Time periodicity and dynamical stability in two-boson systems

TL;DR

This paper investigates the recurrence periods and stability conditions of two-boson dynamical systems, proposing a new notion of stability based on period stability, supported by simulations and applications to coherent population trapping.

Contribution

It introduces a novel approach to defining dynamical stability through period stability and applies it to two-boson systems and coherent population trapping.

Findings

Recurrence periods are calculated for two-boson systems.

A new stability criterion based on period stability is proposed.

Simulation results support the proposed stability scheme.

Abstract

We calculate the period of recurrence of dynamical systems comprising two interacting bosons. A number of theoretical issues related to this problem are discussed, in particular, the conditions for small periodicity. The knowledge gathered in this way is then used to propose a notion of dynamical stability based on the stability of the period. Dynamical simulations show good agreement with the proposed scheme. We also apply the results to the phenomenon known as coherent population trapping and find stability conditions in this specific case.