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Physical Review E

Controlling the motion of dark solitons by means of periodic potentials: Application to Bose-Einstein condensates in optical lattices

Georgios Theocharis, D. J. Frantzeskakis, R. Carretero-González, P. G. Kevrekidis, Boris A. Malomed

Published Jan 6, 2005• 39 citations
Publisher

Abstract

We demonstrate that the motion of dark solitons (DSs) can be controlled by means of periodic potentials. The mechanism is realized in terms of cigar-shaped Bose-Einstein condensates confined in a harmonic magnetic potential, in the presence of an optical lattice (OL). In the case when the OL period is comparable to the width of the DS, we demonstrate that (a) a moving dark soliton can be captured, switching on the OL, and (b) a stationary DS can be dragged by a moving OL.

DOI
10.1103/physreve.71.017602

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We demonstrate that the motion of dark solitons (DSs) can be controlled by means of periodic potentials. The mechanism is realized in terms of cigar-shaped Bose-Einstein condensates confined in a harmonic magnetic potential, in the presence of an optical lattice (OL). In the case when the OL period is comparable to the width of the DS, we demonstrate that (a) a moving dark soliton can be captured, switching on the OL, and (b) a stationary DS can be dragged by a moving OL.
This paper investigates the dynamics of dark solitons in a Bose–Einstein condensate with a magnetic trap and an optical lattice (OL) trap, and analyses the effects of the periodic OL potential on the dynamics by applying the variational approach based on the renormalized integrals of motion. The results show that the dark soliton becomes only a standing-wave and free propagation of the dark soliton is not possible when the periodic length of the OL potential is approximately equal to the effective width of the dark soliton. When the periodic length is very small or very large, the effects of the OL potential on the dark soliton will be sharply reduced. Finally, the numerical results confirm these theoretical findings.
We investigate the stability of dark solitons (DSs) in an effectively one-dimensional Bose-Einstein condensate in the presence of the magnetic parabolic trap and an optical lattice (OL). The analysis is based on both the full Gross-Pitaevskii equation and its tight-binding approximation counterpart (discrete nonlinear Schr\"odinger equation). We find that DSs are subject to weak instabilities with an onset of instability mainly governed by the period and amplitude of the OL. The instability, if present, sets in at large times and it is characterized by quasiperiodic oscillations of the DS about the minimum of the parabolic trap.
An extended variation approach to describing the dynamic evolution of self-attractive Bose—Einstein condensates is developed. We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a time-space periodic optical lattice. The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations. A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate. We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites. In this case, the analytical predictions of Bose—Einstein condensates variational dynamics are found to be in good agreement with numerical simulations. We then find a stable region for successful manipulating matter-wave solitons without collapse, which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.
An extended variation approach to describing the dynamic evolution of self-attractive Bose-Einstein condensates is developed.We consider bright matter-wave solitons in the presence of a parabolic magnetic potential and a timespace periodic optical lattice.The dynamics of condensates is shown to be well approximated by four coupled nonlinear differential equations.A noteworthy feature is that the extended variation approach gives a critical strength ratio to support multiple stable lattice sites for the condensate.We further examine the existence of the solitons and their stabilities at the multiple stable lattice sites.In this case,the analytical predictions of Bose-Einstein condensates variational dynamics are found to be in good agreement with numerical simulations.We then find a stable region for successful manipulating matter-wave solitons without collapse,which are dragged from an initial stationary to a prescribed position by a moving periodic optical lattice.
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An extended variation method for describing the dynamical evolution of Bose-Einstein condensate solitons in the presence of optic-lattice and harmonic potentials was developed.This method agreed well with full numerical simulations and highlighted the dominant physical interactions in the system,namely,amplitude,width,chirp,center-position,and center-frequency dynamics.It further presented the critical strength ratio of optic-lattice to harmonic potential necessary to support multiple stable lattice sites for the Bose-Einstein condensate solitons and demonstrated that the Bose-Einstein condensate solitons could move selectively from one stable lattice site location to arbitrary final position by simply manipulating the optic-lattice potential.In addition,some interesting results for the experiments and applications of the Bose-Einstein condensates were also obtained.