Dispersion control for matter waves and gap solitons in optical superlattices

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.

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“…The BEC system considered here is loaded into a moving superlattice [42] consisting of primary and secondary moving optical lattices of the form…”

Section: Analytical Chaotic Solitonmentioning

confidence: 99%

Relation between chaos probability and zero-point number of the Melnikov function for a Bose-Einstein condensate

2009

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“…Theoretical interest in optical superlattices started only recently. Examples include work on fractional filling Mott insulator domains [20], dark [21] and gap [22] solitons, the Mott-Peierls transition [23], non-mean field effects [24] and phase diagrams of BEC in two-color superlattices [25]. Porter et al [26] have shown that optical superlattices can manipulate and control solitons in BEC.…”

Section: Introductionmentioning

confidence: 99%

Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice

Bhattacherjee

Pietrzyk

2008

Open Physics

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Abstract:We investigate the Bloch and dipole oscillations of a Bose Einstein condensate (BEC) in an optical superlattice. We show that, as the effective mass increases in an optical superlattice, the BEC is localized in accordance with recent experimental observations [J.E. Lye et. al. Phys. Rev. A 75, 061603 (2007)]. In addition, we find that the secondary optical lattice is a useful additional tool to manipulate the dynamics of the atoms.

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“…The superlattice of Eq. (1) with γ = 2 has be widely studied [24]. In such a case, the X N (c 0 ) becomes…”

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confidence: 99%

“…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 traveling velocity and the temporal chaos in other systems.Primary and secondary moving optical lattice compose the superlattice [24] as the formwhere we refer to V 1 cos 2 (kζ) as the primary lattice with V 1 and k corresponding to its depth and wave vector, and V 2 cos 2 (γkζ + φ) as the secondary one with V 2 being its depth, γ the ratio of the two laser wave vectors and φ the phase difference. The spatiotemporal variable ζ = x + v L t contains the velocity of the traveling lattice v L = δ/(2k) with δ being the frequency difference between the two counter-propagating laser beams producing the first lattice.…”

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confidence: 99%

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Transition probability from matter-wave soliton to chaos

2009

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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 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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Dispersion control for matter waves and gap solitons in optical superlattices

Cited by 55 publications

References 31 publications

Relation between chaos probability and zero-point number of the Melnikov function for a Bose-Einstein condensate

Relation between chaos probability and zero-point number of the Melnikov function for a Bose-Einstein condensate

Transport behaviour of a Bose Einstein condensate in a bichromatic optical lattice

Transition probability from matter-wave soliton to chaos

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