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Advanced Science Letters

The Spatial Evolution Chaos of a Trapped Bose-Einstein Condensate in One-Dimensional Optical Lattice Potential

Jianshu Fang, Liyu Luo, Xiangping Liao, Xinye Li

Published May 15, 2012• 0 citations
Publisher
DOI
10.1166/asl.2012.3753

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The spatially chaotic attractor in an elongated cloud of Bose-Einstein condensed atoms perturbed by a weak optical lattice potential is studied. The analytical insolvability and numerical incomputability of the atomic number density are revealed by a perturbed solution that illustrates the unpredictability of the deterministic chaos. Although this could lead the nonphysical explosion and unboundedness to the numerical solution, the theoretical analysis offers a criterion to avoid them. Moreover, the velocity field is investigated that exhibits the superfluid property of the chaotic system.
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 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.