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Journal of Physics B Atomic Molecular and Optical Physics

Effective potential of two coupled binary matter wave bright solitons with spatially modulated nonlinearity

Yongshan Cheng

Published Oct 7, 2009• 18 citations
Publisher

Abstract

The interaction of two coupled binary matter wave bright solitons is investigated by means of the variational approach in the presence of spatially varying nonlinearity. The effective potential characterizing the interaction between the two solitons is obtained. It is shown that the effective potential is composed of three parts, related to the spatially modulated nonlinearity, the external trapping potential and the interaction of the two coupled solitons. The spatially modulated nonlinearity induces a pseudo-potential and the solitons can be accelerated by the spatially modulated nonlinearity. The effect depends on the sign and value of the spatially modulated coefficient. The interaction of two coupled binary matter wave bright solitons is of short range, and may be attractive or repulsive depending on the sign of the interspecies interactions. Under the appropriate condition, the two coupled solitons can evolve stably and do not coalesce. The neighbouring binary Bose-Einstein condensates are also available as media to create symbiotic bright solitons. The validity of the theoretical predictions is verified by the numerical integration of the coupled Gross-Pitaevskii equations.

DOI
10.1088/0953-4075/42/20/205005

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The interaction of two coupled binary matter wave bright solitons is investigated by means of the variational approach in the presence of spatially varying nonlinearity. The effective potential characterizing the interaction between the two solitons is obtained. It is shown that the effective potential is composed of three parts, related to the spatially modulated nonlinearity, the external trapping potential and the interaction of the two coupled solitons. The spatially modulated nonlinearity induces a pseudo-potential and the solitons can be accelerated by the spatially modulated nonlinearity. The effect depends on the sign and value of the spatially modulated coefficient. The interaction of two coupled binary matter wave bright solitons is of short range, and may be attractive or repulsive depending on the sign of the interspecies interactions. Under the appropriate condition, the two coupled solitons can evolve stably and do not coalesce. The neighbouring binary Bose-Einstein condensates are also available as media to create symbiotic bright solitons. The validity of the theoretical predictions is verified by the numerical integration of the coupled Gross-Pitaevskii equations.
Effect of the nonlinear spatial modulation on the evolution of twocomponent linear coupling Bose-Einstein condensate bright solitons trapped in a harmonic potential has been investigated numerically.It is indicated that the atomic density envelope of the soltions is changed with the spatial variation of s-wave scattering length,and the soliton exists in stable state under appropriate conditions.The evolution of solitons depends on the sign and value of the coefficient of the nonlinear spatial modulation.
We analyze the energetic and dynamical properties of bright-bright (BB) soliton pairs in a binary mixture of Bose-Einstein condensates subjected to the action of a combined optical lattice, acting as an external potential for the first species while modulating the intraspecies coupling constant of the second. In particular, we use a variational approach and direct numerical integrations to investigate the existence and stability of bright-bright (BB) solitons in which the two species are either spatially separated (split soliton) or located at the same optical lattice site (overlapped soliton). The dependence of these solitons on the interspecies interaction parameter is explicitly investigated. For repulsive interspecies interaction we show the existence of a series of critical values at which transitions from an initially overlapped soliton to split solitons occur. For attractive interspecies interaction only single direct transitions from split to overlapped BB solitons are found. The possibility to use split solitons for indirect measurements of scattering lengths is also suggested.
Bright solitons in a quasi-1D Bose–Einstein condensate can be used to enhance precision in matter-wave interferometry, due to their inherent robustness and support against dispersion. Such a soliton interferometer typically relies on a potential barrier used to split a single soliton into two smaller coherent solitons which can then be recombined on the same barrier. In this thesis we examine two extensions to this scheme. Firstly, we investigate a binary BEC system consisting of two bright solitons which are coupled through a mutual nonlinear interaction term. We derive a set of conditions under which the two components can be separated on a potential barrier and use numerical simulations to probe the regimes beyond which this mathematical treatment is applicable. We then use the numerical simulations to look at the effect of the nonlinear coupling on the dynamics of the binary solitons interacting with the barrier. We also look at the interference behaviour found by doubling the simulation time in either a ring trap or a harmonic trapping potential (to ensure recombination on the barrier); as well as the case where the solitons start spatially separated on either side of the barrier in order to find conditions under which the solitons will combine on the barrier. We find a good agreement between the analytical predictions and the results of simulations. Beyond the regions of parameter space where the predictions are expected to hold, we find complex transmission and interference behaviour as a result of nonlinear effects. The second part of this thesis consists of an examination of the prospect of using a subwavelength barrier scheme in a soliton interferometry experiment. This involves using two resonant coupling beams in a Λ-system with a spatially varying intensity. Under certain conditions, this can be used to form an effective potential barrier with a width which is not diffraction-limited. We look at suitable parameter regimes for such a barrier to split and recombine solitons in an interferometer and probe the effects of possible complications such as misalignment in the beams and different scattering lengths in the different states. We simulate the soliton interferometer using the full three component GPE as well as the single component analogue with the effective potential in order to characterise the soliton behaviour and the dependence of the interferometer sensitivity on the system parameters. We find a trend towards an idealised soliton interferometer with a decreasing value of the parameter, w, controlling the barrier characteristics. Also, we demonstrate an agreement between the relevant three component GPE and the analogous single component GPE, in the limit of strong coupling fields.
We present two families analytical solutions to the extended Gross-Pitaevskii equation (GPE), which describe the dynamics of bright and dark solitons in Bose-Einstein condensations(BECs) with varying coefficients of two and three-body interactions in a parabolic and complex potential. The properties of the dynamical evolutions of the bright and dark matter-wave solitons are investigated. It is interesting that the matter-wave can be controlled by applying the external magnetic field and a background.
Using time dependent nonlinear (s-wave scattering length) coupling between the components of a weakly interacting two component Bose–Einstein condensate (BEC), we show the possibility of matter wave switching (fraction of atoms transfer) between the components via shape changing/intensity redistribution (matter redistribution) soliton interactions. We investigate the exact bright–bright N-soliton solution of an effective one-dimensional (1D) two component BEC by suitably tailoring the trap potential, atomic scattering length, and atom gain or loss. In particular, we show that the effective 1D coupled Gross–Pitaevskii equations with time dependent parameters can be transformed into the well known completely integrable Manakov model described by coupled nonlinear Schrödinger equations by effecting a change of variables of the coordinates and the wave functions under certain conditions related to the time dependent parameters. We obtain the one-soliton solution and demonstrate the shape changing/matter redistribution interactions of two and three-soliton solutions for the time-independent expulsive harmonic trap potential, periodically modulated harmonic trap potential, and kinklike modulated harmonic trap potential. The standard elastic collision of solitons occur only for a specific choice of soliton parameters.