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arXiv · 2307.06425

Non-Hermitian propagation in Glauber-Fock optical lattices

Ivan Bocanegra·Héctor M. Moya-Cessa
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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.

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Ivan Bocanegra, Héctor M. Moya-Cessa. 2023-07-12. Non-Hermitian propagation in Glauber-Fock optical lattices. https://arxiv.org/abs/2307.06425

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