Collective modes, chaotic behavior and self-trapping in the dynamics of three coupled Bose-Einstein condensates

TL;DR

This paper explores the complex dynamics of three coupled Bose-Einstein condensates, revealing collective modes, chaotic behavior, and the impact of chaos on self-trapping phenomena through analytical and numerical methods.

Contribution

It provides a detailed analytical and numerical study of the collective modes and chaotic dynamics in a three-well Bose-Einstein condensate system, highlighting the destruction of self-trapping by chaos.

Findings

Identification of various collective modes as fixed points.

Observation of chaotic behavior near periodic orbits.

Chaos disrupts self-trapping in dimerlike regimes.

Abstract

The dynamics of 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 analitically 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 neighbourhood of periodic orbits (associated to 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.