Spin and energy transport in a solid-state quantum simulator*

Characterizing the emergence of classical hydrodynamics from strongly correlated quantum systems remains an important experimental challenge. Nuclear spins in solids provide an intriguing platform to study such emergent hydrodynamics; in particular, the ability to use Floquet engineering to tune the effective Hamiltonian can allow for the exploration of different hydrodynamical behaviors using nuclear magnetic resonance techniques. However, a remaining challenge in such systems is to achieve local measurement with collective RF controls, as needed to characterize hydrodynamics. Here, we introduce a novel technique that exploits intrinsic disorder in such systems to enable the measurement of local autocorrelation functions with only global control. With this toolset, we measure both the magnetization and energy transport of nuclear spins in fluorapatite. By tuning the effective Hamiltonian, we demonstrate that the spin transport can be tuned between ballistic and diffusive behavior, while the energy transport remains ballistic throughout the time-scales measured in our experiment. Our work opens the door to studying interacting integrable systems using nuclear magnetic resonance.