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Journal of the Physical Society of Japan

Frequency-Locking Phenomenon of Two Weakly Coupled Bose–Einstein Condensates Induced by Periodic Bias Modulation

Noriaki Tsukada, Kensuke Fukushima, Takashi Suzuki

Published Jan 25, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1143/jpsj.76.024001

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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.
We describe the coherent atomic tunneling between two Bose-Einstein condensates confined in a double-well potential, whose zero-point energies are modulated by a small oscillation of the barrier-laser position. The coupled-mode equations derived from the Gross-Pitaevskii equation describe the dynamics in terms of the population imbalance as a function of the modulation amplitude of the zero-point energies normalized by the modulation frequency. It is predicted that the modulation of the zero-point energies induces the laser-assisted tunneling (LAT) and the resonant peaks of the LATs are remarkably shifted in energy by the nonlinearity due to the many-body interactions. It is also shown that the threshold of the nonlinear self-interaction for the spontaneous symmetry breaking is modified by the potential modulations. These features are qualitatively explained by considering that the coupling (or tunneling) coefficient K is effectively given by $\stackrel{\ensuremath{\rightarrow}}{K}{K}_{n}^{\mathrm{eff}}{=J}_{n}{(E}_{\ensuremath{\omega}}/\ensuremath{\omega})K$ for the nthn\mathrm{th}nth LAT under the influence of the potential modulations, where ${E}_{\ensuremath{\omega}}$ and \ensuremath{\omega} are the modulation amplitude of the zero-point energies and the modulation frequency, respectively.
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