A Flexible Toolbox for Hamiltonian Engineering with Driven Rydberg Atom Arrays

Neutral atom arrays have recently emerged as a powerful platform for programmable quantum simulation and computation. In this project, we introduce a technique for Hamiltonian engineering based on perturbing around time-reversed trajectories. In particular, we illustrate how a multitude of new interaction terms can be controllably engineered in Rydberg atom arrays using time-dependent global driving. We illustrate these techniques in two settings. First, we show how blockade-consistent exchange interactions can be engineered, enabling exploration of novel phases with emergent particle number conservation in near-term analog devices. Then, we show how higher-weight ring-exchange terms can be implemented, enabling studies of dynamics in 2D gauge theories. Extensions incorporating additional control, such as atom reconfiguration, are also discussed.