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Journal of Physics A Mathematical and Theoretical

A biperiodically driven matter-wave nonautonomous deformed soliton

Zejun Li, Wenhua Hai, Yan Deng, Qiongtao Xie

Published Oct 11, 2012• 2 citations
Publisher

Abstract

For a one-dimensional nonautonomous Gross–Pitaevskii system with biperiodically driven interatom interaction and external parabolic potential which satisfy the compatibility conditions (Serkin et al 2007 Phys. Rev. Lett. 98 074102), we derive a set of exact deformed-soliton solutions with amplitudes deviated from the standard hyperbolic-secant form, which describes different single-soliton characteristics of an attractive Bose–Einstein condensate. By defining a deformation factor adjusted by the number of condensed atoms, we find that the analytical height, width, position and velocity of the deformed soliton are controlled by the deformation factor. It is numerically shown that for asymmetric sawtooth driving the temporal ratchet effect can be induced or suppressed, even reversed, by adjusting the factor. The results offer a means of experimentally manipulating directed transports of the nonautonomous solitons.

DOI
10.1088/1751-8113/45/43/435003

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For a one-dimensional nonautonomous Gross–Pitaevskii system with biperiodically driven interatom interaction and external parabolic potential which satisfy the compatibility conditions (Serkin et al 2007 Phys. Rev. Lett. 98 074102), we derive a set of exact deformed-soliton solutions with amplitudes deviated from the standard hyperbolic-secant form, which describes different single-soliton characteristics of an attractive Bose–Einstein condensate. By defining a deformation factor adjusted by the number of condensed atoms, we find that the analytical height, width, position and velocity of the deformed soliton are controlled by the deformation factor. It is numerically shown that for asymmetric sawtooth driving the temporal ratchet effect can be induced or suppressed, even reversed, by adjusting the factor. The results offer a means of experimentally manipulating directed transports of the nonautonomous solitons.
We study exact single-soliton solutions of an attractive Bose—Einstein condensate governed by a one-dimensional nonautonomous Gross—Pitaevskii system. For several different forms of time-dependent atom—atom interaction and external parabolic potential which satisfy the exact integrability scenario, we construct a set of new analytical nonautonomous deformed-soliton solutions, including the macroscopic wave function and the position of soliton's center of mass. The soliton characteristics are modulated by the external field parameters and deformation factors related to the number of the condensed atoms and the initial conditions. The results suggest a simple and effective method for experimentally generating matter-wave deformed solitons and manipulating their motions.
We study the dynamics of bright solitons formed in a Bose-Einstein condensate with attractive atomic interactions perturbed by a weak bichromatic optical lattice potential. The lattice depth is a biperiodic function of time with a zero mean, which realizes a flashing ratchet for matter-wave solitons. We find that the average velocity of a soliton and the soliton current induced by the ratchet depend on the number of atoms in the soliton. As a consequence, soliton transport can be induced through scattering of different solitons. In the regime when matter-wave solitons are narrow compared to the lattice period the dynamics is well described by the effective Hamiltonian theory.
By means of analytical and numerical methods, we reveal the main features of nonautonomous matter-wave solitons near the Feshbach resonance in a one-dimensional Bose-Einstein condensate confined by a harmonic potential with a varying-in-time longitudinal trapping frequency. Based on the generalized nonautonomous Gross-Pitaevskii model, we show that solitons in nonautonomous physical systems exist only under certain conditions so that varying-in-time nonlinearity and confining harmonic potential cannot be chosen independently; they satisfy the exact integrability scenarios and complement each other. We focus on the most physically important examples where the applied magnetic field is either a linearly or a periodically varying-in-time function. In the case of periodically varying scattering length, variations of confining harmonic potential are found to be sign-reversible (periodic attractive and repulsive) to support the soliton-management regime. We investigate the losses of validity of one-dimensional (1D) approximation in the cases when, by the joint action of varying-in-time nonlinearity and confining potential, the atom cloud can be compressed from an initially elongated quasi-1D cigar-shaped geometry to a final ball-shaped three-dimensional geometry and the induced soliton collapse may occur.
To investigate nonautonomous matter waves with time-dependent modulation in a one-dimensional trapped spin-1 Bose-Einstein condensate, we hereby work on the generalized three-coupled Gross-Pitaevskii equations by means of the Hirota bilinear method. By modulating the external trap potential, atom gain or loss, and coupling coefficients, we can obtain several nonautonomous matter-wave solitons and rogue waves including "bright" and "dark" shapes and arrive at the following conclusions: (i) the external trap potential and atom gain or loss can influence the propagation of matter-wave solitons and the duration and frequency of bound solitonic interaction, but they have little effect on the head-on solitonic interaction; (ii) through numerical simulation, stable evolution of the matter-wave solitons is realized with a perturbation of 5% initial random noise, and the spin-exchange interaction of atoms can be affected by the time-dependent modulation; (iii) under the influence of a periodically modulated trap potential and periodic atom gain or loss, rogue waves can emerge in the superposition of localized character and periodic oscillating properties.
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 find a set of exact solutions of coherent bright solitons in the quasi-one-dimensional (1D) Bose-Einstein condensate (BEC) trapped in a harmonic potential, by using a Gaussian laser well (barrier) with oscillating position to balance the repulsive (attractive) interatomic interaction. The bright solitons do not deform in propagation and are controlled accurately by the laser driving which resonates with the trapping potential. The solitonic motion is more stable for the repulsive BEC than that of the attractive BEC. The results reveal a different kind of soliton trains compared to that reported recently in Phys. Rev. Lett. 100, 164102 (2008) and suggest an experimental scheme for generating and controlling the coherent matter-wave solitons.