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Dynamics in Two Periodically Driven and Weakly Coupled

Bose-Einstein Condensates

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

In this paper, dynamics in the oscillations of the relative atomic population in two periodically driven and weakly coupled Bose-Einstein condensates (BECs) was qualitatively studied. Using the well-known Melnikov method, the conditions of existence of the periodic and chaotic coherent atomic tunnellings were given in the model. Our results indicate the typical route from bifurcation of the limited circles to chaos, and are in agreement with the previous numerical results.

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Dynamics in Two Periodically Driven and Weakly Coupled Bose-Einstein Condensates

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In this paper, dynamics in the oscillations of the relative atomic population in two periodically driven and weakly coupled Bose-Einstein eondensates (BECs) was qualitatively studied. Using the well-known Melnikov method, the conditions of existence of the periodic and chaotic coherent atomic tunnellings were given in the model. Our results indicate the typical route from bifurcation of the limited circles to chaos, and are in agreement with the previous numerical results.

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Chaohong Lee, Wenhua Hai, Lei Shi +2 more

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Physical Review A•Oct 2, 2001•101 citations
In this paper, dynamics in the oscillations of the relative atomic population in two periodically driven and weakly coupled Bose-Einstein condensates (BECs) was qualitatively studied. Using the well-known Melnikov method, the conditions of existence of the periodic and chaotic coherent atomic tunnellings were given in the model. Our results indicate the typical route from bifurcation of the limited circles to chaos, and are in agreement with the previous numerical results.
The chaotic coherent atomic tunneling between two periodically driven and weakly coupled Bose-Einstein condensates has been investigated. The perturbed correction to the homoclinic orbit is constructed and its boundedness conditions are established that contain the Melnikov criterion for the onset of chaos. We analytically reveal that the chaotic coherent atomic tunneling is deterministic but not predictable. Our numerical calculation shows good agreement with the analytical result and exhibits nonphysically numerical instability. By adjusting the initial conditions, we propose a method to control the unboundedness, which leads the quantum coherent atomic tunneling to predictable periodical oscillation.
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 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.
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.