Field quantization in inhomogeneous absorptive dielectrics

The quantization of the electromagnetic field in a three-dimensional inhomogeneous dielectric medium with losses is carried out in the framework of a damped-polariton model with an arbitrary spatial dependence of its parameters. The equations of motion for the canonical variables are solved explicitly by means of Laplace transformations for both positive and negative time. The dielectric susceptibility and the quantum noise-current density are identified in terms of the dynamical variables and parameters of the model. The operators that diagonalize the Hamiltonian are found as linear combinations of the canonical variables, with coefficients depending on the electric susceptibility and the dielectric Green function. The complete time dependence of the electromagnetic field and of the dielectric polarization is determined. Our results provide a microscopic justification of the phenomenological quantization scheme for the electromagnetic field in inhomogeneous dielectrics.Comment: 19 page

Quantum-state extraction from high-Q cavities

The problem of extraction of a single-mode quantum state from a high-Q cavity is studied for the case in which the time of preparation of the quantum state of the cavity mode is short compared with its decay time. The temporal evolution of the quantum state of the field escaping from the cavity is calculated in terms of phase-space functions. A general condition is derived under which the quantum state of the pulse built up outside the cavity is a nearly perfect copy of the quantum state the cavity field was initially prepared in. The results show that unwanted losses prevent the realization of a nearly perfect extraction of nonclassical quantum states from high-Q optical microcavities with presently available technology.Comment: RevTeX4, 9 pages with 6 figures; extended version as submitted to Phys. Rev.

Theoretical framework of entangled-photon generation from biexcitons in nano-to-bulk crossover regime with planar geometry

We have constructed a theoretical framework of the biexciton-resonant hyperparametric scattering for the pursuit of high-power and high-quality generation of entangled photon pairs. Our framework is applicable to nano-to-bulk crossover regime where the center-of-mass motion of excitons and biexcitons is confined. Material surroundings and the polarization correlation of generated photons can be considered. We have analyzed the entangled-photon generation from CuCl film, by which ultraviolet entangled-photon pairs are generated, and from dielectric microcavity embedding a CuCl layer. We have revealed that in the nano-to-bulk crossover regime we generally get a high performance from the viewpoint of statistical accuracy, and the generation efficiency can be enhanced by the optical cavity with maintaining the high performance. The nano-to-bulk crossover regime has a variety of degrees of freedom to tune the entangled-photon generation, and the scattering spectra explicitly reflect quantized exciton-photon coupled modes in the finite structure.Comment: 18 pages, 10 figure

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

Resonant Energy Exchange between Atoms in Dispersing and Absorbing Surroundings

Within the framework of quantization of the macroscopic electromagnetic field, a master equation describing both the resonant dipole-dipole interaction (RDDI) and the resonant atom-field interaction (RAFI) in the presence of dispersing and absorbing macroscopic bodies is derived, with the relevant couplings being expressed in terms of the surroundings-assisted Green tensor. It is shown that under certain conditions the RDDI can be regarded as being governed by an effective Hamiltonian. The theory, which applies to both weak and strong atom-field coupling, is used to study the resonant energy exchange between two (two-level) atoms sharing initially a single excitation. In particular, it is shown that in the regime of weak atom-field coupling there is a time window, where the energy transfer follows a transfer-rate law of the type obtained by ordinary second-order perturbation theory. Finally, the spectrum of the light emitted during the energy transfer is studied and the line splittings are discussed.Comment: 9 pages, 5 figs, Proceedings of ICQO'2002, Raubichi, to appear in Optics and Spectroscop

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

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

Quantum state conversion by cross-Kerr interaction

A generalized Mach-Zehnder-type interferometer equipped with cross-Kerr elements is proposed to convert N-photon truncated single-mode quantum states into (N+1)-mode single-photon states, which are suitable for further state manipulation by means of beam splitter arrays and ON/OFF-detections, and vice versa. Applications to the realization of unitary and non-unitary transformations, quantum state reconstruction, and quantum telemanipulation are studied.Comment: 22 pages, 4 figures, using a4.st