Quantum simulation with tunable multi-body interactions in periodically driven Rydberg atom arrays

Neutral atom arrays driven into Rydberg states are a promising approach for realizing programmable quantum systems, where strong interactions associated with Rydberg blockade allow for simulation of complex spin models. In this talk, I will discuss a Floquet engineering technique that extends the capabilities of Rydberg quantum simulators and enables control over new forms of interactions. Our approach is based on time-dependent modulation of Rydberg laser detuning and leverages controlled deviations from periodic many-body trajectories as a resource for operator spreading. Such time-evolved operators provide a basis for engineering effective Hamiltonians with strong, non-perturbative multi-body interactions and we develop an optimization procedure for the time-dependent detuning in order to realize specific many-body models. As applications, we show how to engineer spin chains that dynamically generate large-scale multi-partite entanglement from simple initial states, and how to simulate dynamics of certain two-dimensional lattice gauge theories in previously inaccessible regimes. I will discuss a first experimental implementation of our approach on a Rydberg quantum simulator and give an outlook on promising future directions.