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.

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

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

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

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

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

Entanglement degradation of a two-mode squeezed vacuum in absorbing and amplifying optical fibers

Applying the recently developed formalism of quantum-state transformation at absorbing dielectric four-port devices [L.~Kn\"oll, S.~Scheel, E.~Schmidt, D.-G.~Welsch, and A.V.~Chizhov, Phys. Rev. A {\bf 59}, 4716 (1999)], we calculate the quantum state of the outgoing modes of a two-mode squeezed vacuum transmitted through optical fibers of given extinction coefficients. Using the Peres--Horodecki separability criterion for continuous variable systems [R.~Simon, Phys. Rev. Lett. {\bf 84}, 2726 (2000)], we compute the maximal length of transmission of a two-mode squeezed vacuum through an absorbing system for which the transmitted state is still inseparable. Further, we calculate the maximal gain for which inseparability can be observed in an amplifying setup. Finally, we estimate an upper bound of the entanglement preserved after transmission through an absorbing system. The results show that the characteristic length of entanglement degradation drastically decreases with increasing strength of squeezing.Comment: Paper presented at the International Conference on Quantum Optics and VIII Seminar on Quantum Optics, Raubichi, Belarus, May 28-31, 2000, 11 pages, LaTeX2e, 4 eps figure

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

Surface-induced heating of cold polar molecules

We study the rotational and vibrational heating of diatomic molecules placed near a surface at finite temperature on the basis of macroscopic quantum electrodynamics. The internal molecular evolution is governed by transition rates that depend on both temperature and position. Analytical and numerical methods are used to investigate the heating of several relevant molecules near various surfaces. We determine the critical distances at which the surface itself becomes the dominant source of heating and we investigate the transition between the long-range and short-range behaviour of the heating rates. A simple formula is presented that can be used to estimate the surface-induced heating rates of other molecules of interest. We also consider how the heating depends on the thickness and composition of the surface.Comment: 17 pages, 7 figure