Chaos onset in large rings of Bose-Einstein condensates

TL;DR

This paper investigates how large rings of Bose-Einstein condensates transition from coherent to chaotic states, revealing a critical timescale that delays the loss of coherence despite inherent instabilities.

Contribution

It introduces the concept of a critical timescale that extends coherence lifetime in chaotic regimes of Bose-Einstein condensate rings.

Findings

Chaotic dynamics lead to averaging out circulating currents.

A critical timescale $t_c$ significantly exceeds linear stability predictions.

Chaos onset depends on phase difference and interaction strength.

Abstract

We consider large rings of weakly-coupled Bose-Einstein condensates, analyzing their transition to chaotic dynamics and loss of coherence. Initially, a ring is considered to be in an eigenstate, i.e. in a commensurate configuration with equal site fillings and equal phase differences between neighboring sites. Such a ring should exhibit a circulating current whose value will depend on the initial, non-zero phase difference. The appearance of such currents is a signature of an established coherence along the ring. If phase difference falls between $\pi/2$ and $3\pi/2$ and interparticle interaction in condensates exceeds a critical interaction value $u_c$, the coherence is supposed to be quickly destroyed because the system enters a chaotic regime due to inherent instabilities. This is, however, only a part of the story. It turns out that chaotic dynamics and resulting averaging of circular current to zero is generally offset by a critical time-scale $t_c$, which is almost two orders of magnitude larger than the one expected from the linear stability analysis. We study the critical time-scale in detail in a broad parameter range.