  Simulating quantum dynamics of lattice gauge theories (LGTs) is an exciting
frontier in quantum science. Programmable quantum simulators based on neutral
atom arrays are a promising approach to achieve this goal, since strong Rydberg
blockade interactions can be used to naturally create low energy subspaces that
can encode local gauge constraints. However, realizing regimes of LGTs where
both matter and gauge fields exhibit significant dynamics requires the presence
of tunable multi-body interactions such as those associated with ring exchange,
which are challenging to realize directly. Here, we develop a method for
generating such interactions based on time-periodic driving. Our approach
utilizes controlled deviations from time-reversed trajectories, which are
accessible in constrained PXP-type models via the application of frequency
modulated global pulses. We show that such driving gives rise to a family of
effective Hamiltonians with multi-body interactions whose strength is
non-perturbative in their respective operator weight. We apply this approach to
a two-dimensional U(1) LGT on the Kagome lattice, where we engineer strong
six-body magnetic plaquette terms that are tunable relative to the kinetic
energy of matter excitations, demonstrating access to previously unexplored
dynamical regimes. Potential generalizations and prospects for experimental
implementations are discussed.
