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Physical Review A

Coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment

Yixiao Huang, Qing-Shou Tan, Libin Fu, Xiaoguang Wang

Published Dec 26, 2013• 10 citations
Publisher

Abstract

We investigate the coherence dynamics of a two-mode Bose-Einstein condensate coupled with the environment in the mean-field approximation. We give an analytical result of the time-average coherence in the absence of system-environment coupling, and find that the time-average coherence attains its maximum value at the critical point which corresponds to the boundary between the self-trapping regime and the Josephson oscillation regime. The effect of noise on dynamical coherence is also considered by analyzing the couplings of the condensate to the environment. With the first kind of coupling, the coherence finally stabilizes at a fixed value. Meanwhile, we show that the presence of the noise can even enhance the coherence for some particular interaction. With the second kind of coupling as collisional dephasing, the noise leads a sudden transition of the coherence which then subjects to an exponential decay.

DOI
10.1103/physreva.88.063642

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We study the spread complexity in two-mode Bose-Einstein condensates and unveil that the long-time average of the spread complexity C‾K{\overline{C}}_{K}CK​ can probe the dynamical transition from self-trapping to Josephson oscillation. When the parameter $\ensuremath{\omega}$ increases over a critical value ${\ensuremath{\omega}}_{c}$, we reveal that the spread complexity exhibits a sharp transition from lower to higher value, with the corresponding phase space trajectory changing from self-trapping to Josephson oscillation. Moreover, we scrutinize the eigenspectrum and uncover the relation between the dynamical transition and the excited state quantum phase transition, which is characterized by the emergence of singularity in the density of states at critical energy Ec{E}_{c}Ec​. In the thermodynamical limit, the cross point ${E}_{c}(\ensuremath{\omega})$ and the initial energy ${E}_{0}(\ensuremath{\omega})$ determine the dynamical transition point ${\ensuremath{\omega}}_{c}$. Furthermore, we show that the different dynamical behavior for the initial state at a fixed point can be distinguished by the long-time average of the spread complexity, when the fixed point changes from unstable to stable. Finally, we also examine the sensitivity of C‾K{\overline{C}}_{K}CK​ for the triple-well bosonic model which exhibits the transition from chaotic dynamics to regular dynamics.
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