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Journal of Changchun University of Science and Technology

Controlling chaos in a Bose-Einstein Condensation

Shen Ke

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential is investiga-ted. We suggest a method for eliminating chaos by modulating periodic signals to convert the chaotic state into regular state. As a function of modulation intensity and modulation frequency the maximal Lyapunov exponent is calculated respectively,and the periodic ordits associated with the negative Lyapunov exponent.

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The spatial structure of a Bose-Einstein condensate (BEC) loaded into an optical lattice potential is investiga-ted. We suggest a method for eliminating chaos by modulating periodic signals to convert the chaotic state into regular state. As a function of modulation intensity and modulation frequency the maximal Lyapunov exponent is calculated respectively,and the periodic ordits associated with the negative Lyapunov exponent.
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The spatial structure of a Bose–Einstein condensate (BEC) loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed. A method of chaos control with linear feedback is presented in this paper. By using the method, we propose a scheme of controlling chaotic behavior in a BEC with atomic mirrors. The results of the computer simulation show that controlling the chaos into the stable states could be realized by adjusting the coefficient of feedback only if the maximum Lyapunov exponent of the system is negative.
Chaos control of a Bose–Einstein condensate (BEC) loaded into a moving optical lattice with attractive interaction is investigated on the basis of Lyapunov stability theory. Three methods are designed to control chaos in BEC. As a controller, a bias constant, periodic force, or wavelet function feedback is added to the BEC system. Numerical simulations reveal that chaotic behavior can be well controlled to achieve periodicity by regulating control parameters. Different periodic orbits are available for different control parameters only if the maximal Lyapunov exponent of the system is negative. The abundant effect of chaotic control is also demonstrated numerically. Chaos control can be realized effectively by using our proposed control strategies.