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

¹ Department of Physics and Astronomy, Università di Firenze, CSDC and INFN, Florence section, Via G. Sansone, 1, 50019 Sesto Fiorentino, Italy
² European Laboratory for Non-Linear Spectroscopy, Università di Firenze - Via Nello Carrara 1, 50019 Sesto Fiorentino, Italy
³ John A. Paulson School of Engineering and Applied Sciences, Harvard University - Cambridge, MA 02138, USA
⁴ CESQ and ISIS (UMR 7006), University of Strasbourg and CNRS - 67000 Strasbourg, France
⁵ Université Côte d'Azur, CNRS, Institut de Physique de Nice - 06200 Nice, France

Received: 26 May 2023
Accepted: 24 January 2024

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 the 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 of the real energy value of the eigenmodes. Differently from usual mobility edges it separates extended states from hybrid localized states and it manifests 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 domains of open quantum systems.