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Chinese Physics Letters

Controlling Chaos Probability of a Bose–Einstein Condensate in a Weak Optical Superlattice

Xu Jun, Xiaobing Luo

Published Mar 31, 2009• 4 citations
Publisher

Abstract

The spatial chaos probability of a Bose–Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.

DOI
10.1088/0256-307x/26/4/040305

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The spatial chaos probability of a Bose–Einstein condensate perturbed by a weak optical superlattice is studied. It is demonstrated that the spatial chaotic solution appears with a certain probability in a given parameter region under a random boundary condition. The effects of the lattice depths and wave vectors on the chaos probability are illustrated, and different regions associated with different chaos probabilities are found. This suggests a feasible scheme for suppressing and strengthening chaos by adjusting the optical superlattice experimentally.
For a Bose-Einstein condensate loaded into a weak traveling optical superlattice, it is demonstrated that under a stochastic initial set and in a given parameter region, the solitonic chaos appears with a certain probability. Effects of the lattice depths and wave vectors on the chaos probability are investigated analytically and numerically and different chaotic regions associated with different chaos probabilities are found. The results suggest a method for weakening or strengthening chaos by modulating the moving superlattice.
Abstract We investigate an attractive Bose-Einstein condensate perturbed by a weak traveling optical superlattice. It is demonstrated that under a stochastic initial set and in a given parameter region solitonic chaos appears with a certain probability that is tightly related to the zero-point number of the Melnikov function; the latter depends on the potential parameters. Effects of the lattice depths and wave vectors on the chaos probability are studied analytically and numerically, and different chaotic regions of the parameter space are found. The results suggest a feasible method for strengthening or weakening chaos by modulating the potential parameters experimentally.
For a Bose-Einstein condensate (BEC) confined in a double lattice consisting of two weak laser standing waves we find the Melnikov chaotic solution and chaotic region of parameter space by using the direct perturbation method. In the chaotic region, spatial evolutions of the chaotic solution and the corresponding distribution of particle number density are bounded but unpredictable between their superior and inferior limits. It is illustrated that when the relation k 1 ≈ k 2 between the two laser wave vectors is kept, the adjustment from k 2 < k 1 to k 2 ⩾ k 1 can transform the chaotic region into regular one or the other way round. This suggests a feasible scheme for generating and controlling chaos, which could lead to an experimental observation in the near future.
We examine spatial chaos in a one-dimensional attractive Bose-Einstein condensate interacting with a Gaussian-like laser barrier and perturbed by a weak optical lattice. For a low laser barrier, chaotic regions of the parameters are demonstrated and the chaotic and regular states are illustrated numerically. In the high-barrier case, bounded perturbed solutions that describe a set of discrete chaotic states are constructed for discrete barrier heights and magic numbers of condensed atoms. Chaotic density profiles are exhibited numerically for the lowest quantum number, and analytically bounded but numerically unbounded Gaussian-like configurations are confirmed. It is shown that the chaotic wave packets can be controlled experimentally by adjusting the laser barrier potential.
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.
The spatial structure of a Bose-Einstein condensate loaded into an optical lattice potential is investigated and the spatially chaotic distributions of the condensates are revealed under the tight-binding approximation. Adding a laser pulse on a proper site of the lattice and treating it as a control signal, control of the chaos in the system is carried out by using the Ott-Grebogi-Yorker scheme. For an appropriate laser pulse, we can suppress the chaos and push the system onto a stable manifold of a target orbit. After the control, a regular distribution, which may be expected in experiments or practical applications, of the condensates in the coordinate space is obtained.