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Physical Review A

Phase locking of two weakly coupled Bose-Einstein condensates under a high-frequency driving field

Qiongtao Xie, Wenhua Hai

Published Nov 4, 2008• 4 citations
Publisher

Abstract

We investigate the phase-locking phenomena of two weakly coupled Bose-Einstein condensates in a double-well potential subject to a high-frequency periodic driving field. The conditions for the existence of the phase-locked solutions in this system are derived. The parameter ranges of phase locking are found analytically and confirmed numerically.

DOI
10.1103/physreva.78.053608

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We investigate the phase-locking phenomena of two weakly coupled Bose-Einstein condensates in a double-well potential subject to a high-frequency periodic driving field. The conditions for the existence of the phase-locked solutions in this system are derived. The parameter ranges of phase locking are found analytically and confirmed numerically.
We investigate the effect of an external periodic driving to the self-trapping transitions of two weakly coupled Bose-Einstein condensates in a double-well potential. It is shown that the self-trapping can be effectively controlled by modulating the double-well with a high frequency driving and thus renormalizing the transition parameters. In particular, an exact solution is constructed under the balance condition between the external field and the nonlinear interaction among particles, which allows one to precisely control theself-trapping states.
We investigate nonlinear Floquet states and quasienergies of a Bose-Einstein condensate in a double-well potential subject to a high-frequency driving field. A multiple time scale method is used to obtain the nonlinear Floquet states and quasienergies in both weak and strong nonlinearity regimes. It is shown that there are more nonlinear Floquet states without linear counterparts in the strong nonlinearity regime than in the weak nonlinearity regime, and they are phase-locked to an integer multiple of the external driving frequency. The validity of the effective description in the two different regimes is discussed. The stability criterion for these nonlinear Floquet states is found analytically and confirmed numerically.
We investigate the effect of periodic bias modulation on two weakly coupled Bose–Einstein condensates in a symmetric double-well potential and find a frequency-locking phenomenon at the transition frequency between the symmetric and antisymmetric states. Frequency-locking phenomenon becomes noticeable when the amplitude of the bias modulation is increased. The transition frequency becomes constant over a certain region of positive and negative nonlinear parameters due to the population mixing between the two states induced by the bias modulation. The frequency-locking phenomenon is also found in the multiple quantum transitions. Furthermore, an analogue of nonlinear Landau–Zener tunneling induced by the bias modulation is discussed.
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We study the effects of chaotic dynamics on atomic tunneling between two weakly coupled Bose-Einstein condensates driven by a double-frequency periodic field. Under the Melnikov's chaos criterion, we divide the parameter space into three parts of different types, regular region, low-chaoticity region, and high-chaoticity region, and give the accurate boundaries between the different regions. It is found that the atomic tunneling can be enhanced in the presence of chaos. Particularly, in the high-chaoticity regions, the chaos-induced inversion of the population imbalance is observed numerically.