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arXiv:0705.0807 · Physical Review A

Electromagnetic field quantization in a magnetodielectric medium with external charges

Majid Amooshahi, Fardin Kheirandish

Published Dec 5, 2007• 22 citations
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Abstract

The electromagnetic field inside a cubic cavity filled with a linear magnetodielectric medium and in the presence of external charges is quantized by modeling the magnetodielectric medium with two independent quantum fields. The electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. The Maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the Heisenberg equations using a minimal coupling scheme. The spontaneous emission of a two-level atom embedded in a magnetodielectric medium is calculated in terms of the electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity, as an application of the model.

DOI
10.1103/physreva.76.062103

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The electromagnetic field inside a cubic cavity filled with a linear magnetodielectric medium and in the presence of external charges is quantized by modeling the magnetodielectric medium with two independent quantum fields. The electric and magnetic polarization densities of the medium are defined in terms of the ladder operators of the medium and eigenmodes of the cavity. The Maxwell and constitutive equations of the medium together with the equation of motion of the charged particles have been obtained from the Heisenberg equations using a minimal coupling scheme. The spontaneous emission of a two-level atom embedded in a magnetodielectric medium is calculated in terms of the electric and magnetic susceptibilities of the medium and the Green function of the cubic cavity, as an application of the model.
We present a quantization scheme for the electromagnetic field interacting with atomic systems in the presence of dispersing and absorbing magnetodielectric media, including left-handed material having negative real part of the refractive index. The theory is applied to the spontaneous decay of a two-level atom at the center of a spherical free-space cavity surrounded by magnetodielectric matter of overlapping band-gap zones. Results for both big and small cavities are presented, and the problem of local-field corrections within the real-cavity model is addressed.
The van der Waals interaction between two ground-state atoms is calculated for two electrically or magnetically polarizable particles embedded in a dispersive magnetodielectric medium. Unlike previous calculations which infer the atom-atom interaction from the dilute-medium limit of the macroscopic, many-body van der Waals interaction, the interaction is calculated directly for the system of two atoms in a magnetodielectric medium. Two approaches are presented, the first based on the quantized electromagnetic field in a dispersive medium without absorption and the second on Green functions that allow for absorption. We show that the correct van der Waals interactions are obtained regardless of whether absorption in the host medium is explicitly taken into account.
The macroscopic electromagnetic field is quantized in the presence of a uniformly moving permeable dielectric medium. We begin with the Maxwell-Minkowski equations, and the fields are quantized with the help of the Green function scheme. It is shown that for a homogeneous material, though the medium is assumed to be isotropic in its rest frame, it displays anisotropic character for the observer who detects the field observables in the laboratory frame. The field operators are expressed in terms of two independent infinite sets of bosonic field operators. Special attention is paid to the vacuum field fluctuation in moving media.
The electromagnetic field in a linear absorptive dielectric medium is quantized in the framework of the damped polarization model by a new minimal coupling scheme. A Hamiltonian containing a reservoir with continuous degrees of freedom is proposed. The reservoir minimally couples to the dielectric polarization and the electromagnetic field. The Langevin equation is obtained as the equation of motion of the polarization field. Finally, the equations of motion are solved for homogeneous dielectrics.
A quantization scheme for the phenomenological Maxwell theory of the full electromagnetic field in an inhomogeneous three-dimensional, dispersive, and absorbing dielectric medium is developed. The classical Maxwell equations with spatially varying and Kramers-Kronig consistent permittivity are regarded as operator-valued field equations, introducing additional current- and charge-density operator fields in order to take into account the noise associated with the dissipation in the medium. It is shown that the equal-time commutation relations between the fundamental electromagnetic fields $\mathbf{E}^$ and $\mathbf{B}^$ and the potentials $\mathbf{A}^$ and $\stackrel{^}{\ensuremath{\varphi}}$ in the Coulomb gauge can be expressed in terms of the Green tensor of the classical problem. From the Green tensors for bulk material and an inhomogeneous medium consisting of two bulk dielectrics with a common planar interface it is explicitly proven that the well-known equal-time commutation relations of QED are preserved.