Spontaneous formation of persistent square pattern in a driven superfluid

The emergence of patterns from simple physical laws belongs to the most striking topics in natural science. In particular, the spontaneous formation of structures from an initially homogeneous state can eventually lead to stable, non-homogeneous states of matter. Here we report on the spontaneous formation of square lattice patterns in a rotationally symmetric and driven Bose-Einstein condensate, confined in a two-dimensional box potential with absorptive boundaries. The drive is realized by globally modulating the two-particle interaction periodically in time. After a primary phase of randomly oriented stripes that emerge as a consequence of the Faraday instability, we observe the subsequent formation of persistent square lattice patterns in the highly occupied regime, where phonon-phonon interactions become relevant. We show theoretically that this state can be understood as an attractive fixed point of coupled nonlinear amplitude equations. Establishing the existence of this fixed point opens the perspective for engineering new, highly correlated states of matter in driven superfluids.