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

We observe experimentally the spontaneous formation of star-shaped surface patterns in driven Bose-Einstein condensates. Two-dimensional star-shaped patterns with /-fold symmetry, ranging from quadru-pole (I = 2) to heptagon modes (1 = 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 arc 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.

Automated summary

Star-shaped surface patterns are experimentally observed in driven Bose-Einstein condensates, with varying symmetries and instability in certain modes. The oscillation amplitude increases exponentially during modulation, with only the l=6 mode being unstable. Experimental results are in excellent agreement with the mean-field framework.