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Chinese Physics Letters

Boundary-Dependent Chaotic Regions for a Bose–Einstein Condensate Interacting with Laser Field

Zhu Qian-Quan, Hai Wen-Hua, Haiming Deng

Published Oct 17, 2007• 2 citations
Publisher

Abstract

Spatial chaos of a Bose–Einstein condensate perturbed by a weak laser standing wave and a weak laser δ pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant c 0 determined by the boundary conditions. It is shown that when the | c 0 | values are small, the chaotic region corresponds to small values of laser wave vector k , and the chaotic region for the larger k values is related to the large | c 0 | values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincaré section for the two different parameter regions. Thus, for a fixed c 0 the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.

DOI
10.1088/0256-307x/24/11/017

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Spatial chaos of a Bose–Einstein condensate perturbed by a weak laser standing wave and a weak laser δ pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant c 0 determined by the boundary conditions. It is shown that when the | c 0 | values are small, the chaotic region corresponds to small values of laser wave vector k , and the chaotic region for the larger k values is related to the large | c 0 | values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincaré section for the two different parameter regions. Thus, for a fixed c 0 the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.
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.
For a weakly and periodically driven two-component Bose-Einstein condensate (BEC) the Melnikov chaotic solution and boundedness conditions are derived from a direct perturbation theory that leads to the chaotic regions in the parameter space. Differing from the usual results, the chaotic regions depend on the initial conditions directly and can be controlled by setting the initial phase and modulating the frequency and amplitude of laser. It is demonstrated that the order-chaos transitions can be controlled by tuning the laser frequency only.
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 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.
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.