Critical exponents near the Liouvillian exceptional structure in Rydberg vapors

In a dissipative Rydberg vapor, the interplay of many-body effects and non-Hermiticity gives rise to a Liouvillian exceptional structure, where exceptional arcs merge at a higher-order exceptional point of the Liouvillian superoperator. Spectral features of the exceptional structure naturally give rise to critical dynamics, which have interesting implications for experiments. In this work, we study the response of the system to perturbations near the Liouvillian exceptional structure, and evaluate the critical exponents. The results are consistent with those in linear non-Hermitian Hamiltonians, thus confirming the exceptional nature of the structures herein. We also discuss how these exponents can be measured experimentally.