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Journal of Physics Conference Series

Chaos in BEC trapped in tilted optical superlattice potential with attractive interaction

Priyanka Verma, Aranya B. Bhattacherjee, Man Mohan

Published Mar 14, 2012• 4 citations
Publisher

Abstract

The chaos in Bose-Einstein condensate (BEC) in a 1-D tilted optical superlattice potential is studied numerically in this paper. Numerical analysis using the Gross- Pitaevskii (G-P) equation for the system with attractive interaction reveals that as the tilt of the optical superlattice potential is increased the chaos in the BEC increases. This makes the system more unstable and the phase-space orbit increases. The chaos increases as the secondary optical lattice potential increases.

DOI
10.1088/1742-6596/350/1/012003

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The chaos in Bose-Einstein condensate (BEC) in a 1-D tilted optical superlattice potential is studied numerically in this paper. Numerical analysis using the Gross- Pitaevskii (G-P) equation for the system with attractive interaction reveals that as the tilt of the optical superlattice potential is increased the chaos in the BEC increases. This makes the system more unstable and the phase-space orbit increases. The chaos increases as the secondary optical lattice potential increases.
The chaotic dynamic characteristic in Bose-Einstein Condensate (BEC) system of a 1D tilted optical superlattice potential with attractive interaction is investigated in this paper. The spatial evolution of chaos was shown numerically by resolving Gross-Pitaevskii (G-P) equation for the system with the fourth Runge-Kutta(RK) algorithm. Numerical analysis reveals that as the tilt or the amplitude of the optical superlattice potential is increased the chaos in the BEC system increases. These elements make the chaotic system more unstable and the phase-space orbit becomes more chaotic. The chaotic system can be effectively controlled to a stable periodic orbit through adjusting the amplitude of the optical superlattice potential and initial condition. Controlling chaos can also be realized by spatial constant bias in the BEC system of a 1D tilted optical superlattice potential with attractive interaction. Phase orbits are suppressed gradually then the chaotic states of the BEC system are converted into period one through quais-period.
Using the direct perturbation technique,a general unstable chaotic solution was obtained of the Bose-Einstein condensates trapped in one-dimensional tilted optical lattice potential.The dynamical phase dia-gram of this system was studied.Theoretical analysis results and the corresponding numerical results showed the chaotic behavior of the system.It was found that Bose-Einstein condensate chaos could be controlled by chang-ing the wave length of the incident laser light or adjusting the system parameters.
We consider the Bose-Einstein condensate trapped in optical lattice, which is formed from two kinds of deep potentials. The tight-binding approximation was used. Steady state distribution of the probability amplitudes and the site population in the one dimensional optical superlattice were found. It was shown that this solution of the equations which describe the dynamics of the Bose-Einstein condensate in superlattice is unstable at the sufficiently high density of the bosons. The expression for increment of the modulational instability was found on base of the linear stability analysis. Numerical simulation demonstrates the evolution of the steady state distributions of bosons into the space array of the solitary peaks before the chaotic regime generation.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.
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.
Using the direct perturbation technique, this paper obtains a general perturbed solution of the Bose—Einstein condensates trapped in one-dimensional tilted optical lattice potential. We also gave out two necessary and sufficient conditions for boundedness of the perturbed solution. Theoretical analytical results and the corresponding numerical results show that the perturbed solution of the Bose-Einstein condensate system is unbounded in general and indicate that the Bose—Einstein condensates are Lyapunov-unstable. However, when the conditions for boundedness of the perturbed solution are satisfied, then the Bose-Einstein condensates are Lyapunov-stable.