Floquet engineering with multilevel dipole-interacting Rydberg atoms for quantum simulation

Qubit-based quantum simulators have demonstrated success in investigating quantum magnetism and non-equilibrium many-body phenomena. The emerging control of atomic systems featuring rich multi-level internal structure, presents new prospects for quantum simulation with higher- dimensional spin systems. Here, we explore new opportunities for quantum simulation and non- equilibrium many body dynamics using three-level Rydberg atoms in a programmable tweezer array. Alongside naturally occurring spin exchange dipolar interactions, we demonstrate that periodically driving transitions between the Rydberg levels with microwave fields can additionally lead to the emergence of the density-density interactions and even new spin-exchange interactions that were previously dipole forbidden. The relative strength of all these interactions is finely tunable, con- tingent upon selection of participating Rydberg states and the specifics of the applied microwave driving. By strategically manipulating a precise sequence of drives between the different Rydberg levels, we show how the above interactions can be combined to realize a diverse variety of Floquet Hamiltonians. Within this setting we explore non-equilibrium spin relaxation as a function of initial spin configuration, interaction strengths in system. Our results can be relevant for studies of non- equilibrium dynamics and many-body state preparation in a broad range of AMO systems featuring multilevel exchange interactions.