Non-Hermitian transport in Glauber-Fock optical lattices
DOI:
https://doi.org/10.31349/RevMexFis.70.041303Keywords:
Glauber-Fock waveguide array; non-unitary transformation; non-hermitian hamiltoniansAbstract
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.
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