Quantum phenomena in nonstationary media

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-Perot 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 reAection 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.PACS number(s): 42.50.Dv

Optical properties of atomic Mott insulators: From slow light to dynamical Casimir effects

“…The most celebrated example of DCE is predicted for a metallic cavity whose length is varied in time by means of a mechanical motion of its mirrors [21]. Another possibility consists of varying the effective length of the cavity by modulating the mirror conductivity [23,24], by mimicking moving mirrors via a suitably chosen χ (2) non-linear optical element [25], or by varing the bulk refractive index of the cavity material [22,43]. A generalization of this latter scheme is the subject of the present paper: the modulation of the dielectric properties of the atomic medium is created by varying in time the dressing field amplitude.…”

On a hidden symmetry of quantum harmonic oscillators

“…One may imagine other possible applications, for example, in molecular spectroscopy [46], theory of crystals, quantum optics [24], [66], and cavity quantum electrodynamics [12], [13], [22], [35], [67]. We believe in a dynamic character of the nature [28].…”

“…More applications include, but are not limited to charged particle traps and motion in uniform magnetic fields, molecular spectroscopy and polyatomic molecules in varying external fields, crystals through which an electron is passing and exciting the oscillator modes, and other mode interactions with external fields. Quadratic Hamiltonians have particular applications in quantum electrodynamics because the electromagnetic field can be represented as a set of generalized driven harmonic oscillators [13], [20].…”

“…More applications include, but are not limited to charged particle traps and motion in uniform magnetic fields, molecular spectroscopy and polyatomic molecules in varying external fields, crystals through which an electron is passing and exciting the oscillator modes, and other mode interactions with external fields. Quadratic Hamiltonians have particular applications in quantum electrodynamics because the electromagnetic field can be represented as a set of generalized driven harmonic oscillators [13], [20].The maximal kinematical invariance group of the simple harmonic oscillator [50] provides the six-parameter family of solutions, namely (1.2) and (1.3)-(1.9), for an arbitrary choice of the initial data (of the corresponding Ermakov-type system [17], [39], [41], [44]). These "hidden parameters" usually disappear after evaluation of matrix elements and cannot be observed from the spectrum.…”

Parametric oscillator in a Kerr medium: evolution of coherent states

“…A particularly relevant realization of the parametric oscillator is cavity quantum electrodynamics (CQED) where the frequency of a given field mode in the cavity can change in time due to the motion of the cavity walls or to changes in the dielectric function of the medium [25]. For instance, Wineland et.…”