Time‐dependent photon statistics in variable media

Abstract

We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, which describes a generic model of variable media in the case of multiparameter squeezed input photon configuration. The corresponding probability amplitudes and photon statistics are also derived in the Schrödinger picture in an abstract operator setting of the quantum electrodynamics; a comparison discussion is made in Heisenberg's picture as well. The unitary transformation and an extension of the squeeze/evolution operator are introduced formally. The time‐dependent photon probability amplitudes with respect to the Fock basis are indeed derived in an operator form. Further, explicit expressions for the matrix elements of the displacement and squeeze operators are derived in terms of hypergeometric functions and solutions of a certain Ermakov‐type system. In the Supporting Information, we provide a computer algebra verification of the derivation of the Ermakov‐system and of the solutions of the Heisenberg equations.

Photon and photon-added intelligent states of coupled parametric oscillators

“…The time evolution of the operators χ(t) is entirely described, in the Heisenberg picture, by imaginary exponential functions χj (t) = χj (0) exp(iω j t), χj+N (t) = χj+N (0) exp(−iω j t), (5) where the j index runs from 1 to N and the ω j are the Floquet exponents of the system. These are the quantized Floquet modes of the classical system.…”

“…With the recent increasing interest in non-Gaussian quantum states of the radiation field (see [22,23] and references therein), we believe that the analysis of a nonstationary and multimode generalization of the photonadded coherent states is necessary. With that in mind we will study a system of N quantum parametric oscillators described by the Hamiltonian [2,3,5]…”