Generalized Coherent States for Quantized Electromagnetic Fields in Time-varying Linear Media

Abstract

If the parameters of the materials, such as electric permittivity, magnetic perme- ability, and conductivity, vary explicitly with time, the corresponding Hamiltonian is a time- dependent form and such materials are classifled as the time-varying media of light. The quan- tization of electromagnetic flelds in time-varying linear media is well described by means of the invariant operator theory of Lewis-Riesenfeld. The Coulomb gauge is chosen in the development of theory, which allows us to evaluate quantized electric and magnetic flelds by expanding only the vector potential in charge free space, since the scalar potential in this situation vanishes. The generalized coherent state, i.e., Gaussian-Klauder state, of electromagnetic flelds conflned inside a cavity fllled with a nontrivial conductive medium is investigated. The Gaussian-Klauder state provides a general means of construction for Husimi-Wigner distributions and can be used to show the quantum and classical correspondence. We conflrmed that the uncertainty product in Gaussian-Klauder state is the same as the minimum uncertainty product in number state. This property of the generalized coherent state is well agree with that of the well known Glauber coherent state.