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Journal of Hebei Normal University

Dynamics of Bose-Einstein Condensates in a Driven Double-well

HE Xiao-yan

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

The dynamic of Bose-Einstein condensates in a double-well under a monochromatic external driving force is studied.With the different driving intensity and frequency,the motion of the classical particle can be either regular or chaotic or even both of them.The equation that describes the Bose-Einstein condensates is Gross-Pitaevskii equation.Firstly,the study gets the Gross-Pitaevskii equation′s classical form by a superposition of the single well wave function,then,studies the dynamics of their phase space and the self-trapping behavior of Bose-Einstein condensate under periodic driving force.

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The dynamic of Bose-Einstein condensates in a double-well under a monochromatic external driving force is studied.With the different driving intensity and frequency,the motion of the classical particle can be either regular or chaotic or even both of them.The equation that describes the Bose-Einstein condensates is Gross-Pitaevskii equation.Firstly,the study gets the Gross-Pitaevskii equation′s classical form by a superposition of the single well wave function,then,studies the dynamics of their phase space and the self-trapping behavior of Bose-Einstein condensate under periodic driving force.
The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.
The response of a trapped Bose-Einstein condensed gas to a periodic driving force is studied theoretically in the framework of the nonlinear Gross-Pitaevskii equation. The monopole mode is driven by periodical modulation of the frequency of the isotropic harmonic trapping potential. Period-doubled motion is shown to occur when the driving is strong and close to resonance with the monopole mode. A variational model predicts chaotic oscillations but is found to disagree with the full solutions to the Gross-Pitaevskii equation.
We study dynamical behaviors of the weakly interacting Bose-Einstein condensate in the one-dimensional optical lattice with an overall double-well potential by solving the time-dependent Gross-Pitaevskii equation. It is observed that the double-well potential dominates the dynamics of such a system even if the lattice depth is several times larger than the height of the double-well potential. This result suggests that the condensate flows without resistance in the periodic lattice just like the case of a single particle moving in periodic potentials. Nevertheless, the effective mass of atoms is increased, which can be experimentally verified since it is connected to the Josephson oscillation frequency. Moreover, the periodic lattice enhances the nonlinearity of the double-well condensate, making the condensate more “self-trapped” in the π -mode self-trapping regime.
We investigate the dynamics of a weakly open Bose-Einstein condensate with attractive interaction in a magneto-optical double-well trap. A set of time-dependent ordinary differential equations describing the complex dynamics are derived by using a two-mode approximation. The stability of the stationary solution is analyzed and some stability regions on the parameter space are displayed. In the symmetric well case, the numerical calculations reveal that by adjusting the feeding from the nonequilibrium thermal cloud or the two-body dissipation rate, the system could transit among the periodic motions, chaotic self-trapping states of the Lorenz model, and the steady states with the zero relative atomic population or with the macroscopic quantum self-trapping (MQST). In the asymmetric well case, we find the periodic orbit being a stable two-sided limited cycle with MQST. The results are in good agreement with that of the direct numerical simulations to the Gross-Pitaevskii equation.