Non-Hermitian propagation in Glauber-Fock optical lattices
Optics
2023-10-16 v2
Abstract
The effect of a non-unitary transformation on an initial Hermitian operator is studied. The initial (Hermitian) optical system is a Glauber-Fock optical lattice. The resulting non-Hermitian Hamiltonian models an anisotropic (Glauber-Fock) waveguide array of the Hatano-Nelson-type. Several cases are analyzed and exact analytical solutions for both the Hermitian and non-Hermitian Schr\"odinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric (SUSY) transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.
Keywords
Cite
@article{arxiv.2307.06425,
title = {Non-Hermitian propagation in Glauber-Fock optical lattices},
author = {Ivan Bocanegra and Héctor M. Moya-Cessa},
journal= {arXiv preprint arXiv:2307.06425},
year = {2023}
}