Crystallization of bosonic quantum Hall states in a rotating quantum gas.

The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids 1 , to atoms in optical lattices 2 and twisted bilayer graphene 3 . Crystalline phases often compete with correlated quantum liquids, and transitions between them occur when the energy cost of forming a density wave approaches zero. A prime example occurs for electrons in high-strength magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal 4-9 is heralded by a roton-like softening of density modulations at the magnetic length 7,10-12 . Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states 13-21 . However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases 18,21 . Here we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate 22 in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons 7,10 , excitations visible as density modulations at the magnetic length. Increasing the cloud density smoothly connects this behaviour to a quantum version of the Kelvin-Helmholtz hydrodynamic instability, driven by the sheared internal flow profile of the rapidly rotating condensate. At long times the condensate self-organizes into a persistent array of droplets separated by vortex streets, which are stabilized by a balance of interactions and effective magnetic forces.