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Chaos An Interdisciplinary Journal of Nonlinear Science

Coupled matter-wave solitons on oscillating reflectors under the effects of gravity

Kajal Krishna Dey, Golam Ali Sekh

Published Aug 1, 2022• 2 citations
Publisher

Abstract

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.

DOI
10.1063/5.0096721

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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.
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 have proposed a mechanical model that corresponds to the Newton equation for describing the dynamics of an oscillon, viz., a soliton-like cluster of the Bose–Einstein condensate (with atomic attraction) placed above an oscillating atomic mirror in a uniform gravitational field. The model describes the stochastic Fermi acceleration and periodic, quasi-periodic, and chaotic motion of the oscillon center, as well as hysteresis phenomena in the case of a slow variation of mirror oscillation frequency, which are in good agreement with the results obtained using the Gross–Pitaevskii equation.
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.
Abstract We consider matter–wave solitons in spin–orbit coupled Bose–Einstein condensates embedded in an optical lattice and study the dynamics of the soliton within the framework of Gross–Pitaevskii equations. We express spin components of the soliton pair in terms of nonlinear Bloch equations and investigate the effective spin dynamics. It is seen that the effective magnetic field that appears in the Bloch equation is affected by optical lattices, and thus the optical lattice influences the precessional frequency of the spin components. We make use of numerical approaches to investigate the dynamical behavior of density profiles and center-of-mass of the soliton pair in the presence of the optical lattice. It is shown that the spin density is periodically varying due to flipping of spinors between the two states. The amplitude of spin-flipping oscillation increases with lattice strength. We find that the system can also exhibit interesting nonlinear behavior for chosen values of parameters. We present a fixed point analysis to study the effects of optical lattices on the nonlinear dynamics of the spin components. It is seen that the optical lattice can act as a control parameter to change the dynamical behavior of the spin components from periodic to chaotic.
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.
We investigate the properties of modulational instability in the Salerno equation in quasi-one dimension in Bose-Einstein condensate (BEC). We analyzed the regions of modulational instability of nonlinear plane waves and determine the conditions of its existence in BEC. The existence and stability of strongly localized modes in discrete media is investigated with the framework of the Salerno model by using a linear analysis method. The regions of stability and instability are determined. Also the existence of localized modes for different values of parameters is shown numerically by homoclinic orbits intersection method. The response of Bose–Einstein condensates is studied with strong dipole–dipole atomic interactions to periodically varying perturbation. The dynamics is governed by the Gross–Pitaevskii equation with an additional nonlinear term, corresponding to nonlocal dipolar interactions. A mathematical model, based on the variational approximation, has been developed and applied to study parametric excitation of the condensates due to coefficient of nonlocal nonlinearity varying periodically. The model predicts the waveform of solitons in dipolar condensates and describes their small amplitude dynamics quite accurately. Theoretical predictions are verified by numerical simulations of the nonlocal Gross–Pitaevskii equation and a good agreement between them is found. The results can lead to better understanding of the properties of ultra-cold quantum gases, such as 52Cr, 164Dy and 168Er, where the long-range dipolar atomic interactions dominate the usual contact interactions. 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 iv 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 with the results of numerical simulations of the Gross-Pitaevskii equation and a qualitative agreement between them is found.