Canonical quantization of electromagnetic field in an anisotropic polarizable and magnetizable medium with spatial-temporal dispersion

Modeling an anisotropic spatially and temporarily dispersive magnetodielectric medium by two independent collections of three dimensional vector fields, we demonstrate a fully canonical quantization of electromagnetic field in the presence of such a medium. Two tensor fields which couple the electromagnetic field with the medium and have an important role in this quantization method are introduced. The electric and magnetic polarization fields of the medium naturally are concluded in terms of the coupling tensors and the dynamical variables modeling the magnetodielectric medium. In Heisenberg picture, the constitutive equations of the medium together with the Maxwell laws are obtained as the equations of motion of the total system and the susceptibility tensors of the medium are calculated in terms of the coupling tensors. Following a perturbation method the Green function related to the total system is found and the time dependence of electromagnetic field operators is derived.Comment: 19 pages, No figur

Green functions and propagation of waves in strongly inhomogeneous media

We show that Green functions of second-order differential operators with singular or unbounded coefficients can have an anomalous behaviour in comparison to the well-known properties of Green functions of operators with bounded coefficients. We discuss some consequences of such an anomalous short or long distance behaviour for a diffusion and wave propagation in an inhomogeneous medium

Van-der-Waals potentials of paramagnetic atoms

We study single- and two-atom van der Waals interactions of ground-state atoms which are both polarizable and paramagnetizable in the presence of magneto-electric bodies within the framework of macroscopic quantum electrodynamics. Starting from an interaction Hamiltonian that includes particle spins, we use leading-order perturbation theory for the van der Waals potentials expressed in terms of the polarizability and magnetizability of the atom(s). To allow for atoms embedded in media, we also include local-field corrections via the real-cavity model. The general theory is applied to the potential of a single atom near a half space and that of two atoms embedded in a bulk medium or placed near a sphere, respectively.Comment: 18 pages, 3 figures, 1 tabl

Casimir Forces and Graphene Sheets

The Casimir force between two infinitely thin parallel sheets in a setting of $N$ such sheets is found. The finite two-dimensional conductivities, which describe the dispersive and absorptive properties of each sheet, are taken into account, whereupon the theory is applied to interacting graphenes. By exploring similarities with in-plane optical spectra for graphite, the conductivity of graphene is modeled as a combination of Lorentz type oscillators. We find that the graphene transparency and the existence of a universal constant conductivity $e^2/(4\hbar)$ result in graphene/graphene Casimir interaction at large separations to have the same distance dependence as the one for perfect conductors but with much smaller magnitude

Field quantization in inhomogeneous anisotropic dielectrics with spatio-temporal dispersion

A quantum damped-polariton model is constructed for an inhomogeneous anisotropic linear dielectric with arbitrary dispersion in space and time. The model Hamiltonian is completely diagonalized by determining the creation and annihilation operators for the fundamental polariton modes as specific linear combinations of the basic dynamical variables. Explicit expressions are derived for the time-dependent operators describing the electromagnetic field, the dielectric polarization and the noise term in the latter. It is shown how to identify bath variables that generate the dissipative dynamics of the medium.Comment: 24 page

Casimir-Polder forces: A non-perturbative approach

Within the frame of macroscopic QED in linear, causal media, we study the radiation force of Casimir-Polder type acting on an atom which is positioned near dispersing and absorbing magnetodielectric bodies and initially prepared in an arbitrary electronic state. It is shown that minimal and multipolar coupling lead to essentially the same lowest-order perturbative result for the force acting on an atom in an energy eigenstate. To go beyond perturbation theory, the calculations are based on the exact center-of-mass equation of motion. For a nondriven atom in the weak-coupling regime, the force as a function of time is a superposition of force components that are related to the electronic density-matrix elements at a chosen time. Even the force component associated with the ground state is not derivable from a potential in the ususal way, because of the position dependence of the atomic polarizability. Further, when the atom is initially prepared in a coherent superposition of energy eigenstates, then temporally oscillating force components are observed, which are due to the interaction of the atom with both electric and magnetic fields.Comment: 23 pages, 3 figures, additional misprints correcte

Cavity-assisted spontaneous emission as a single-photon source: Pulse shape and efficiency of one-photon Fock state preparation

Within the framework of exact quantum electrodynamics in dispersing and absorbing media, we have studied the quantum state of the radiation emitted from an initially in the upper state prepared two-level atom in a high-$Q$ cavity, including the regime where the emitted photon belongs to a wave packet that simultaneously covers the areas inside and outside the cavity. For both continuing atom--field interaction and short-term atom--field interaction, we have determined the spatio-temporal shape of the excited outgoing wave packet and calculated the efficiency of the wave packet to carry a one-photon Fock state. Furthermore, we have made contact with quantum noise theories where the intracavity field and the field outside the cavity are regarded as approximately representing independent degrees of freedom such that two separate Hilbert spaces can be introduced.Comment: 16 pages, 7 eps figures; improved version as submitted to Phys. Rev.

Characterization of unwanted noise in realistic cavities

The problem of the description of absorption and scattering losses in high-Q cavities is studied. The considerations are based on quantum noise theories, hence the unwanted noise associated with scattering and absorption is taken into account by introduction of additional damping and noise terms in the quantum Langevin equations and input--output relations. Completeness conditions for the description of the cavity models obtained in this way are studied and corresponding replacement schemes are discussed.Comment: Contribution to XI International Conference on Quantum Optics, Minsk, Belarus, 26-31 May, 200

Three-dimensional quantization of the electromagnetic field in dispersive and absorbing inhomogeneous 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 $\hat E$ and $\hat B$ and the potentials $\hat A$ and $\hat \phi$ 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

Trapping cold atoms near carbon nanotubes: thermal spin flips and Casimir-Polder potential

We investigate the possibility to trap ultracold atoms near the outside of a metallic carbon nanotube (CN) which we imagine to use as a miniaturized current-carrying wire. We calculate atomic spin flip lifetimes and compare the strength of the Casimir-Polder potential with the magnetic trapping potential. Our analysis indicates that the Casimir-Polder force is the dominant loss mechanism and we compute the minimum distance to the carbon nanotube at which an atom can be trapped.Comment: 8 pages, 3 figure