Non-Hermitian dynamics and $\mathcal{PT}$-symmetry breaking in interacting mesoscopic Rydberg platforms

TL;DR

This paper explores the rich non-Hermitian and $ ext{PT}$-symmetry breaking phenomena in interacting mesoscopic Rydberg systems, revealing new phase transitions and dynamical behaviors through simulations and parameter modulation.

Contribution

It introduces a detailed simulation of $ ext{PT}$-symmetry phases in long-range Rydberg systems, highlighting the impact of interactions and configurations on phase transitions.

Findings

Identification of $ ext{PT}$-symmetric and $ ext{PT}$-broken phases.

Discovery of new $ ext{PT}$-phase transitions due to long-range interactions.

Observation of oscillatory and exponential dynamics in different phases.

Abstract

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 $\mathcal{PT}$ symmetry. We find rich $\mathcal{PT}$-phase diagrams with $\mathcal{PT}$-symmetric and $\mathcal{PT}$-broken phases. The dynamical regimes can be further enriched by modulating tunable parameters of the system. We outline how the $\mathcal{PT}$ 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 show that for realistic parameters, long-range interactions allow the emergence of new $\mathcal{PT}$-symmetric regions, generating new $\mathcal{PT}$-phase transitions. In addition, such $\mathcal{PT}$-symmetry phase transitions are found by changing the Rydberg atoms configurations. We monitor the transitions by accessing the populations of the Rydberg states. Their dynamics display oscillatory or exponential dependence in each phase.