ABSTRACT
The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids1, to atoms in optical lattices2 and twisted bilayer graphene3. 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 crystal4-9 is heralded by a roton-like softening of density modulations at the magnetic length7,10-12. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states13-21. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases18,21. Here we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate22 in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons7,10, 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.
ABSTRACT
The equivalence between particles under rotation and charged particles in a magnetic field relates phenomena as diverse as spinning atomic nuclei, weather patterns, and the quantum Hall effect. For such systems, quantum mechanics dictates that translations along different directions do not commute, implying a Heisenberg uncertainty relation between spatial coordinates. We implement squeezing of this geometric quantum uncertainty, resulting in a rotating Bose-Einstein condensate occupying a single Landau gauge wave function. We resolve the extent of zero-point cyclotron orbits and demonstrate geometric squeezing of the orbits' centers 7 decibels below the standard quantum limit. The condensate attains an angular momentum exceeding 1000 quanta per particle and an interatomic distance comparable to the cyclotron orbit. This offers an alternative route toward strongly correlated bosonic fluids.
