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Chaos An Interdisciplinary Journal of Nonlinear Science

Chaotic atomic tunneling between two periodically driven Bose–Einstein condensates

Qiongtao Xie, Wenhua Hai, Guishu Chong

Published Aug 29, 2003• 47 citations
Publisher

Abstract

The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.

DOI
10.1063/1.1578971

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The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.
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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.
The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.
For a weakly and periodically driven two-component Bose-Einstein condensate (BEC) the Melnikov chaotic solution and boundedness conditions are derived from a direct perturbation theory that leads to the chaotic regions in the parameter space. Differing from the usual results, the chaotic regions depend on the initial conditions directly and can be controlled by setting the initial phase and modulating the frequency and amplitude of laser. It is demonstrated that the order-chaos transitions can be controlled by tuning the laser frequency only.