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Journal of Physics B Atomic Molecular and Optical Physics

Quantum tunnelling of a weakly open Bose–Einstein condensate in a double well under periodic driving

Xiaobing Luo, Jun Xu, Huijun Wan, Yu Guo

Published Nov 29, 2010• 1 citation
Publisher

Abstract

We analyse the dynamics of a weakly open Bose–Einstein condensate (BEC) with attractive atomic interactions in a double-well potential under periodic driving. We find that the inclusion of weakly dissipative effects can dramatically modify the quantum tunnelling of the periodically driven BEC, and some new interesting dynamical properties arise, including a pitchfork bifurcation that leads to two stable nonsymmetric states by adjusting the dissipative parameters. The numerical results based on the approximate two-mode model are also analysed.

DOI
10.1088/0953-4075/43/24/245301

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We analyse the dynamics of a weakly open Bose–Einstein condensate (BEC) with attractive atomic interactions in a double-well potential under periodic driving. We find that the inclusion of weakly dissipative effects can dramatically modify the quantum tunnelling of the periodically driven BEC, and some new interesting dynamical properties arise, including a pitchfork bifurcation that leads to two stable nonsymmetric states by adjusting the dissipative parameters. The numerical results based on the approximate two-mode model are also analysed.
We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.
We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.
With phase space analysis approach, we investigate the self-trapping phenomenon for two weakly coupled Bose-Einstein condensates (BECs) in a symmetric double well potential. We identify two kinds of self-trapping by their different relative phase behavior. By applying a periodic modulation on the energy bias of the system we find that the self-trapping can be controlled, in other words, the transition parameters can be adjusted effectively by the periodic modulation. Analytic expressions for the dependence of the transition parameters on the modulation parameters are derived for high- and low-frequency modulations. For an intermediate-frequency modulation, we find the resonance between the periodic modulation and nonlinear Rabi oscillation dramatically affect the tunneling dynamics and demonstrate many phenomena. Finally, we study the effects of many-body quantum fluctuation on the self-trapping and discuss the possible experimental realization.