Pattern formation in a driven Bose-Einstein condensate

Two-dimensional density patterns with two-, four- and six-fold symmetries emerge in homogeneous Bose-Einstein condensates when the atomic interactions are modulated at multiple frequencies causing the coherent mixing of excitations. Pattern formation is ubiquitous in nature at all scales, from morphogenesis and cloud formation to galaxy filamentation. How patterns emerge in a homogeneous system is a fundamental question across interdisciplinary research including hydrodynamics(1), condensed matter physics(2), nonlinear optics(3), cosmology(4) and bio-chemistry(5,6). Paradigmatic examples, such as Rayleigh-Benard convection rolls and Faraday waves(7,8), have been studied extensively and found numerous applications(9-11). How such knowledge applies to quantum systems and whether the patterns in a quantum system can be controlled remain intriguing questions. Here we show that the density patterns with two- (D-2), four- (D-4) and six-fold (D-6) symmetries can emerge in Bose-Einstein condensates on demand when the atomic interactions are modulated at multiple frequencies. The D-6 pattern, in particular, arises from a resonant wave-mixing process that establishes phase coherence of the excitations that respect the symmetry. Our experiments explore a novel class of non-equilibrium phenomena in quantum gases, as well as a new route to prepare quantum states with desired correlations.