Lifshitz tail states in non-Hermitian disordered photonic lattices

TL;DR

This paper explores how Lifshitz tail states, rare localized states near the band edges, can dominate dynamics in non-Hermitian disordered photonic lattices, especially when disorder is introduced via imaginary potentials, revealing new observable phenomena.

Contribution

It demonstrates that Lifshitz tail states become significant and observable in non-Hermitian photonic lattices with imaginary disorder, a scenario where they are typically negligible.

Findings

Lifshitz tail states can dominate system dynamics in non-Hermitian lattices.

Imaginary disorder induces observable Lifshitz tail states.

Rare states significantly influence localization and transport properties.

Abstract

In lattices with uncorrelated on-site potential disorder, Anderson localization near the band edges can exhibit anomalously weak localization in the form of Lifshitz tail states. These states correspond to clusters of contiguous sites with nearly identical on-site energies, allowing excitations to extend significantly beyond the characteristic localization length determined by the inverse of Lyapunov exponent. Since Lifshitz tail states are rare events, with an exponentially small density of states, they are typically considered of limited practical importance. In this work, we demonstrate that when Anderson localization is induced by disorder in an imaginary on-site potential, Lifshitz tail states can dominate the system's dynamics and become experimentally observable. This phenomenon is illustrated through the Anderson-Bernoulli model in a non-Hermitian photonic lattice, shedding light on the unique interplay between disorder and non-Hermiticity in such systems