Pattern formation in a driven Bose-Einstein Condensate

TL;DR

This paper investigates how driven Bose-Einstein condensates develop various symmetric density patterns through nonlinear wave interactions, with pattern symmetry controlled by driving frequency ratios.

Contribution

It demonstrates the formation of specific symmetric density patterns in BECs driven at two frequencies, revealing the role of resonant wave mixing in pattern symmetry control.

Findings

Density patterns with D2, D4, D6 symmetries observed

Pattern symmetry controlled by frequency ratio

Resonant wave mixing enhances symmetry-specific excitations

Abstract

Pattern formation is ubiquitous in nature from morphogenesis and cloud formation to galaxy filamentation. More often than not, patterns arise in a medium driven far from equilibrium due to the interplay of dynamical instability and nonlinear wave mixing. We report, based on momentum and real space pattern recognition, formation of density patterns with two- (D$_2$), four- (D$_4$) and six-fold (D$_6$) symmetries in Bose-Einstein condensates (BECs) with atomic interactions driven at two frequencies. The symmetry of the pattern is controlled by the ratio of the frequencies. The D$_6$ density waves, in particular, arise from a resonant wave mixing process that coherently correlates and enhances the excitations that respect the symmetry.