Tuning and probing local thermalization of a Floquet-engineered dipolar ensemble

We experimentally study the many-body out-of-equilibrium dynamics of a three-dimensional, dipolar-interacting spin system with tunable XYZ Heisenberg anisotropy. We utilize advanced Hamiltonian engineering techniques and leverage the inherent disorder in the system to probe global and local spin autocorrelation functions for various XYZ Hamiltonians. The out-of-equilibrium dynamics of global and local observables display striking differences in the vicinity of SU(2)-symmetric Heisenberg Hamiltonians, where global observables are conserved, but local thermalization nonetheless proceeds. The decay shapes of local correlators further exhibit a stretched exponential controlled by the form of the Hamiltonian, which are explained by a model that explicitly realizes the system acting as its own bath. In particular, tuning the Hamiltonian modifies the correlation times and effective fields driving dynamics, thus leading to different thermalization behavior. Our results provide detailed microscopic mechanisms of the relaxation of closed, interacting quantum many-body systems as they approach local thermal equilibrium.