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arXiv:cond-mat/0204300 · Journal of Physics B Atomic Molecular and Optical Physics

Motion of a condensate in a shaken and vibrating harmonic trap

Y Japha, Y B Band

Published May 9, 2002• 15 citations
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Abstract

The dynamics of a Bose-Einstein condensate (BEC) in a time-dependent harmonic trapping potential is determined for arbitrary variations of the position of the center of the trap and its frequencies. The dynamics of the BEC wavepacket is soliton-like. The motion of the center of the wavepacket, and the spatially and temporally dependent phase (which affects the coherence properties of the BEC) multiplying the soliton-like part of the wavepacket, are analytically determined.

DOI
10.1088/0953-4075/35/10/315

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The dynamics of a Bose-Einstein condensate (BEC) in a time-dependent harmonic trapping potential is determined for arbitrary variations of the position of the center of the trap and its frequencies. The dynamics of the BEC wavepacket is soliton-like. The motion of the center of the wavepacket, and the spatially and temporally dependent phase (which affects the coherence properties of the BEC) multiplying the soliton-like part of the wavepacket, are analytically determined.
A variational method is developed to describe the dynamics of a Bose-Einstein condensate (BEC) trapped in an applied external potential consisting of both a harmonic and periodic component. Using this variational method, the BEC dynamics is shown to be well approximated by four coupled nonlinear differential equations, which describe the fundamental interactions in the system arising from the interplay of amplitude (width), chirp, center position, and center frequency. The simplified analytic theory allows for an efficient and convenient method for characterizing the experimental BEC behavior when localized condensates are generated. It further gives the critical strength ratio of harmonic to periodic potential necessary to support multiple stable lattice sites for the condensate and demonstrates that there can be an underlying chaotic behavior in the condensate system.
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.
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.
Bose-Einstein condensate has become a highly tunable physical system, which is proven to mimic a number of interesting physical phenomena in condensed matter physics. We study the dynamics of a two-dimensional Bose Einstein condensate (BEC) in the presence of a flat harmonic confinement and time-dependent sharp potential peak. Condensate density can be meticulously controlled with time by tuning the physically relevant parameters: frequency of the harmonic trap, width of the peaks, frequency of their oscillations, initial density etc. By engineering various trap profile, we solve the system, numerically, and explore the resulting spatial interference patters.
A Bose-Einstein condensate with time varying scattering length in time-dependent harmonic trap is analytically investigated and soliton-like solutions of the Gross-Pitaeviskii equation are obtained to describe single soliton, bisoliton and N-soliton properties of the matter wave. The influences of the geometrical property and modulate frequency of trapping potential on soliton behaviour are discussed. When the trap potential has a very sinall trap aspect ratio or oscillates with a high frequency, the matter wave preserves its shape nearly like a soliton train in propagation, while the breathing behaviour, which displays the periodic collapse and revival of the matter wave, is found for a relatively large aspect ratio or slow varying potential. Meanwhile mass centre of the matter wave translates and/or oscillates for different trap aspect ratio and trap frequencies.