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Physical Review A

Nonlinear dynamics of a dipolar Bose-Einstein condensate in an optical lattice

Zhengwei Xie, Ze-Xian Cao, Efim I Kats, W. M. Liu

Published Feb 15, 2005• 50 citations
Publisher

Abstract

The dynamics of Bose-Einstein condensates in optical lattices with the long-range dipole-dipole interactions, the short-range on-site interactions, and hopping terms is reduced to the generalized discrete nonlinear Schr\"odinger equation. We present the different types of solitary excitations which appear in different parameter regions. We anticipate that these excitations will be observable and discuss how the model parameters can be tuned in experiments.

DOI
10.1103/physreva.71.025601

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The dynamics of Bose-Einstein condensates in optical lattices with the long-range dipole-dipole interactions, the short-range on-site interactions, and hopping terms is reduced to the generalized discrete nonlinear Schr"odinger equation. We present the different types of solitary excitations which appear in different parameter regions. We anticipate that these excitations will be observable and discuss how the model parameters can be tuned in experiments.
The present work is devoted to the theoretical investigation of the dynamics of Bose –Einstein condensates (BEC) in optical lattice with the long range magnetic dipole-dipole interaction between atoms. The system is described by a nonlocal nonlinear Schrodinger equation (NLSE). We consider the case when the lattice depth is sufficiently large (tight binding approximation). In this case nonlocal NLSE can be reduced to discrete NLSE equation. We show that discrete NLSE equation for some range of parameters can be reduced further to integrable Ablowitz-Ladik equation which supports moving solitons. Taking the one-soliton solution of Ablowitz-Ladik equation as an initial condition we have performed detailed numerical study of a soliton dynamics in both nonlocal NLSE and discrete NLSE. The conditions of existence and stability of moving solitons in dipolar BEC in an optical lattice are numerically revealed. Also the applicability limits for the tight binding approximation for the experimentally achievable range of parameters are investigated.
We obtain the multisolitary solutions of the extended Bose–Hubbard model which describes dipolar Bose–Einstein condensates in optical lattices under time-dependent magnetic fields, and indicate that the nonlinearity is due to both on-site short-range interactions and also (long-range) dipole-dipole interactions which can act between neighboring sites. The discrete breathers as nonlinear excitations are always oscillatory in time and can also be spatially localized, while the oscillatory frequencies are determined by an external field. We show that these excitations will be observable and discuss how the parameters can be tuned in future experiments.
Abstract. The motto of this paper is: Let's face Bose-Einstein condensation through nonUnear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose-Einstein condensates via the time-dependent Gross-Pitaevskii equation into Hamiltonian systems that can be studied using the methods of nonUnear dynamics. We consider in particular cold quantum gases where long-range interactions between the neutral atoms are present, in addition to the conventional short-range contact interaction, viz. gravity-Uke interactions, and dipole-dipole interactions. The residts obtained serve as a useful giude in the search for nonlinear dynamics effects in numerically exact quantum calcinations for Bose-Einstein condensates. A main residt is the prediction of the existence of stable islands as well as chaotic regions for excited states of dipolar condensates, which coidd be checked experimentally. Keywords: Bose-Einstein condensation, Gross-Pitaevskii equation, nonlinear dynamics effects PACS: 03.75.Kk, 34.20.Cf, 02.30.-f, 47.20.Ky 1.
We study the stabilization properties of dipolar Bose–Einstein condensate in a deep one-dimensional optical lattice with an additional external parametrically modulated harmonic trap potential. Through both analytical and numerical methods, we solve a dimensionless nonlocal nonlinear discrete Gross–Pitaevskii equation with both the short-range contact interaction and the long-range dipole–dipole interaction. It is shown that, the stability of dipolar condensate in modulated deep optical lattice can be controled by coupled effects of the contact interaction, the dipolar interaction and the external modulation. The system can be stabilized when the dipolar interaction, the contact interaction, the average strength of potential and the ratio of amplitude to frequency of the modulation satisfy a critical condition. In addition, the breather state, the diffused state and the attractive-interaction-induced-trapped state are predicted. The dipolar interaction and the external modulation of the lattice play important roles in stabilizing the condensate.