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Chaotic Dynamics in Two Coupled Bose-Einstein Condensates with Three-body Interaction

Shaoying Chen

Published Jan 1, 2006• 0 citations
OpenAlex

Abstract

Weakly coupled Bose-Einstein subjected to the double-well potential with time-dependent atomic scattering length is studied in this paper.Two cases are considered:a stable stationary solution of the time-independent system exist in the first case;in the second case,the time-independent system have three stationary solutions,including two stable ones and one instable one.Chaos can appear in the time-dependent system,We have discussed the dynamic of the system.

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Weakly coupled Bose-Einstein subjected to the double-well potential with time-dependent atomic scattering length is studied in this paper.Two cases are considered:a stable stationary solution of the time-independent system exist in the first case;in the second case,the time-independent system have three stationary solutions,including two stable ones and one instable one.Chaos can appear in the time-dependent system,We have discussed the dynamic of the system.
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.
We investigate the dynamics of two tunnel-coupled Bose-Einstein condensates (BECs) in a double-well potential. The effects of the three-body recombination loss and the feeding of the condensates from the thermal cloud are studied in the case of attractive interatomic interaction. An imaginary three-body interaction term is considered and a two-mode approximation is used to derive three coupled equations which describe the total atomic numbers of the two condensates, the relative population and relative phase respectively. Theoretical analyses and numerical calculations demonstrate the existence of chaotic and hyperchaotic behaviour by using a periodically time-varying scattering length.
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.
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 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 investigate the dynamics of two Bose–Einstein condensates (BECs) tunnel coupled by a double-well potential. In the case of attractive interatomic interaction, the effects of the three-body recombination losses and the feeding of the condensates from the thermal cloud are studied by using a two-mode approximation. It is shown that the stability region of the parameter space could be enlarged by increasing the three-body losses or the tunnelling coefficient. The numerical results also reveal some interesting motion characteristics of the BECs for different s-wave scattering lengths, including macroscopic quantum self-trapping of non-stationary state BECs, and periodic oscillation of the population whose phase orbit tends to a stable limit cycle.