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Chaos An Interdisciplinary Journal of Nonlinear Science

Dynamics of self-reinforcing matter-wave in gravito-optical surface trap

Golam Ali Sekh, Pallavi Kalikotay

Published Oct 1, 2019• 6 citations
Publisher

Abstract

We consider matter-wave solitons/oscillons in the presence of gravito-optical surface traps within the framework of mean-field equations. We pay special attention to the dynamics of both solitons and oscillons against the reflecting platform, the position of which can either be varied periodically or quasiperiodically with time. It is seen that with the temporal variation of reflector's vertical position, the dynamics of the soliton can change from periodic to quasiperiodic while that of the oscillon can change from regular to chaotic. We find that the transition from regular to chaotic motion is prominent in Poincaré maps for different relevant recurrence times.

DOI
10.1063/1.5116328

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We consider matter-wave solitons/oscillons in the presence of gravito-optical surface traps within the framework of mean-field equations. We pay special attention to the dynamics of both solitons and oscillons against the reflecting platform, the position of which can either be varied periodically or quasiperiodically with time. It is seen that with the temporal variation of reflector's vertical position, the dynamics of the soliton can change from periodic to quasiperiodic while that of the oscillon can change from regular to chaotic. We find that the transition from regular to chaotic motion is prominent in Poincaré maps for different relevant recurrence times.
We consider coupled matter-waves solitons in Bose-Einstein condensates and study the dynamics under the combined effects of gravity and reflecting potential. The dynamics of matter-wave near a reflector oscillating periodically with time generates the dynamics of a special kind of localized structure called oscillon. We derive a mechanical model for the coupled oscillon dynamics. We pay special attention to the inter-component interaction and see that effective potential depends on the type (repulsive/attractive) and strength of interaction. We find that the inter-component interaction affects the frequency of oscillation and introduces an initial phase-shift between the reflector and the oscillon. This phase-shift, in addition to instantaneous phase change due to the oscillation of the reflector, results in interesting dynamics. The coupled oscillon is found to execute quasi-periodic and chaotic dynamics for both attractive and repulsive inter-component interactions. We analyze the maximum value of Lyapunov exponents and show that the dynamical response of the coupled oscillon depends on the ratio of the center of mass position and their separation.
The dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the effect of gravity has been studied by analytical and numerical means. The analytical description is based on the variational approach. Resonant oscillations of the soliton's center of mass and width, induced by appropriate modulation of the atomic scattering length and the slope of the linear potential, are analyzed. In numerical experiments we observe the Fermi-type acceleration of the soliton when the vertical position of the reflecting surface is periodically varied in time. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.
The dynamics of the soliton in a self-attractive Bose–Einstein condensate under the gravity are investigated. First, we apply the inverse scattering method, which gives rise to equation of motion for the center-of-mass coordinate of the soliton. We analyze the amplitude-frequency characteristic for nonlinear resonance. Applying the Krylov–Bogoliubov method for the small parameters the dynamics of soliton on the phase plane are considered. Hamiltonian chaos under the action of the gravity on the Poincaré map are studied.
We consider, by analytical and numerical means, the dynamics of a matter-wave soliton bouncing on the reflecting surface (atomic mirror) under the influence of gravity, when twobody interactions between atoms are periodically modulated in time. The analytical description is based on the variational approach. The frequencies of small amplitude oscillations of the soliton's center-of-mass and width are obtained. Analytical predictions are compared to the results of numerical simulations of the Gross-Pitaevskii equation and qualitative agreement between them is found.
Abstract Using the time-dependent variational approach and the numerical solution of the Gross–Pitaevskii (GP) equation, the dynamics of a matter-wave soliton are investigated in a two-dimensional constant external force field. Firstly, the time-dependent variational approach is used to study the movements of the center-of-mass position in a simple harmonic trap and a two-dimensional weakly transmissive reflective barrier. Because the mathematical model for describing soliton dynamics in simple harmonic traps is simple, the analytic dynamical results of a soliton wave packet center-of-mass position is given directly. Since the model describing the weakly transmissive reflective barrier is difficult to solve analytically, we give the Newton’s equation of the center-of-mass position of motion, and then use the numerical solution method to study the movement of the center-of-mass in the case of several parameters. To study the motion of the soliton in the harmonic potential trap in the two-dimensional external force field under rotation , we use the split-step finite difference method to solve the two-dimensional GP equation; the motion of the center-of-mass position is discussed under the conditions of several parameter combinations. The results show that the rotation has a very important influence on the movement of the center-of-mass. When there is no rotation effect, the center-of-mass position acts as a simple harmonic motion under the combined action of the external force field and the potential well. When there is a rotation effect, the center-of-mass position is almost static.
We consider, analytically and numerically, the dynamics of an atomic Bose–Einstein condensate soliton bouncing in a magnetic or optical trap between two ideal barriers oscillating harmonically with coinciding frequency and opposite phases. There are zones of parametric instability of the soliton’s central position in the trap for certain ranges of the frequency of the barriers’ oscillations. We demonstrate the Fermi–Pasta–Ulam recurrence in the Fermi–Ulam scheme for solitons: the soliton’s deviations from the trap’s center grow and decay quasi-periodically in time. The results allow one to excite and investigate various structures of matter waves in traps and to manipulate their localization and dynamics.