Localization of light in three dimensions: a mobility edge in the imaginary axis in non-Hermitian Hamiltonians

TL;DR

This paper demonstrates a novel localization transition for light in three dimensions, characterized by a mobility edge along the imaginary energy axis in non-Hermitian Hamiltonians, influenced by disorder and cooperative effects.

Contribution

It introduces the concept of a mobility edge in the imaginary energy axis, revealing a new type of localization transition in non-Hermitian systems with potential applications in quantum control.

Findings

Identification of a mobility edge along the imaginary energy axis.

Localization transition influenced by disorder and cooperative effects.

Eigenstates show hybrid localized and extended characteristics.

Abstract

Searching for Anderson localization of light in three dimensions has challenged experimental and theoretical research for the last decades. Here the problem is analyzed through large scale numerical simulations, using a radiative Hamiltonian i.e. a non-Hermitian long-range hopping Hamiltonian, well suited to model light-matter interaction in cold atomic clouds. Light interaction in atomic clouds is considered in presence of positional and diagonal disorder. Due to the interplay of disorder and cooperative effects (sub- and super-radiance) a novel type of localization transition is shown to emerge, differing in several aspects from standard localization transitions which occur along the real energy axis. The localization transition discussed here is characterized by a mobility edge along the imaginary energy axis of the eigenvalues which is mostly independent from the real energy value of the eigenmodes. Differently from usual mobility edges it separates extended states from hybrid localized states and it manifest itself in the large moments of the participation ratio of the eigenstates. Our prediction of a mobility edge in the imaginary axis, i.e. depending on the eigenmode lifetime, paves the way to achieve control both in the time and space domain of open quantum systems.