Table of contents

A brief comment concerning the history of Central European Workshops on Quantum Optics and the development of quantum optics is presented.

We present a two-dimensional metamaterial with left-handed properties in a certain frequency range where both effective dielectric permittivity and magnetic permeability is simultaneously negative. A wedge-shaped metamaterial structure is employed for refractive index measurements. At the left-handed frequency range the structure is shown to have negative refractive index. Phase shift between consecutive number of layers of metamaterial structures are measured and a negative refractive index value is calculated from the amount of the phase shift. The structure is shown to have negative phase velocity. The refractive index values obtained from two different and independent methods are in good agreement.

Certain crystals, consisting of molecules with unusually large spin, exhibit macroscopically observable signatures of quantum tunneling, when a slowly varying external magnetic field is applied parallel to the easy axis of the crystal. Recently it has been observed that jumps in the magnetization are sometimes accompanied by the emission of infrared radiation. We discuss the connection of the tunneling with the electromagnetic transition, and we address the questions: to what extent can the radiation be considered as a collective, superradiant emission, and what is the role played by the cavity in the experiments? Our conclusion is that among the reported experimental coditions the radiation is not superradidance, but rather a maserlike effect.

It is shown how to construct generic entangled states for an arbitrary system of n-state quantum objects (qunits) by means of the (n × n) cyclic permutation operator.

We investigate properties of exponential operators preserving the particle number using combinatorial methods developed in order to solve the boson normal ordering problem. In particular, we apply generalized Dobiński relations and methods of multivariate Bell polynomials which enable us to understand the meaning of perturbation-like expansions of exponential operators. Such expansions, obtained as formal power series, are everywhere divergent but the Padé summation method is shown to give results which very well agree with exact solutions got for simplified quantum models of the one mode bosonic systems.

Parametrization of qutrits on the complex projective plane CP² = SU(3)/U(2) is given explicitly. A set of constraints that characterize mixed state density matrices is found.

In this work, we study the negative refraction and focusing effect by a metallodielectric photonic crystal. We show that by using a metallodielectric photonic crystal it is possible to obtain negative refraction for large incidence angles. In addition, our experimental and theoretical work reveal that the metallodielectric photonic crystal can be used as aflat-lens.

We studied the diffraction of electromagnetic waves from subwavelength metallic circular apertures in the microwave spectrum. The metallic samples had a subwavelength hole with a diameter of 8 mm and had concentric grooves with a periodicity of 16 mm. We present the angular transmission distributions from circular annular apertures, and circular annular apertures surrounded by concentric periodic grooves. At the surface mode resonance frequency the transmitted electromagnetic waves from the subwavelength circular annular aperture surrounded by concentric periodic grooves have a strong angular confinement with an angular divergence of ±3°. This represents a fourfold reduction when compared to the angular divergence of the beam transmitted from the subwavelength circular aperture.

On the coherent states |α⟩ any entire function of creation and annihilation operators may be defined. We show that it is not the case for non-entire functions. Use of |α⟩⟨α| as identity operator for a non-entire function may lead to contradictory results. On the example of the phase operator we show how these possible contradictions may be avoided.

Based on our previous publication [U. Herzog and J. A. Bergou, Phys. Rev. A 71, 050301(R)(2005)] we investigate the optimum measurement for the unambiguous discrimination of two mixed quantum states that occur with given prior probabilities. Unambiguous discrimination of nonorthogonal states is possible in a probabilistic way, at the expense of a nonzero probability of inconclusive results, where the measurement fails. Along with a discussion of the general problem, we give an example illustrating our method of solution. We also provide general inequalities for the minimum achievable failure probability and discuss in more detail the necessary conditions that must be fulfilled when its absolute lower bound, proportional to the fidelity of the states, can be reached.

Two celebrated statistical principles- Principle of Maximum Likelihood and Principle of Maximum Entropy are merged establishing a novel estimation scheme for statistical inversion.

