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Journal of Experimental and Theoretical Physics

Controlling chaos in the Bose-Einstein condensate

Fuzhong Cong, Zhixia Wang, Hongtu Hua, Shichun Pang, Shouyu Tong

Published Mar 1, 2012• 2 citations
Publisher

Abstract

The spatial structure of the Bose-Einstein condensate (BEC) is investigated and spatially chaotic distributions of the condensates are revealed. By means of changing the s -wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s -wave scattering lengths only if the Lyapunov exponent of the system is negative.

DOI
10.1134/s1063776112020197

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The spatial structure of the Bose-Einstein condensate (BEC) is investigated and spatially chaotic distributions of the condensates are revealed. By means of changing the s -wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s -wave scattering lengths only if the Lyapunov exponent of the system is negative.
The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated, and spatially chaotic distributions of the condensates are revealed. By means of changing of the s-wave scattering length with a Feshbach resonance, the chaotic behavior can be well controlled to enter into periodicity. Numerical simulation shows that there are different periodic orbits according to different s-wave scattering lengths only if the maximal Lyapunov exponent of the system is negative.
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.