical instabilities, quantum corrections to the MFT becomes important [J. R. Anglin and A. Vardi, Phys. Rev. A64, 013605 (2001)]. Recently the adiabatic dynamics of the double-well BEC is investigated under the MFT in terms of a dark variable [C. Ottaviani et al., Phys. Rev. A81, 043621 (2010)], which generalizes the adiabatic passage techniques in quantum optics to the nonlinear matter-wave case. We give a fully quantized version of it using second-quantization and introduce new correction terms from higher order interactions beyond the on-site interaction, which are interactions between the tunneling particle and the particle in the well and interactions between the tunneling particles. If only the on-site interaction is considered, this reduces to the usual two-mode BEC.
The dynamics of quantum fluctuations of weakly coupled Bose–Einstein condensates (BECs) can be described by an effective Bose–Josephson Hamiltonian. By requiring that the mean-field approximation on this effective Hamiltonian reproduces the low energy dynamics of the Gross–Pitaevskii equation, we obtain parameters for the effective Hamiltonian. This approach is particularly suitable when the BECs are in the Thomas–Fermi regime. Considering the problem of the splitting of a trapped BEC into two BEC fragments, our results for the dynamics of the depletion, collapses and revivals of the phase coherence are in good agreement with a recent numerical microscopic calculation from Streltsov et al (2007 Phys. Rev. Lett. 99 030402). In addition, the excitation energy of the lowest symmetric mode, which is the first relevant mode for the symmetric splitting process, is reproduced with reasonable accuracy all the way from the mean-field Josephson regime to the Fock regime.
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.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the mean-field approximation. Decoherence effects are considered by analyzing the couplings of the condensate to the environment. Two kinds of coupling are taken into account. With the first kind of coupling dominating, decoherence can enhance self-trapping by increasing the damping of the oscillations in the dynamics, while decoherence from the second kind of condensate-environment coupling leads to spoiling of the quantum tunneling and self-trapping.