Quantum state transformation by dispersive and absorbing four-port devices

The recently derived input-output relations for the radiation field at a dispersive and absorbing four-port device [T. Gruner and D.-G. Welsch, Phys. Rev. A 54, 1661 (1996)] are used to derive the unitary transformation that relates the output quantum state to the input quantum state, including radiation and matter and without placing frequency restrictions. It is shown that for each frequency the transformation can be regarded as a well-behaved SU(4) group transformation that can be decomposed into a product of U(2) and SU(2) group transformations. Each of them may be thought of as being realized by a particular lossless four-port device. If for narrow-bandwidth radiation far from the medium resonances the absorption matrix of the four-port device can be disregarded, the well-known SU(2) group transformation for a lossless device is recognized. Explicit formulas for the transformation of Fock-states and coherent states are given.Comment: 24 pages, RevTe

Photonic excess noise and wave localization

This is a theory for the effect of localization on the super-Poissonian noise of radiation propagating through an absorbing disordered waveguide. Localization suppresses both the mean photon current I and the noise power P, but the Fano factor P/I is found to remain unaffected. For strong absorption the Fano factor has the universal value 1+3f/2 (with f the Bose-Einstein function), regardless of whether the waveguide is long or short compared to the localization length.Comment: 3 pages including 3 figure

The Energy Density in the Casimir Effect

We compute the expectations of the squares of the electric and magnetic fields in the vacuum region outside a half-space filled with a uniform dispersive dielectric. We find a positive energy density of the electromagnetic field which diverges at the interface despite the inclusion of dispersion in the calculation. We also investigate the mean squared fields and the energy density in the vacuum region between two parallel half-spaces. Of particular interest is the sign of the energy density. We find that the energy density is described by two terms: a negative position independent (Casimir) term, and a positive position dependent term with a minimum value at the center of the vacuum region. We argue that in some cases, including physically realizable ones, the negative term can dominate in a given region between the two half-spaces, so the overall energy density can be negative in this region.Comment: 16 pages, 4 figures; 3 references and some new material in Sect. 4.4 adde

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

Spontaneous decay in the presence of dispersing and absorbing bodies: general theory and application to a spherical cavity

A formalism for studying spontaneous decay of an excited two-level atom in the presence of dispersing and absorbing dielectric bodies is developed. An integral equation, which is suitable for numerical solution, is derived for the atomic upper-state-probability amplitude. The emission pattern and the power spectrum of the emitted light are expressed in terms of the Green tensor of the dielectric-matter formation including absorption and dispersion. The theory is applied to the spontaneous decay of an excited atom at the center of a three-layered spherical cavity, with the cavity wall being modeled by a band-gap dielectric of Lorentz type. Both weak coupling and strong coupling are studied, the latter with special emphasis on the cases where the atomic transition is (i) in the normal-dispersion zone near the medium resonance and (ii) in the anomalous-dispersion zone associated with the band gap. In a single-resonance approximation, conditions of the appearance of Rabi oscillations and closed solutions to the evolution of the atomic state population are derived, which are in good agreement with the exact numerical results.Comment: 12 pages, 6 figures, typos fixed, 1 figure adde

Alternative approach to electromagnetic field quantization in nonlinear and inhomogeneous media

A simple approach is proposed for the quantization of the electromagnetic field in nonlinear and inhomogeneous media. Given the dielectric function and nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is determined completely by this quantization method. From Heisenberg's equations we derive Maxwell's equations for the field operators. When the nonlinearity goes to zero, this quantization method returns to the generalized canonical quantization procedure for linear inhomogeneous media [Phys. Rev. A, 43, 467, 1991]. The explicit Hamiltonians for the second-order and third-order nonlinear quasi-steady-state processes are obtained based on this quantization procedure.Comment: Corrections in references and introductio

Spontaneous emission of an atom in front of a mirror

Motivated by a recent experiment [J. Eschner {\it et al.}, Nature {\bf 413}, 495 (2001)], we now present a theoretical study on the fluorescence of an atom in front of a mirror. On the assumption that the presence of the distant mirror and a lens imposes boundary conditions on the electric field in a plane close to the atom, we derive the intensities of the emitted light as a function of an effective atom-mirror distance. The results obtained are in good agreement with the experimental findings.Comment: 8 pages, 6 figures, revised version, references adde

Noise-free scattering of the quantized electromagnetic field from a dispersive linear dielectric

We study the scattering of the quantized electromagnetic field from a linear, dispersive dielectric using the scattering formalism for quantum fields. The medium is modeled as a collection of harmonic oscillators with a number of distinct resonance frequencies. This model corresponds to the Sellmeir expansion, which is widely used to describe experimental data for real dispersive media. The integral equation for the interpolating field in terms of the in field is solved and the solution used to find the out field. The relation between the in and out creation and annihilation operators is found which allows one to calculate the S-matrix for this system. In this model, we find that there are absorption bands, but the input-output relations are completely unitary. No additional quantum noise terms are required.Comment: Revtex, submitted to Physical Review

Casimir force on amplifying bodies

Based on a unified approach to macroscopic QED that allows for the inclusion of amplification in a limited space and frequency range, we study the Casimir force as a Lorentz force on an arbitrary partially amplifying system of linearly locally responding (isotropic) magnetoelectric bodies. We demonstrate that the force on a weakly polarisable/magnetisable amplifying object in the presence of a purely absorbing environment can be expressed as a sum over the Casimir--Polder forces on the excited atoms inside the body. As an example, the resonant force between a plate consisting of a dilute gas of excited atoms and a perfect mirror is calculated

Dynamical Casimir effect without boundary conditions

The moving-mirror problem is microscopically formulated without invoking the external boundary conditions. The moving mirrors are described by the quantized matter field interacting with the photon field, forming dynamical cavity polaritons: photons in the cavity are dressed by electrons in the moving mirrors. The effective Hamiltonian for the polariton is derived, and corrections to the results based on the external boundary conditions are discussed.Comment: 12 pages, 2 figure