Dipolar Interacting Systems: Quantum Thermalization and Turbulence

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We propose to use two complementary experimental ultracold gas setups with strongly magnetic dysprosium (Dy) and chromium (Cr) atoms to explore the general laws governing the dynamics of a long-range interacting closed quantum system. In both cases, we will first bring the system out of equilibrium and then study the fascinating processes that take place on the way to equilibrium under the influence of dipole-dipole interactions. Our project will thus allow the study of quantum thermalization from two complementary perspectives. First, our Dy experiment will be a continuous polarized fluid in tailored geometries, and thermalization in the wake of quantum turbulence will be studied. Second, our Cr experiment realizes a lattice spin model in which thermalization occurs through spin entanglement. This collaboration will benefit firstly from strong technical synergies: the groups will work simultaneously on similar experimental developments, building on each other's expertise. They will improve their production of stable and controllable dipolar quantum gases, the stability of the external magnetic field and the resolution of their imaging. They will develop novel probing schemes to measure spatial and momentum distributions, correlations, and spin entanglement as well as light-based protocols to engineer the Hamiltonian and perform excitations. These improvements aim to overcome important bottlenecks in detection and coherent control to characterize emergent quantum properties. With these tools at our disposal, we will be able to explore fundamental aspects of quantum thermalization in long-range systems, in close relation to the eigenstate thermalization hypothesis. First, we will tune the gas geometry, which is known to have a key influence on long-range interacting systems, and study thermalization while changing both the system symmetries and the initial total energy. Secondly, we will vary the underlying equilibrium phases, and study thermalization with respect to either spatially disordered (superfluid) or ordered (Mott insulator or supersolid) phases. Our aim is to derive general rules linking the quantum thermalization of long-range interacting systems to their underlying phases and phase transitions. In this way, we expect this project to be a major step forward in an area of research that has barely been touched upon experimentally.