Exceptional points and phase transitions in non-Hermitian binary systems

TL;DR

This paper explores the relationship between exceptional points and phase transitions in non-Hermitian binary systems, revealing that exceptional points are where stable and unstable solutions merge, and that phase transitions can occur even in weak coupling regimes.

Contribution

It clarifies the role of exceptional points in phase transitions, showing they are not always endpoints, and extends the analysis to weak coupling regimes with persistent oscillations.

Findings

Exceptional points are where stable and unstable solutions coalesce.

Phase transitions can occur in the weak coupling regime.

Persistent Rabi-like oscillations are demonstrated.

Abstract

Recent study demonstrated that steady states of a polariton system may show a first-order dissipative phase transition with an exceptional point that appears as an endpoint of the phase boundary [R. Hanai et al., Phys. Rev. Lett. 122, 185301 (2019)]. Here, we show that this phase transition is strictly related to the stability of solutions. In general, the exceptional point does not correspond to the endpoint of a phase transition, but rather it is the point where stable and unstable solutions coalesce. Moreover, we show that the transition may occur also in the weak coupling regime, which was excluded previously. In a certain range of parameters, we demonstrate permanent Rabi-like oscillations between light and matter fields. Our results contribute to the understanding of nonequilibrium light-matter systems, but can be generalized to any two-component oscillatory systems with gain and loss.