Parametric resonance of a Bose-Einstein condensate in a ring trap with periodically driven interactions

TL;DR

This paper investigates how periodic modulation of interactions in a ring-shaped Bose-Einstein condensate leads to parametric resonance, resulting in observable temporal and spatial patterns, with insights into non-linear dynamics and mode-locking mechanisms.

Contribution

It introduces a three-mode model to analyze non-linear dynamics of a driven ring BEC and demonstrates pattern robustness against disorder.

Findings

Temporal and spatial patterns emerge due to parametric resonance.

A three-mode model effectively captures non-linear dynamics.

Patterns remain robust despite disorder.

Abstract

We study the instability of a ring Bose-Einstein condensate under a periodic modulation of inter-atomic interactions. The condensate exhibits temporal and spatial patterns induced by the parametric resonance, which can be characterized by Bogoliubov quasi-particle excitations in the Floquet basis. As the ring geometry significantly limits the number of excitable Bogoliubov modes, we are able to capture the non-linear dynamics of the condensate using a three-mode model. We further demonstrate the robustness of the temporal and spatial patterns against disorder, which are attributed to the mode-locking mechanism under the ring geometry. Our results can be observed in cold atomic systems and are also relevant to physical systems described by the non-linear Schrodinger's equation.