Physical meaning of non-Hermitian Hamiltonian

Abstract

A four-level system coupled with lasers is analyzed in terms of dressed-atom model by introducing auto-ionization decay which leads to a non-Hermitian Hamiltonian. The population of the system obtained by means of solving the secular equation of the Hamiltonian is found in good agreement with that from numerical solution of time-dependent Schrdinger equation. This result suggests that non-Hermitian Hamiltonian can be introduced into the framework of quantum mechanics , and the imaginary part of the corresponding eigenvalue represents the populati on decaying of systems.