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Laser Physics

Instability Effects in the Dynamics of three Coupled Bosonic Wells

Pierfrancesco Buonsante, Roberto Franzosi, Vittorio Penna

Published Jan 1, 2003• 3 citations
OpenAlex

Abstract

We report on the dynamics of three bosonic wells (trimer model) coupled cyclically and occupied by N bosons within the standard mean-field picture. Based on the identification of the fixed points of the dynamics, we find periodic solutions representing the trimer proper modes (the system behavior is discussed for initial conditions close to such states in some relevant cases) and the origin of dynamical instabilities. A diffused chaotic behavior and various macroscopic phenomena are detected numerically. Their dependence on macroscopic model parameters is evaluated as well. Finally, we consider the trimer dynamics for an open chain in the case when the central well has an adjustable depth.

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Laser Physics•Jan 1, 2002•1 citation
We report on the dynamics of three bosonic wells (trimer model) coupled cyclically and occupied by N bosons within the standard mean-field picture. Based on the identification of the fixed points of the dynamics, we find periodic solutions representing the trimer proper modes (the system behavior is discussed for initial conditions close to such states in some relevant cases) and the origin of dynamical instabilities. A diffused chaotic behavior and various macroscopic phenomena are detected numerically. Their dependence on macroscopic model parameters is evaluated as well. Finally, we consider the trimer dynamics for an open chain in the case when the central well has an adjustable depth.
The dynamics of the three coupled bosonic wells (trimer) containing N bosons is investigated within a standard (mean-field) semiclassical picture based on the coherent-state method. Various periodic solutions (configured as pi-like, dimerlike, and vortex states) representing collective modes are obtained analytically when the fixed points of trimer dynamics are identified on the N=const submanifold in the phase space. Hyperbolic, maximum and minimum points are recognized in the fixed-point set by studying the Hessian signature of the trimer Hamiltonian. The system dynamics in the neighborhood of periodic orbits (associated with fixed points) is studied via numeric integration of trimer motion equations, thus revealing a diffused chaotic behavior (not excluding the presence of regular orbits), macroscopic effects of population inversion, and self-trapping. In particular, the behavior of orbits with initial conditions close to the dimerlike periodic orbits shows how the self-trapping effect of dimerlike integrable subregimes is destroyed by the presence of chaos.
We analyze thoroughly the mean-field dynamics of a linear chain of three coupled Bose-Einstein condensates, where both the tunneling and the central-well relative depth are adjustable parameters. Owing to its nonintegrability, entailing a complex dynamics with chaos occurrence, this system is a paradigm for longer arrays whose simplicity still allows a thorough analytical study. We identify the set of dynamics fixed points, along with the associated proper modes, and establish their stability character depending on the significant parameters. As an example of the remarkable operational value of our analysis, we point out some macroscopic effects that seem viable to experiments.
The dynamics of the three coupled dipolar Bose—Einstein condensates containing N bosons is investigated within a mean-field semiclassical picture based on the coherent-state method. Varieties of periodic solutions (configured as vortex, single depleted well, and dimerlike states) are obtained analytically when the fixed points are identified on the N = constant. The system dynamics are studied via numeric integration of trimer motion equations, thus revealing macroscopic effects of population inversion and self-trapping with different initial states. In particular, the trajectory of the oscillations of the populations in each well shows how the dynamics of the condensates are effected by the presence of dipole—dipole interaction and gauge field.
The dynamics of a mean-field model of three coupled condensates is studied for initial states characterized by twin condensates. Condensates occupy an open three-well chain, where the central potential-well depth is an independent parameter. Despite its diversity from the closed-chain symmetric model, such model is shown to have an integrable regime involving a predictable evolution for twin-condensate initial states. After establishing the dependence of the phase-space topology on the model parameters, the latter are shown to allow the control of various macroscopic effects such as rapid population inversions, pulsed phase changes, self-trapping and long-duration periodic oscillations. Finally, based on quantizing the system in terms of suitable ``microscopic'' canonical variables, the stability conditions of the integrable regime are related to the su(1,1) structure of the Hamiltonian spectrum.
The dynamics of a mean-field model of three coupled condensates is studied for initial states characterized by twin condensates. Condensates occupy an open three-well chain, where the central potential-well depth is an independent parameter. Despite its diversity from the closed-chain symmetric model, such model is shown to have an integrable regime involving a predictable evolution for twin-condensate initial states. After establishing the dependence of the phase-space topology on the model parameters, the latter are shown to allow the control of various macroscopic effects such as rapid population inversions, pulsed phase changes, self-trapping and long-duration periodic oscillations. Finally, based on quantizing the system in terms of suitable ``microscopic'' canonical variables, the stability conditions of the integrable regime are related to the su(1,1) structure of the Hamiltonian spectrum.
We study the energy spectrum structure of a system of two interacting bosonic wells (dimer model) occupied by N bosons and compare it with the phase-space topology of the same model within the mean-field approach. To this end, we characterize the structure of energy eigenstates by using the symmetry properties of the Hamiltonian, and show that the energy levels are nondegenerate. The presence of doublets leads to recover in the classical limit the self-trapping effect exhibited by the mean-field dimer model. Finally, we do some comments on trimer dynamics to show how the interaction with a third well can cause both dimer-like regimes and strongly chaotic behaviors.