Mesoscopic Möbius ladder lattices as non-Hermitian model systems

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 Möbius 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 Möbius 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.