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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Chaotic probability density in two periodically driven and weakly coupled Bose-Einstein condensates

Wenhua Hai, Chaohong Lee, Guishu Chong, Lei Shi

Published Aug 6, 2002• 93 citations
Publisher

Abstract

Using the idea of the macroscopic quantum wave function and the definition of the classical chaos, we analytically reveal that the probability density of two periodically driven and weakly coupled Bose-Einstein condensates is deterministic but not predictable. Numerical calculation for the time evolutions of the chaotic probability density demonstrates the analytical result and exhibits the nonphysical implosions and ultimate unboundedness. A method for controlling the implosions and unboundedness is proposed through adjustment of the initial conditions that leads the probability density to periodically oscillate.

DOI
10.1103/physreve.66.026202

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Using the idea of the macroscopic quantum wave function and the definition of the classical chaos, we analytically reveal that the probability density of two periodically driven and weakly coupled Bose-Einstein condensates is deterministic but not predictable. Numerical calculation for the time evolutions of the chaotic probability density demonstrates the analytical result and exhibits the nonphysical implosions and ultimate unboundedness. A method for controlling the implosions and unboundedness is proposed through adjustment of the initial conditions that leads the probability density to periodically oscillate.
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.