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arXiv:0811.4337 · Physical Review A

Nonlinear dynamics of a cigar-shaped Bose-Einstein condensate in an optical cavity

J. M. Zhang, Fu-Cheng Cui, D. L. Zhou, W. M. Liu

Published Mar 3, 2009• 68 citations
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Abstract

We investigate the nonlinear dynamics of a combined system which is composed of a cigar-shaped Bose-Einstein condensate and an optical cavity with the two sides coupled dispersively. This system is characterized by the cavity-induced nonlinearity; after integrating out the fast degree of freedom of the cavity mode, the potential felt by the condensate depends on the condensate itself. Adopting a discrete-mode approximation for the condensate, we map out the steady configurations of the system. It is found that due to the nonlinearity of the system, the nonlinear levels of the system may fold up in some parameter regimes. That will lead to the breakdown of adiabatic evolution of the system. Analysis of the dynamical stability of the steady states indicates that the same level structure also results in optical bistability.

DOI
10.1103/physreva.79.033401

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We investigate the nonlinear dynamics of a system composed of a cigar-shaped Bose—Einstein condensate and an optical cavity with the two sides coupled dispersively. By adopting discrete-mode approximation for the condensate, taking atom loss as a necessary part of the model to analyze the evolution of the system, while using trial and error method to find out steady states of the system as a reference, numerical simulation demonstrates that with a constant pump, atom loss will trigger a quantum optical bi-stability switch, which predicts a new interesting phenomenon for experiments to verify.
An interacting cigar-shaped Bose-Einstein condensate (BEC) inside a driven optical cavity exhibits an intrinsic cross-Kerr (CK) nonlinearity due to the interaction with the optical mode of the cavity. Although the CK coupling is much weaker than those of the radiation pressure and the atom-atom interactions, it can affect the bistability behavior of the system when the intensity of the laser pump is strong enough. On the other hand, there is a competition between the CK nonlinearity and the atom-atom interaction so that the latter can neutralize the effect of the former. Furthermore, the CK nonlinearity causes the effective frequency of the Bogoliubov mode of the BEC as well as the quantum fluctuations of the system to be increased by increasing the cavity driving rate. However, in the dispersive interaction regime the effect of the CK nonlinearity is negligible. In addition, we show that by increasing the sss-wave scattering frequency of atomic collisions one can generate a strong stationary quadrature squeezing in the Bogoliubov mode of the BEC.
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The nonlinear dynamics of the photon number in an optical cavity filled with a cigar-shaped Bose-Einstein condensate is investigated. We find that the way of adding the field is crucial to the switching close to the critical transition point. If the pump field is changed abruptly, the system may jump from one branch to the other even if the pump field intensity has not reached the critical transition point yet. This behavior is similar to the anomalous switching in the dispersive optical bistability.