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arXiv:0804.0906 · Physical Review E

Transition probability from matter-wave soliton to chaos

Qianquan Zhu, Wenhua Hai, Shiguang Rong

Published Jul 7, 2009• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreve.80.016203

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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.
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.
Chaotic space-time evolution is investigated for the particle number density of a Bose-Einstein condensate with attractive interatomic interaction loaded into a traveling optical lattice. Melnikov chaos is studied and the weakly chaotic regime is presented analytically. Transitions from transient to stationary chaos in the space-time evolution are illustrated numerically. The results show that, on increasing the strength of the optical potential, the transient chaos falls onto several different attractors. Meanwhile, these attractors undergo a series of period-doubling bifurcations when the optical potential intensity is increased continuously, and eventually stationary chaos arises for a critical depth of the optical lattice. The obstructions to chaos caused by the damping and the motion of lattice are also demonstrated.
We have shown that the application of modulating the secondary lattice is an efficient route to suppressing the generation of chaotic traveling waves of a Bose–Einstein Condensate with attractive interatomic interaction loaded into a moving optical superlattice consisting of two lattices. With the Melnikov method, we obtain the optimal value of the relative phase between the two lattice harmonics for the control of chaos. We also find that the regularization route as the potential depth of the secondary lattice is varied and fairly rich, including the period-doubling bifurcations.
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.
We study the spatially chaoticity-dependent spin-motion entanglement of a spin-orbit (SO) coupled Bose-Einstein condensate with a source of ultracold atoms held in an optical superlattice. In the case of phase synchronization, we analytically demonstrate that (a) the SO coupling (SOC) leads to the generation of spin-motion entanglement; (b) the area of the high-chaoticity parameter region inversely relates to the SOC strength which renormalizes the chemical potential; and (c) the high-chaoticity is associated with the lower chemical potential and the larger ratio of the short-lattice depth to the longer-lattice depth. Then, we numerically generate the Poincaré sections to pinpoint that the chaos probability is enhanced with the decrease in the SOC strength and/or the spin-dependent current components. The existence of chaos is confirmed by computing the corresponding largest Lyapunov exponents. For an appropriate lattice depth ratio, the complete stop of one of (or both) the current components is related to the full chaoticity. The results mean that the weak SOC and/or the small current components can enhance the chaoticity. Based on the insensitivity of chaos probability to initial conditions, we propose a feasible scheme to manipulate the ensemble of chaotic spin-motion entangled states, which may be useful in coherent atom optics with chaotic atom transport.