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Physical Review A

Quantum phenomena in nonstationary media

V. V. Dodonov, A. B. Klimov, Dmitri E. Nikonov

Published May 1, 1993• 135 citations
Publisher

Abstract

The problem of electromagnetic-field quantization in time-dependent nonuniform linear nondispersive media is investigated. The explicit formulas for the number of photons generated from the initial vacuum state due to the change in time of dielectric permeability of the medium are obtained in the case when the spatial and temporal dependences are factorized. The concrete time dependences include adiabatic and sudden changes of permeability, the parametric resonance at twice the eigenfrequency of the mode, Epstein's symmetric and transition profiles, ``temporal Fabry-P\'erot resonator,'' and some others. The upper and lower bounds for the squeezing and correlation coefficients of the field in the final state are given in terms of the reflection coefficient from an equivilent potential barrier or the number of created quanta. The problem of impulse propagation in a spatially uniform but time-dependent dielectric medium is discussed.

DOI
10.1103/physreva.47.4422

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The macroscopic electromagnetic field is quantized in a linear isotropic permeable-dielectric medium by associating a proper damped quantum-mechanical harmonic oscillator with each mode of the radiation field. We introduce a particular form of the Langevin equation with two memory functions and two random impulses to describe the motion of a damped oscillator. A fully canonical approach is used to quantize the damped oscillator, the conjugate momentum is defined and the quantum-mechanical Hamiltonian is introduced. This brings forth a direct method for the quantization of the radiation field and at the same time introduces an effective Hamiltonian operator. Special attention is paid to the vacuum field fluctuation in permeable dielectrics.
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