Uncovering Emergent Spacetime Supersymmetry with Rydberg Atom Arrays.

In the zoo of emergent symmetries in quantum many-body physics, the previously unrealized emergent spacetime supersymmetry (SUSY) is particularly intriguing. Although it was known that spacetime SUSY could emerge at the (1+1)d tricritical Ising transition, an experimental realization is still absent. In this Letter, we propose to realize emergent spacetime SUSY using reconfigurable Rydberg atom arrays featuring two distinct sets of Rydberg excitations, tailored for implementation on dual-species platforms. In such systems, the spacetime SUSY manifests itself in the respective correlation functions of a bosonic mode and its fermionic partner. However, the correlation function of the fermionic mode inevitably involves a string operator, making direct measurement challenging in the conventional setting. Here, we leverage the hybrid analog-digital nature of the Rydberg atom arrays, which allows for the simulation of a physical Hamiltonian and the execution of a digital quantum circuit on the same platform. This hybrid protocol offers a new perspective for uncovering the hidden structure of emergent spacetime SUSY.