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Chinese Physics B

Phase transition of Bose—Einstein condensate under decoherence

Qiang Zheng, Shan-Feng Yi, Changgang Hu

Published Feb 1, 2014• 0 citations
Publisher

Abstract

The effect of decoherence on the phase transition of a Bose—Einstein condensate in a symmetric double-well potential is determined by the mean atom number difference. It still has two phases, the tunneling phase and the self-trapping phase, even under decoherence. The density matrix and the operator fidelity also show very different behaviors in the two phases. This suggests that operator fidelity can be used to characterize the phase transition of this Bose—Einstein condensate model, even under decoherence.

DOI
10.1088/1674-1056/23/2/026401

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The effect of decoherence on the phase transition of a Bose—Einstein condensate in a symmetric double-well potential is determined by the mean atom number difference. It still has two phases, the tunneling phase and the self-trapping phase, even under decoherence. The density matrix and the operator fidelity also show very different behaviors in the two phases. This suggests that operator fidelity can be used to characterize the phase transition of this Bose—Einstein condensate model, even under decoherence.
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.
We investigate the nonlinear self-trapping phenomenon of a Bose-Einstein condensate (BEC) in a symmetric double well, emphasizing its underlying dynamical phase transition. As the nonlinear parameter characterizing the interaction between the degenerate atoms increases, the BEC becomes self-trapped, manifesting an asymmetric distribution of the atomic density profile. The essence of this phenomenon is revealed to be a continuous phase transition and the underlying critical behavior is studied analytically and found to follow a logarithmic scaling law. We then go beyond the mean-field treatment and extend our treatment to discuss the effect of many-body quantum fluctuations on the transition. It is found that the transition point is shifted and the scaling law is broken. In particular, the quantum phase transition is accompanied by a change of the entanglement entropy, which is found to reach a maximum at the transition point. The underlying physics is revealed.
We discuss the dynamics of Bose-Einstein condensates in a double-well potential subject to decoherence (or particle loss). Starting from the full many-body dynamics described by the master equation, an effective Gross-Pitaevskii-like equation is derived in the mean-field approximation. By numerically solving the GP equation, we find that macroscopic quantum self-trapping disappears for strong decoherence, while generalized self-trapping occurs under weak decoherence. The fixed points have been calculated, and we find that an abrupt change from elliptic to an attractor and a repeller occurs, reflecting the metastable behavior of the system around these points.
In the framework of semi-classical theory,the author plots and analyzes the dynamical behaviors of Bose-Einstein condensate when initial phase difference is 0 and π,respectively,in a symmetric trap in weak interaction,without damping effects and periodical modulation.For the system is conservative,atoms never stop random oscillations in critical states instead of stopping automatically oscillations with damping effects.Atomic oscillations display properties of both Josephson oscillation and self-trapping oscillation in critical states between these two kinds of oscillation,and two kinds of properties of self-trapping oscillation in critical states between π phase mode self-trapping oscillation and running phase mode self-trapping oscillation.
Abstract Some dynamical features of partially coherent Bose‐Einstein condensate systems confined in double‐well potentials are investigated in mean field approximation. For one‐component system, the phenomena of self‐trapping is studied and it is shown that the partially coherent system, like completely coherent one, can also exhibit self‐trapping phenomena which are affected by both the degree of coherence and the initial relative phase. The adiabatic properties are also studied by introducing the fidelity for mixed state. It is shown that the introduced fidelity can characterize the adiabatic condition of the partially coherent system. For two‐component system, the time evolution of the degree of coherence for a time‐dependent tunneling strength is investigated. The corresponding results imply that the degree of coherence for such a two‐component system can exhibit decoherence phenomena even without the condensate‐environment coupling.
We study the dynamics of a Bose-Einstein condensate in a double-well potential in the two-mode approximation. The dissipation of energy from the condensate is described by the coupling to a thermal reservoir of noncondensate modes. As a consequence of the coupling, the self-locked population imbalance in the macroscopic quantum self-trapping decays away. We show that a coherent state predicted by spontaneous symmetry breaking is not robust and decoheres rapidly into a statistical mixture due to the interactions between condensate and noncondensate atoms. However, via stochastic simulations we find that with a sufficiently fast measurement rate of the relative phase between the two wells the matter wave coherence is established even in the presence of the decoherence.