Phase transition through the splitting of self-dual spectral singularity in optical potentials

TL;DR

This paper explores how spectral singularities in optical media with antilinear symmetry can split into complex conjugate pairs, revealing a novel phase transition mechanism distinct from traditional PT-symmetry breaking.

Contribution

It demonstrates that spectral singularities in such media are always self-dual and introduces the concept of their splitting into conjugate eigenvalues as a new phase transition scenario.

Findings

Spectral singularities are always self-dual in antilinear symmetric media.

Splitting of spectral singularities signifies a phase transition similar to PT-symmetry breaking.

Local antilinear symmetry prevents the existence of spectral singularities.

Abstract

We consider optical media which feature antilinear symmetries. We show that: (i) spectral singularities of such media (if any) are always self-dual, i.e., correspond to CPA-lasers; (ii) under the change of a system's parameter the self-dual spectral singularity may split into a pair of isolated complex conjugate eigenvalues, which corresponds to an unconventional and overlooked in the most of previous studies scenario of the phase transition (known as $PT$-symmetry breaking in systems obeying parity-time symmetry); (iii) if the antilinear symmetry is local, i.e., does not involve any spatial reflection, then no spectral singularity is possible. Our findings are illustrated with several examples including a $PT$-symmetric bilayer and other complex potentials discussed in recent literature.