Stable-fixed-point description of square-pattern formation in driven two-dimensional Bose-Einstein condensates

TL;DR

This paper models how periodic modulation of interactions in two-dimensional Bose-Einstein condensates leads to stable square grid density patterns, identified as nonequilibrium steady states through a fixed-point analysis.

Contribution

It introduces a fixed-point framework for understanding pattern formation in driven BECs, extending beyond initial instabilities to stable nonlinear patterns.

Findings

Stable square grid density pattern identified

Fixed points correspond to observed patterns

Pattern stability confirmed through analysis

Abstract

We investigate pattern formation in two-dimensional Bose-Einstein condensates (BECs) caused by periodic driving of the interatomic interaction. We show that this modulation generically leads to a stable square grid density pattern, due to nonlinear effects beyond the initial Faraday instability. We take the amplitudes of two waves parametrizing the two-dimensional density pattern as order parameters in pattern formation. For these amplitudes, we derive a set of coupled time evolution equations from the Gross--Pitaevskii (GP) equation with a time-periodic interaction. We identify the fixed points of the time evolution and show by stability analysis that the inhomogeneous density exhibits a square grid pattern, which can be understood as a manifestation of a stable fixed point. Our stability analysis establishes the pattern in BECs as a nonequilibrium steady state.