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Journal of Zhejiang Normal University

Controlled manipulation of Bose-Einstein condensate solitons in complex potentials

Feng-De Zong

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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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.
An extended variational method for describing the dynamics of a Bose-Einstein condensate （BEC） chirped soliton in the presence of periodic and harmonic potentials is developed. It is shown that the BEC chirped soliton dynamics can be deduced via the extended variational method to a set of four coupled nonlinear differential equations. This deduced set of equations agrees remarkably well with full numerical simulations and highlights the dominant physical interactions in the system, namely amplitude, width, chirp, center-position, and center-frequency dynamics. The extended analytic theory provides a useful, accurate, and greatly simplified description of the governing BEC chirped soliton dynamics. It further gives the critical strength ratio of periodic to harmonic potential necessary to support multiple stable lattice sites for the BEC chirped soliton and demonstrates that the BEC chirped soliton can move selectively from one lattice site to another by simply manipulating the potentials. In addition, some interesting results for the experiments and applications of the BEC are also obtained.
By means of an extended variational approach, we study dynamics for gap solitons in a repulsive interaction Bose—Einstein condensate under both a harmonic and an optical lattice confinement. The simplified analytic theory gives the critical strength ratio of harmonic to optical lattice necessary to support multiple stable lattice sites for the condensate. Moreover, we use numerical experiments to guide and manipulate the gap solitons to an arbitrary position via a time-dependent potential. All predictions of the extended variational approach are reasonably close to results of the simulations. In particular, the variational model helps capture the composition relationship between the variations of chirp and amplitude.
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.
The dynamics of a Bose?Einstein condensate under the influence of a confining double-well potential and a periodic potential (optical lattice) is studied by the well-known variational method. The variational principle leads to coupled nonlinear differential equations for the amplitude (width), chirp, center position and the center frequency of the condensate. The interplay between the condensate parameters leads to various regimes of its time evolution which depend on the relative strengths of the double-well and the periodic potentials. In particular, we show that by adjusting the strengths of the applied potentials appropriately, one can control and manipulate the condensate in several ways including tunneling from one well to the other and the to-and-fro motion between the two wells.
A model of the perturbed complex Toda chain (PCTC) to describe the dynamics of a Bose–Einstein condensate (BEC) N-soliton train trapped in an applied combined external potential consisting of both a weak harmonic and tilted periodic component is first developed. Using the developed theory, the BEC N-soliton train dynamics is shown to be well approximated by 4N coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude, velocity, centre-of-mass position, and phase. The simplified analytic theory allows for an efficient and convenient method for characterizing the BEC N-soliton train behaviour. It further gives the critical values of the strength of the potential for which one or more localized states can be extracted from a soliton train and demonstrates that the BEC N-soliton train can move selectively from one lattice site to another by simply manipulating the strength of the potential.