Pattern formation in a driven Bose–Einstein condensate

Abstract

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-chemistry^5,6. Paradigmatic examples, such as Rayleigh–Bénard 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<inf>2</inf>), four- (D<inf>4</inf>) and six-fold (D<inf>6</inf>) symmetries can emerge in Bose–Einstein condensates on demand when the atomic interactions are modulated at multiple frequencies. The D<inf>6</inf> 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.