Spontaneous Formation of Star-Shaped Surface Patterns in a Driven Bose-Einstein Condensate

TL;DR

This study experimentally demonstrates the spontaneous emergence of star-shaped surface patterns with various symmetries in a driven Bose-Einstein condensate, linking pattern formation to surface mode dispersion and instability analysis.

Contribution

It introduces a method to excite and analyze star-shaped surface patterns in BECs using modulation near Feshbach resonances, connecting pattern formation to collective excitation dispersion.

Findings

Observation of star-shaped patterns with 2-7 fold symmetry.

Identification of the $l=6$ mode as uniquely unstable.

Precise measurement of the collective excitation dispersion relation.

Abstract

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with $l$-fold symmetry, ranging from quadrupole ($l=2$) to heptagon modes ($l=7$), are parametrically excited by modulating the scattering length near the Feshbach resonance. An effective Mathieu equation and Floquet analysis are utilized, relating the instability conditions to the dispersion of the surface modes in a trapped superfluid. Identifying the resonant frequencies of the patterns, we precisely measure the dispersion relation of the collective excitations. The oscillation amplitude of the surface excitations increases exponentially during the modulation. We find that only the $l=6$ mode is unstable due to its emergent coupling with the dipole motion of the cloud. Our experimental results are in excellent agreement with the mean-field framework. Our work opens a new pathway for generating higher-lying collective excitations with applications, such as the probing of exotic properties of quantum fluids and providing a generation mechanism of quantum turbulence.