Pattern formation in a driven Bose–Einstein condensate

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 hydrodynamics1, condensed matter physics2, nonlinear optics3, cosmology4 and bio-chemistry5,6. Paradigmatic examples, such as Rayleigh–Benard convection rolls and Faraday waves7,8, have been studied extensively and found numerous applications9–11. 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- (D2), four- (D4) and six-fold (D6) symmetries can emerge in Bose–Einstein condensates on demand when the atomic interactions are modulated at multiple frequencies. The D6 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. 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.