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Chinese Physics B

The dynamics of nonstationary solutions in one-dimensional two-component Bose—Einstein condensates

Bin-Bin Lü, Xue Hao, Qiang Tian

Published Feb 1, 2011• 0 citations
Publisher

Abstract

This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose—Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.

DOI
10.1088/1674-1056/20/2/020308

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This paper investigates the dynamical properties of nonstationary solutions in one-dimensional two-component Bose—Einstein condensates. It gives three kinds of stationary solutions to this model and develops a general method of constructing nonstationary solutions. It obtains the unique features about general evolution and soliton evolution of nonstationary solutions in this model.
We study the dynamics of two-component Bose–Einstein condensates in periodic potentials in one dimension. Elliptic potentials which have the sinusoidal optical potential as a special case are considered. We construct exact nonstationary solutions to the mean-field equations of motion. Among the solutions are two types of temporally periodic solutions—in one type there are condensate oscillations between neighbouring potential wells, while in the other the condensates oscillate from side to side within the wells. Our numerical studies of the stability of these solutions suggest the existence of one-parameter families of stable nonstationary solutions.
We investigate dynamics in two-component Bose-Einstein condensates in the context of coupled Gross-Pitaevskii equations and derive results for the evolution of the total density fluctuations. Using these results, we show how, in many cases of interest, the dynamics can be accurately described with an effective one-component Gross-Pitaevskii equation for one of the components, with the trap and interaction coefficients determined by the relative differences in the scattering lengths. We discuss the model in various regimes, where it predicts breathing excitations, and the formation of vector solitons. An effective nonlinear evolution is predicted for some cases of current experimental interest. We then apply the model to construct quasistationary states of two-component condensates.
We study the nonlinear dynamics of two-component Bose–Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross–Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.