Non-Hermitian dynamics and PT-symmetry breaking in interacting mesoscopic Rydberg platforms

We simulate the dissipative dynamics of a mesoscopic system of long-range interacting particles which can be mapped into non-Hermitian spin models with a PT symmetry. We find rich PT phase diagrams with PT-symmetric and PT-broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the PT symmetries of such systems may be probed by studying their dynamics. We note that systems of Rydberg atoms and systems of Rydberg ions with strong dipolar interactions are particularly well suited for such studies. We present a viable proposal for implementing non-Hermitian physics with PT symmetry in Rydberg systems. We show that for realistic parameters, long-range interactions allow the emergence of new PT-symmetric regions, generating new PT phase transitions. In addition, such PT-symmetry phase transitions are found by changing the configurations of the Rydberg atoms. We propose a postselection scheme on an ensemble of Rydberg ions described by an effective three-level system. Detecting the population dynamics, the system shows an oscillatory behavior in the PT-unbroken phase and a stationary population for long times in the PT-broken phase.