Dynamics of a Bose-Einstein condensate in a symmetric triple-well trap

TL;DR

This paper provides a comprehensive analysis of Bose-Einstein condensate dynamics in a symmetric triple-well trap, combining classical and quantum approaches to explore stability, interactions, and chaos in the system.

Contribution

It introduces a classical variational method using SU(3) coherent states and examines the effects of off-site interactions and quantum-classical correspondence in the system.

Findings

Identification of equilibrium points and their stability

Analytical demonstration of twin-condensate dynamics as an integrable sub-regime

Quantification of classicality through generalized purity measures

Abstract

We present a complete analysis of the dynamics of a Bose-Einstein condensate trapped in a symmetric triple-well potential. Our classical analogue treatment, based on a time-dependent variational method using SU(3) coherent states, includes the parameter dependence analysis of the equilibrium points and their local stability, which is closely related to the condensate collective behaviour. We also consider the effects of off-site interactions, and how these "cross-collisions" may become relevant for a large number of trapped bosons. Besides, we have shown analytically, by means of a simple basis transformation in the single-particle space, that an integrable sub-regime, known as twin-condensate dynamics, corresponds in the classical phase space to invariant surfaces isomorphic to the unit sphere. However, the quantum dynamics preserves the twin-condensate defining characteristics only partially, thus breaking the invariance of the associated quantum subspace. Moreover, the periodic geometry of the trapping potential allowed us to investigate the dynamics of finite angular momentum collective excitations, which can be suppressed by the emergence of chaos. Finally, using the generalized purity associated to the su(3) algebra, we were able to quantify the dynamical classicality of a quantum evolved system, as compared to the corresponding classical trajectory.