Non-Hermitian transport in Glauber-Fock optical lattices

• I.A. Bocanegra-Garay ^[1] ; H.M. Moya-Cessa ^[1]
  1. [1] Instituto Nacional de Astrofísica Ótica y Electrónica, Puebla, México
• Localización: Revista Mexicana de Física, ISSN-e 0035-001X, Vol. 70, Nº. 4, 2024
• Idioma: inglés
• Enlaces
  • Texto completo
• Resumen

  • 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 Schrödinger problems are given, as they are simply connected. Indeed, such transformation can be regarded as a non-unitary Supersymmetric transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.