Mesoscopic M\"obius ladder lattices as non-Hermitian model systems

TL;DR

This paper explores non-Hermitian physics in mesoscopic systems, specifically in optical microcavities and M"obius ladder lattices, revealing unique spectral phenomena like PT-broken phases and exceptional points.

Contribution

It introduces mesoscopic M"obius ladder lattices as a new non-Hermitian model system, demonstrating how topology influences spectral properties and phase transitions.

Findings

M"obius topology induces a new form of level crossing.

Non-Hermitian coupling leads to PT-broken phases.

Effective models reveal symmetry and complexity in mode interactions.

Abstract

While classic quantum chaos originated from the idea to set into context nonlinear physics and Hermitian quantum mechanics, non-Hermitian models have enhanced the field in recent years. At the same time, low-dimensional effective matrix models have proven to be a powerful tool in accessing the physical properties of a system in a semiquantitative manner. Here, we focus on two realizations of non-Hermitian physics in mesoscopic systems. First, we consider spiral optical microcavities in which the asymmetric scattering between whispering gallery modes induces the non-Hermitian behaviour. Second, for parity-time (PT) symmetric ladder lattices we compare circular and M\"obius geometries. We find the effective coupling between even and odd parity modes to be symmetric but complex in a microscopically derived 2 x 2 matrix model, resulting in non-Hermitian behaviour as well. Most importantly, the M\"obius topology acts like a scatterer that induces a qualitatively new form of (avoided) level crossing - a PT-broken phase terminated by exceptional points - resulting from the symmetric but non-Hermitian coupling.