Simulating generic spin exchange models in Rydberg atom arrays via Floquet engineering

Arrays of atoms in Rydberg states are a highly promising platform for simulating quantum spin systems. It was previously proposed that Rydberg atoms could be used to simulate any type of spin exchange, by using two interleaved arrays - one for control and the other for simulation. However, since this paradigm is currently out of experimental reach, Rydberg atom arrays are limited in practice to emulating very specific models. Here, we propose a new paradigm to generate generic spin exchange models in Rydberg atom arrays, based on periodic sequences of global addressing via microwave pulses and local addressing via selective light shifts. We show how spin-exchange models beyond the reach of current experiments - in particular, Dzyaloshinskii-Moriya and Kitaev interactions - can be generated using this approach. We verify our proposal numerically via matrix product state (MPS)-based simulations of large Rydberg atom arrays, demonstrating the successful generation of effective spin models using realistic addressing sequences. Our proposal is based solely on capabilities that were already demonstrated in experiment, providing a viable path towards investigating a myriad of exotic quantum spin systems.