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Journal of Physics Conference Series

Quantum Description of Electromagnetic Waves in Time-Dependent Linear Media

I. A. Pedrosa

Published Jul 8, 2011• 5 citations
Publisher

Abstract

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.

DOI
10.1088/1742-6596/306/1/012074

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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.
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 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.
We present a simple description of classical and quantum light propagating through homogeneous conducting linear media. With the choice of Coulomb gauge, we demonstrate that this description can be performed in terms of a damped harmonic oscillator which is governed by the Caldirola-Kanai Hamiltonian. By using the dynamical invariant method and the Fock states representation we solve the time-dependent Schrödinger equation associated with this Hamiltonian and write its solutions in terms of a special solution of the Milne-Pinney equation. We also construct coherent states for the quantized light and show that they are equivalent to the well-known squeezed states. Finally, we evaluate some important properties of the quantized light such as expectation values of the amplitude and momentum of each mode, their variances and the respective uncertainty principle.
If the parameters of the materials, such as electric permittivity, magnetic perme- ability, and conductivity, vary explicitly with time, the corresponding Hamiltonian is a time- dependent form and such materials are classifled as the time-varying media of light. The quan- tization of electromagnetic flelds in time-varying linear media is well described by means of the invariant operator theory of Lewis-Riesenfeld. The Coulomb gauge is chosen in the development of theory, which allows us to evaluate quantized electric and magnetic flelds by expanding only the vector potential in charge free space, since the scalar potential in this situation vanishes. The generalized coherent state, i.e., Gaussian-Klauder state, of electromagnetic flelds conflned inside a cavity fllled with a nontrivial conductive medium is investigated. The Gaussian-Klauder state provides a general means of construction for Husimi-Wigner distributions and can be used to show the quantum and classical correspondence. We conflrmed that the uncertainty product in Gaussian-Klauder state is the same as the minimum uncertainty product in number state. This property of the generalized coherent state is well agree with that of the well known Glauber coherent state.