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Physical Review Letters

Electromagnetic Field Quantization in Time-Dependent Linear Media

I. A. Pedrosa, Alexandre Rosas

Published Jul 1, 2009• 52 citations
Publisher

Abstract

We present a quantization scheme for the electromagnetic field in time-dependent homogeneous nondispersive conducting and nonconducting linear media without sources. Using the Coulomb gauge, we demonstrate this quantization can be mapped into a damped (attenuated) time-dependent quantum harmonic oscillator. Remarkably, we find that the time dependence of the permittivity, for epsilon>0, gives rise to an attenuation of the radiation field. Afterwards, we obtain the exact wave functions for this problem and consider an exponential time accretion of the permittivity as a particular case.

DOI
10.1103/physrevlett.103.010402

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We present a quantization scheme for the electromagnetic field in time-dependent homogeneous nondispersive conducting and nonconducting linear media without sources. Using the Coulomb gauge, we demonstrate this quantization can be mapped into a damped (attenuated) time-dependent quantum harmonic oscillator. Remarkably, we find that the time dependence of the permittivity, for epsilon>0, gives rise to an attenuation of the radiation field. Afterwards, we obtain the exact wave functions for this problem and consider an exponential time accretion of the permittivity as a particular case.
In this work, we present a quantum description of electromagnetic waves propagating through time-dependent homogeneous nondispersive linear media without sources. By using the Coulomb gauge, we show that this description can be perfomed in terms of a time-dependent quantum harmonic oscillator. In addition, we construct conherent states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinate and momentum as well as the uncertainty product for each mode of the electromagnetic field.
We present a quantum description of electromagnetic waves propagating through time-dependent homogeneous nondispersive conducting and nonconducting linear media without charge sources. Based on the Coulomb gauge and the quantum invariant method, we find the exact wave functions for this problem. In addition, we construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinate and momentum space as well as the uncertainty product for each mode of the electromagnetic field.
In the Coulomb gauge, the solution to the Maxwell equations for slowly time-varying homogeneous nondispersive conducting linear media without charge source is obtained. We show that the electromagnetic field acquires the extra geometrical Hannay angle associated to the time-dependent generalized harmonic oscillator. The quantization scheme for the electromagnetic field provides a connection between the classical Hannay angle and the quantum adiabatic Berry phase shifts. We confirm that the interference pattern in the optical system is more or less altered by the existence of the geometric phase.
In this work we investigate the quantization of electromagnetic waves propagating through homogeneous conducting linear media with no charge density. We use Coulomb's gauge to reduce the problem to that of a time-dependent harmonic oscillator, which is described by the Caldirola–Kanai Hamiltonian. Furthermore, we obtain the corresponding exact wave functions with the help of quadratic invariants and of the dynamic invariant method. These wave functions are written in terms of a particular solution of the Milne–Pinney equation. We also construct coherent and squeezed states for the quantized electromagnetic waves and evaluate the quantum fluctuations in coordinates and momentum as well as the uncertainty product for each mode of the electromagnetic field.
In this paper, we use the Coulomb gauge, linear invariants and the dynamical invariant method in the framework of the Schrödinger equation to obtain a quantum description of light propagation through homogeneous conducting linear media with no charge density. We obtain exact wavefunctions for this problem in terms of solutions of a second-order ordinary differential equation which describes the amplitude of the classical damped harmonic oscillator. In addition, we construct Gaussian wave packet solutions and calculate the fluctuations in coordinate and momentum as well as the quantum correlations for each mode of the quantized electromagnetic field.
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.