Beyond_Anderson · Non-Hermitian Transport in Anderson forbidden land

This proposal is centered around the recently discovered (by the PI) ground-breaking way of transport in strongly Anderson localized non-Hermitian media. Initially Anderson localization was studied on electrons but it was later realized that photons provide an alternative cleaner route. However, one fundamental problem of photonics is that of inherent material losses. As the paradigm of parity-time symmetric optics indicates, the resolution of this problem is the judicious combination of gain and loss via index engineering. Such non-Hermitian paradigm provides the opportunity to overcome Anderson localization after sixty years by proposing a novel way of transport unique in the complex photonic media, something that is experimentally impossible in condensed matter physics. The key idea is the inclusion of appropriate gain-loss index profiles that allow light to cross the forbidden land of Anderson via sudden jumps, despite the fact that all eigenstates are localized. My proposal is focused on four directions that span out of the main theme of sudden jumps. The first one is the role of openness in the most general case of uncorrelated disorder. A second open question is that of existence of jumps in correlated media that support constant-intensity states. For both questions the maximization of the effect based on wavefront shaping and index engineering is important. A third question is the possibility of topologically protected jumpy transport in disordered topological insulators. Finally, I intend to examine the more difficult and fundamental problem of many-body effects on non-Hermitian jumpy transport. The underlying mathematical framework, is that of non-Hermitian random matrix theory and pseudospectrum, a widely used method in turbulence studies of fluid mechanics. My project is expected to open a new path in both disordered photonics that exploit the unique features of non-Hermiticity, namely extreme sensitivity, exceptional points, and novel lasing schemes.