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Physical Review A

Rectified motion of a Bose-Einstein condensate in a horizontally vibrating shallow optical lattice

Yousef Azizi, Alireza Valizadeh

Published Jan 24, 2011• 6 citations
Publisher

Abstract

We consider a Bose-Einstein condensate, described by the Gross-Pitaevskii equation, in a horizontally vibrating shallow optical lattice. We study the dynamics of a bright soliton using the collective coordinate approximation. We show that depending on the parameters, amplitude, and frequency of the vibration of the lattice, the phase space of the equation of motion for the soliton center of mass shows multistability. In the frequency locked regions, in which the soliton has a nonzero average velocity determined by the external frequency, the motion is quasiperiodic, and between the locked regions the soliton moves chaotically.

DOI
10.1103/physreva.83.013614

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We consider a Bose-Einstein condensate, described by the Gross-Pitaevskii equation, in a horizontally vibrating shallow optical lattice. We study the dynamics of a bright soliton using the collective coordinate approximation. We show that depending on the parameters, amplitude, and frequency of the vibration of the lattice, the phase space of the equation of motion for the soliton center of mass shows multistability. In the frequency locked regions, in which the soliton has a nonzero average velocity determined by the external frequency, the motion is quasiperiodic, and between the locked regions the soliton moves chaotically.
We consider a solitonic solution of the self-attractive Bose-Einstein condensate in a one-dimensional external potential of a shallow optical lattice with large periodicity when the lattice is horizontally shaken. We investigate the dynamics of the bright soliton through the properties of the fixed points. The special type of bifurcation results in a simple criterion for the stability of the fixed points depending only on the amplitude of the shaking lattice. Because of the similarity of the equations with those of an ac-driven Josephson junction, some results may find applications in other branches of physics.
We study the formation of a dynamically-stabilized dissipation-managed bright soliton in a quasi-one-dimensional Bose–Einstein condensate by including an imaginary three-body recombination loss term and an imaginary linear feeding one in the Gross–Pitaevskii equation, trapped in a shallow optical-lattice potential. Based on the direct approach of perturbation theory for the nonlinear Schrödinger equation, we demonstrate that the height (as well as width) of bright soliton may have little change through selecting experimental parameters.
Dynamics of solitons in a one-dimensional trap with motionless and moving walls is studied by the example of bright solitons of an atomic Bose-Einstein condensate. Newton-type equations of the soliton's center motion are proposed and analyzed, and regimes of periodic, almost-periodic, and deterministically chaotic dynamics are presented. The predictions based on these approximate equations are in excellent agreement with that based on the Gross-Pitaevskii equation in the case of sufficiently narrow and slow solitons.
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.
The characteristics of two coupled Bose-Einstein Condensate (BEC) bright solitons trapped in an optical lattice are investigated with the variational approach and direct numerical simulations of the Gross-Pitaevskii equation. It is found that the optical lattice can be controllably used to capture and drag the coupled BEC solitons. Its effect depends on the initial location of the BEC solitons, the lattice amplitude and wave-number, and the amplitude of the coupled BEC solitons. The effective interaction between the two coupled solitons is the attractive effect.
We have investigated the dynamics of bright solitons in a spin–orbit coupled spin-1 Bose–Einstein condensate analytically and numerically. By using the hyperbolic sine function as the trial function to describe a plane wave bright soliton with a single finite momentum, we have derived the motion equations of soliton’s spin and center of mass, and obtained its exact analytical solutions. Our results show that the spin–orbit coupling couples the soliton’s spin with its center-of-mass motion, the spin oscillations induced by the exchange of atoms between components result in the periodical oscillation of center-of-mass, and the motion of center of mass of soliton can be viewed as a superposition of periodical and linear motions. Our analytical results have also been confirmed by the direct numerical simulations of Gross–Pitaevskii equations.