Integrals of motion and Robertson-Schr\"odinger correlated states of electromagnetic field in time-dependent linear media

TL;DR

This paper investigates the quantum properties of electromagnetic fields in time-dependent media, deriving invariants and states that minimize uncertainty, revealing effects like squeezing due to medium conductivity and permeability.

Contribution

It introduces a method to construct eigenstates of invariants for quantized fields in time-dependent media, demonstrating their properties and evolution.

Findings

Time-dependent media induce squeezing and covariances in electromagnetic fields.

Time-evolved states minimize Robertson-Schrödinger uncertainty relations.

Explicit solutions for field states in complex media are provided.

Abstract

Integrals of motion and statistical properties of quantized electromagnetic field (e.-m. field) in time-dependent linear dielectric and conductive media are considered, using Choi-Yeon quantization, based on Caldirola-Kanai type Hamiltonian. Eigenstates of quadratic and linear invariants are constructed, the solutions being expressed in terms of a complex parametric function that obeys classical oscillator equation with time-varying frequency. The time evolutions of initial Glauber coherent states and Fock states are considered. The medium conductivity and the time-dependent electric permeability are shown to generate squeezing and non-vanishing covariances. In the time-evolved coherent and squeezed states all the second statistical moments of the electric and magnetic field components are calculated and shown to mminimize the Robertson-Schr\"odinger uncertainty relation.