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Chinese Physics

Atomic population oscillations between two coupled Bose–Einstein condensates with time-dependent nonlinear interaction

Li Fei, Shu Wei-Xing, Luo Hai-Lu, Zhongzhou Ren

Published Feb 26, 2007• 12 citations
Publisher

Abstract

The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.

DOI
10.1088/1009-1963/16/3/016

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The atomic population oscillations between two Bose–Einstein condensates with time-dependent nonlinear interaction in a double-well potential are studied. We first analyse the stabilities of the system's steady-state solutions. And then in the perturbative regime, the Melnikov chaotic oscillation of atomic population imbalance is investigated and the Melnikov chaotic criterion is obtained. When the system is out of the perturbative regime, numerical calculations reveal that regulating the nonlinear parameter can lead the system to step into chaos via period doubling bifurcations. It is also numerically found that adjusting the nonlinear parameter and asymmetric trap potential can result in the running-phase macroscopic quantum self-trapping (MQST). In the presence of a weak asymmetric trap potential, there exists the parametric resonance in the system.
We study the quantum coherent tunneling between two Bose-Einstein condensates separated through an oscillating trap potential. The cases of slow and rapid varying in the time trap potential are considered. In the case of a slowly varying trap, we study the nonlinear resonances and chaos in the oscillations of the relative atomic population. Using the Melnikov function approach, we find the conditions for chaotic macroscopic quantum-tunneling phenomena to exist. Criteria for the onset of chaos are also given. We find the values of frequency and modulation amplitude which lead to chaos on oscillations in the relative population, for any given damping and the nonlinear atomic interaction. In the case of a rapidly varying trap, we use the multiscale expansion method in the parameter $\ensuremath{\varepsilon}=1/\ensuremath{\Omega},$ where \ensuremath{\Omega} is the frequency of modulations, and we derive the averaged system of equations for the modes. The analysis of this system shows that new macroscopic quantum self-trapping regions, in comparison with the constant trap case, exist.
We have investigated the chaotic and frequency-locked population oscillations between two coupled Bose-Einstein condensates with time-dependent asymmetric potential and damping. Under the deterministic perturbation, there exist stable oscillations close to the separatrix solution, which are Melnikov chaotic. Numerical results reveal that, in the nondissipative regime, regular oscillations gradually tend to chaotic with the increase of the trap asymmetry, the long-term localization disappears, and short-term localization can be changed from one of the Bose-Einstein condensates to the other through the route of Rabi oscillation. But in the dissipative regime, stationary chaos disappears and transient chaos is a common phenomenon before the regular stable frequency-locked oscillations, and a proper damping can keep the localization long lived.
We study the dynamics of two Bose–Einstein condensates (BECs) tunnel-coupled by a double-well potential. A real three-body interaction term is considered and a two-mode approximation is used to derive two coupled equations, which describe the relative population and relative phase. By solving the equations and analyzing the stability of the system, we find the stable stationary solutions for a constant atomic scattering length. When a periodically time-varying scattering length is applied, Melnikov analysis and numerical calculation demonstrate the existence of chaotic behavior and the dependence of chaos on the three-body interaction parameters.
In this paper, we have investigated the stability and population oscillations in a spin–orbit coupled Bose–Einstein condensate. For the time-independent system parameters, the stability of the steady-state solutions was analyzed with the linear stability theorem. For the asymmetric case, we demonstrated that a larger relative energy can enhance macroscopic quantum self-trapping. A larger relative energy or a stronger population transfer strength can assist or suppress the tunneling rate, depending on the initial population. Finally, the chaotic parameter regions and the chaotic atomic tunneling between two periodically driven Bose–Einstein condensates have been investigated. The results reveal that chaos can notably enhance the tunneling rate. The results could be significant in the quantum transport of the spin–orbit coupled cold-atom system.
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 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.