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Journal of Physics B Atomic Molecular and Optical Physics

Dynamical evolutions of matter-wave bright solitons in an inverted parabolic potential

Guishu Chong, Wenhua Hai

Published Dec 20, 2006• 14 citations
Publisher

Abstract

A family of analytical solutions to a quasi one-dimensional time-dependent Gross–Pitaevskii equation with inverted parabolic potentials and time-varying nonlinear two-body interactions are presented, which simulate the dynamical evolutions of nonlinear matter-wave bright solitons. Synchronous behaviour between the variations of nonlinear interaction and compression or expansion of the solitons is demonstrated. For the case of higher order solitons, collision features are investigated. For travelling two solitons, different kinds of collisions are discussed for π and 0 phase difference between the two solitons at the collision point. Furthermore, a moving two-soliton 'bound' state is demonstrated. During the propagation, the solitons oscillate and collide many times.

DOI
10.1088/0953-4075/40/1/019

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A family of analytical solutions to a quasi one-dimensional time-dependent Gross–Pitaevskii equation with inverted parabolic potentials and time-varying nonlinear two-body interactions are presented, which simulate the dynamical evolutions of nonlinear matter-wave bright solitons. Synchronous behaviour between the variations of nonlinear interaction and compression or expansion of the solitons is demonstrated. For the case of higher order solitons, collision features are investigated. For travelling two solitons, different kinds of collisions are discussed for π and 0 phase difference between the two solitons at the collision point. Furthermore, a moving two-soliton 'bound' state is demonstrated. During the propagation, the solitons oscillate and collide many times.
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.
We investigate the dynamics of matter-wave solitons in the presence of a spatially varying atomic scattering length and nonlinearity. The dynamics of bright and dark solitary waves is studied using the corresponding Gross-Pitaevskii equation. The numerical results are shown to be in very good agreement with the predictions of the effective equations of motion derived by adiabatic perturbation theory. The spatially dependent nonlinearity is found to lead to a gravitational potential, as well as to a renormalization of the parabolic potential coefficient. This feature allows one to influence the motion of fundamental as well as higher-order solitons.
An analytical study on the dynamics of bright solitons of Bose–Einstein condensates (BEC) with a time-varying atomic scattering length in a time-varying expulsive parabolic potential is presented. Exact solutions of the one-dimensional Gross–Pitaevskii equation are obtained. The results show that the bright soliton (including the higher-order bright soliton) can be compressed into a desired width and amplitude in a controllable manner by changing the scattering length and external potential. Furthermore, it is shown numerically that the present method is also efficient for the two-dimensional BEC's compression.
We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by increasing the absolute value of the atomic scattering length, which can provide an experimental tool for investigating the range of validity of the one-dimensional Gross-Pitaevskii equation. We also find that the number of atoms in the bright soliton keeps dynamic stability: a time-periodic atomic exchange is formed between the bright soliton and the background.
We investigate dynamical effects of a bright soliton in Bose–Einstein condensed (BEC) systems with local and smooth space variations of the two-body atomic scattering length. It includes a discussion about the possible observation of a new type of standing nonlinear atomic matter wave in cigar-type traps. A rich dynamics is observed in the interaction between the soliton and an inhomogeneity. By considering an analytical time-dependent variational approach and also full numerical simulation of one-dimensional and three-dimensional Gross–Pitaevskii equations, we study processes such as trapping, reflection and transmission of the bright matter soliton due to the impurity. We also derive conditions for the collapse of the bright solitary wave, considering a quasi-one-dimensional BEC with attractive local inhomogeneity.
The dynamics of a bright matter wave soliton in a quasi one-dimensional Bose–Einstein condensate (BEC) with a periodically rapidly varying time trap is considered. The governing equation is based on averaging the fast modulations of the Gross–Pitaevskii (GP) equation. This equation has the form of a GP equation with an effective potential of a more complicated structure than an unperturbed trap. In the case of an inverted (expulsive) quadratic trap corresponding to an unstable GP equation, the effective potential can be stable. For the bounded space trap potential it is showed that bifurcation exists, i.e. the single-well potential bifurcates to the triple-well effective potential. The stabilization of a BEC cloud on-site state in the temporary modulated optical lattice is found. This phenomenon is analogous to the Kapitza stabilization of an inverted pendulum. The analytical predictions of the averaged GP equation are confirmed by numerical simulations of the full GP equation with rapid perturbations.