Transition probability from matter-wave soliton to chaos

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 feasible method for eliminating or strengthening chaos by modulating the moving superlattice experimentally.PACS numbers: 03.75. Lm, 05.45.Ac, 03.75.Kk, 05.45.Gg Many phenomena observed in Bose-Einstein condensates (BECs) are well modelled by nonlinear Schrödinger Equation (NLSE), also known as Gross-Pitaevskii equation (GPE), which includes many fantastic nonlinear effects, such as chaos [1,2], soliton [3,4], and so on. Chaotic soliton behaviors, which are of particular interest, have been studied theoretically in a NLSE with a periodic perturbation [5,6,7]. Lately, there are a few remarkable works on chaotic dynamics of soliton in BEC systems, including the chaos and energy exchange [8], the discrete soliton and chaotic dynamics in an array of BECs [9], and the bright matter-wave soliton collision [10]. Recently, increasing interest is excited in a BEC held in an optical superlattices for the periodic [11,12] and quasiperiodic [13,14,15] cases which are in close analogies with the fields of supercrystals and quasicrystals [16]. The BECs interacting with a traveling lattice have also been successfully treated experimentally [17,18] and theoretically [19,20,21] that shows many fantastic results such as lensing effect [18], gap soliton generation [19], spatiotemporal chaos [20,21], and so on. From the above analyzes we get a physical motivation, namely using a moving optical superlattices to study the transitions from soliton to chaos in BEC matter.It is well known that for stochastic initial and boundary conditions and fixed parameters, chaos does not always appear in a chaotic system [20], but with certain probability. Chaos probability may play a significant role for the control of chaos. Many works have focused on suppressing chaos which results in zero chaos probability. Whereas, in some realistic applications such as secure communication based on chaos[22], higher chaoticity is desired [23], which calls for higher chaos probability. In this paper, we show that in a BEC system perturbed by a moving optical superlattice consists of two lattices of different depths and wave vectors, the superlattice can separate the chaotic region into several parts with different chaos probabilities. Furthermore, for a fixed first lattice the adjustment to the secondary lattice could turn the * Corresponding Author:W. Hai; Electronic address: whhai2005@yahoo.com.cn chaos probability to zero or higher one. The results suggest a feasible method for eliminating or strengthening chaos experimentally. Such a method can be extended to the controls of the spatial chaos with zero traveli...

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