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Exact Dynamics and Bloch Oscillations in a Non-Hermitian Zigzag Glauber–Fock Lattice

G.S. Fahara-Ojeda, Luis Arturo Tapia Alarcón, Braulio Misael Villegas-Martínez, George K. Thiruvathukal, Antônio Francisco Neto, Sandra Gesing, Torey Battelle, Vlado Stankovski, Ivan A. Bocanegra-Garay, Araceli Venegas Gomez, J. Jesús Escobedo, Roberto Alan Beltran Vargas

Published Jan 1, 2025• 0 citations
Publisher
DOI
10.2139/ssrn.5208618

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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.
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 (SUSY) transformation and the resulting non-Hermitian Hamiltonian can be considered as representing an open system that interchanges energy with the environment.