Transition to Instability in a Periodically Kicked Bose-Einstein Condensate on a Ring

TL;DR

This paper investigates the stability and transition to chaos in a periodically kicked Bose-Einstein condensate on a ring, revealing how interactions lead to instability and chaos through analytical and numerical methods.

Contribution

It introduces a nonlinear model of a kicked BEC on a ring, analyzes the stability regimes, and identifies the critical interaction strength causing instability and chaos.

Findings

Weak interactions sustain quasiperiodic motion and stability.

Beyond a critical interaction strength, the system becomes chaotic and unstable.

Arnold diffusion facilitates transition to higher energy levels leading to instability.

Abstract

A periodically kicked ring of a Bose-Einstein condensate is considered as a nonlinear generalization of the quantum kicked rotor, where the nonlinearity stems from the mean field interactions between the condensed atoms. For weak interactions, periodic motion (anti-resonance) becomes quasiperiodic (quantum beating) but remains stable. There exists a critical strength of interactions beyond which quasiperiodic motion becomes chaotic, resulting in an instability of the condensate manifested by exponential growth in the number of noncondensed atoms. In the stable regime, the system remains predominantly in the two lowest energy states and may be mapped onto a spin model, from which we obtain an analytic expression for the beat frequency and discuss the route to instability. We numerically explore parameter regime for the occurrence of instability and reveal the characteristic density profile for both condensed and noncondensed atoms. The Arnold diffusion to higher energy levels is found to be responsible for the transition to instability. Similar behavior is observed for dynamically localized states (essentially quasiperiodic motions), where stability remains for weak interactions but is destroyed by strong interactions.