Observation of pattern stabilization in a driven superfluid

TL;DR

This paper reports the experimental observation of stable square pattern formation in a driven two-dimensional Bose-Einstein condensate, explained by nonlinear interactions and fixed-point dynamics.

Contribution

It demonstrates the stabilization mechanism of patterns via high-order phonon interactions and fixed-point analysis in a quantum gas system.

Findings

Observation of stable square patterns in a BEC

Identification of fixed points governing pattern dynamics

Experimental validation of theoretical flow towards stable fixed points

Abstract

The formation of patterns in driven systems has been studied extensively, and their emergence can be connected to a fine balance of instabilities and stabilization mechanisms. While the early phase of pattern formation can be understood on the basis of linear stability analyses, the long-time dynamics can only be described by accounting for the interactions between the excitations generated by the drive. Here, we observe the stabilization of square patterns in an interaction-driven, two-dimensional Bose-Einstein condensate. These patterns emerge due to inherent high-order processes that become relevant in the regime of large phonon occupations. Theoretically, this can be understood as the emergence of a stable fixed point of coupled nonlinear amplitude equations, which include phonon-phonon interactions. We experimentally probe the predicted flows towards such a stable fixed-point, as well as repulsion from a saddle fixed-point, using the experimental control unique to quantum gases.