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.

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The dominance of interactions over kinetic energy lies at the heart of strongly correlated quantum matter, from fractional quantum Hall liquids, to atoms in optical lattices and twisted bilayer graphene. 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 magnetic fields, where the instability of quantum Hall liquids towards a Wigner crystal is heralded by a roton-like softening of density modulations at the magnetic length. Remarkably, interacting bosons in a gauge field are also expected to form analogous liquid and crystalline states. However, combining interactions with strong synthetic magnetic fields has been a challenge for experiments on bosonic quantum gases. Here, we study the purely interaction-driven dynamics of a Landau gauge Bose-Einstein condensate in and near the lowest Landau level. We observe a spontaneous crystallization driven by condensation of magneto-rotons, 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.

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In order to build more powerful sources of sound for energy conversion, the synchronization of two thermoacoustic heat engines has been studied. Experiments were performed on engines in the acoustic frequency range of 2.6 kHz and also on very small engines in the ultrasonic range of 24 kHz. In both cases, the engines were mounted on a cylindrical cavity, and they were coupled mainly by the acoustic field in the surrounding air at one atmosphere. They were driven by heaters of resistance wire in contact with the hot heat exchanger. At a specific coupling between the 2.6 kHz, engines' synchronization occurred, and also for the 24 kHz devices; frequency pulling in each pair of engines led to a common frequency in each set, i.e., in-phase synchronization. The strength of the synchronization was determined as a function of detuning of engines. Mutual entrainment was observed at the onset of oscillations and this is attributed to drive by fluctuations. Moreover, as a result of synchronization, the critical temperature gradient for onset of oscillations was reduced from that of the individual values. Delays between two oscillators in the start up led to quenching of the generated sound output ( oscillation “death” of Rayleigh).