Phase transitions in Wick-rotated $\mathcal{PT}$-symmetric optics

TL;DR

This paper explores spectral phase transitions in Wick-rotated $ ext{PT}$-symmetric optical systems, demonstrating how optical setups can serve as experimental platforms for studying non-Hermitian phase phenomena.

Contribution

It introduces optical analogues of Wick-rotated $ ext{PT}$-symmetric models, linking theoretical spectral phase transitions to practical optical cavity experiments.

Findings

Optical cavities with variable reflectivity exhibit spectral phase transitions.

Hydrodynamic and nonlinear dimer models have optical analogues demonstrating these transitions.

Optics provides an accessible test bed for non-Hermitian spectral phase phenomena.

Abstract

$\mathcal{PT}$-symmetric models with a Wick rotation of time ($ t \rightarrow \pm i t$) show spectral phase transitions that are similar to those of dissipative systems driven out of equilibrium. Optics can provide an accessible test bed to explore spectral phase transitions of Wick-rotated $\mathcal{PT}$-symmetric models. This is shown by considering the transverse dynamics of laser light in optical cavities with variable reflectivity and tilted mirrors. As examples, we discuss in details the optical analogue of the hydrodynamic Squire model of vorticity and the Wick-rotated $\mathcal{PT}$-symmetric nonlinear dimer model.