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

TL;DR

This paper proposes a method to measure the Witten index, a topological invariant indicating supersymmetry, in quantum simulators using Rydberg atom arrays, demonstrating its robustness in a supersymmetric spin model.

Contribution

It introduces an averaging technique to infer the Witten index in quantum analog simulators, linking topological physics with Rydberg atom systems.

Findings

The method successfully infers the Witten index from open system data.

Numerical simulations show the topological robustness of the Witten index.

The approach provides a route for identifying many-body topological physics in quantum simulators.

Abstract

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 analog 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 Letter defines a route for quantum analog simulators to directly identify many-body topological physics.