Coherent state approach to the cross collisional effects in the population dynamics of a two-mode Bose-Einstein condensate

TL;DR

This paper uses a semiclassical coherent state approach to analyze the effects of cross collisions on the population dynamics of a two-mode Bose-Einstein condensate, revealing bifurcations and regime transitions.

Contribution

It introduces a coherent state-based semiclassical method to incorporate cross collisions in BEC dynamics, providing analytical insights into bifurcations and regime changes.

Findings

Cross collisions significantly alter tunneling dynamics at large atom numbers.

A bifurcation transition parameter is analytically identified.

Dynamical regimes depend on initial conditions and collisional parameters.

Abstract

We reanalyze the non-linear population dynamics of a Bose-Einstein Condensate (BEC) in a double well trap considering a semiclassical approach based on a time dependent variational principle applied to coherent states associated to SU(2) group. Employing a two-mode local approximation and hard sphere type interaction, we show in the Schwinger's pseudo-spin language the occurrence of a fixed point bifurcation that originates a separatrix of motion on a sphere. This separatrix corresponds to the borderline between two dynamical regimes of Josephson oscillations and mesoscopic self-trapping. We also consider the effects of interaction between particles in different wells, known as cross collisions. Such terms are usually neglected for traps sufficiently far apart, but recently it has been shown that they contribute to the effective tunneling constant with a factor growing linearly with the particle number. This effect changes considerably the effective tunneling of the system for sufficiently large number of trapped atoms, in perfect accord with experimental data. Finally, we identify analytically the transition parameter associated to the bifurcation in the generalized phase space of the model with cross-collision terms, and show how the dynamical regime depends on the initial conditions of the system and the collisional parameters values.