Toward Quantum Analogue Simulation of Many-Body Supersymmetry with Rydberg Atom Arrays

A topological quantum number, the Witten index, characterizes supersymmetric models by probing for zero energy modes and the possibility of supersymmetry breaking. We propose an averaging method to infer the Witten index in quantum analogue simulators. Motivated by recent work on Rydberg atoms trapped in optical tweezer arrays, we consider a related supersymmetric XXZ spin model. We show how to infer the Witten index from open system averaging and numerically demonstrate its topological robustness in this model. Our work defines a route for quantum analogue simulators to directly identify many-body topological physics.