The use of continuous feedback control of the center of mass of a 1D trapped bosonic gas for probing atom-atom correlations is studied. Based on the Schwarz inequality an experimentally observable criterium for distinguishing between classical and truly quantum correlations is introduced. It is shown that thermal equilibrium states, including the case T = 0, will exhibit purely classical correlations.

We report the results of coincidence counting experiments at the output of a Michelson interferometer using the zero-phonon-line emission of a single molecule at 1.4 K. Under continuous wave excitation, we observe the absence of coincidence counts as an indication of two-photon interference. This corresponds to the observation of Hong-Ou-Mandel correlations.

A fermionic version of the quantum marginal problem was known from the early sixties as N-representability problem. In 1995 it was mentioned by the National Research Council of the USA as one of ten most prominent research challenges in quantum chemistry. In spite of this recognition the progress was very slow, until a couple of years ago the problem came into focus again, now in the framework of quantum information theory. In the paper I give a survey of the recent development.

The paper contains a brief review of an approach to quantum entanglement based on analysis of dynamic symmetry of systems and quantum uncertainties, accompanying the measurement of mean value of certain basic observables. The latter are defined in terms of the orthogonal basis of Lie algebra, corresponding to the dynamic symmetry group. We discuss the relativity of entanglement with respect to the choice of basic observables and a way of stabilization of robust entanglement in physical systems.

An approach to the unconditional security of quantum key distribution protocols is presented, which is based on the uncertainty principle. The approach applies to every case that has been treated via the argument by Shor and Preskill, but it is not necessary to find quantum error correcting codes. It can also treat the cases with uncharacterized apparatuses. The proof can be applied to cases where the secret key rate is larger than the distillable entanglement.

In the case of the Mach-Zehnder interferometer fed with Fock states we speak of estimation of the cosine of phase instead of estimation of the phase. In case the numbers of input photons are equal, we pay attention to a proposal by Kim, et al. (1998). Then we restrict ourselves to the estimation of the cosine of double phase. Although such restrictions can be lifted, they harbinger a unified approach both to the phase sensitivity and to the Cramér-Rao lower bound of the estimator variance.

We develop quantum theory of process of the parametric optical image amplification at high-frequency pumping which is accompanied by up - conversion one. Such interactions can be implemented by two coupled three-frequency optical processes. The theory developed takes into account the diffraction effect and the difference of group velocities of interacting waves. The expressions for mean photon numbers and noise figures of the interacting waves are obtained and the dependence of these parameters on the interaction length are examined.

We discuss a couple of models aimed to describe memory effects in quantum channels. We start from a rather intuitive model and arrive to a more abstract one which turns out to be more general.

Review of different representations of signals including the phase-space representations and tomographic representations is presented. The signals under consideration are either linear or nonlinear ones. The linear signals satisfy linear quantumlike Schrödinger and von Neumann equations. Nonlinear signals satisfy nonlinear Schrödinger equations as well as Gross-Pitaevskii equation describing solitons in Bose-Einstein condensate. The Ville-Wigner distributions for solitons are considered in comparison with tomographic-probability densities describing solitons completely. different kinds of tomographies — symplectic tomography, optical tomography and Fresnel tomography are reviewed. New kind of map of the signals onto probability distributions of discrete photon number-like variable is discussed. Mutual relations between different transformations of signal functions are established in explicit form. Such characteristics of the signal-probability distribution as entropy is discussed.

We study the properties of spin tomograms and tomographic entropy and information. The specific structure of joint probability distributions of standard probability theory are compared with the spin-tomogram properties for two-qubits.

We investigate macroscopic quantum tunneling of magnetization in a a spinor Bose- Einstein condensate trapped in a double-well potential. Using the mean field theory applicable for large condensates, and employing the single spatial mode approximation we derive dynamical equations for magnetization, independent from density mode, for certain initial conditions. We show that they can be reduced to standard Josephson junction dynamics equations under certain conditions.

The exact dynamics of a pair of not directly coupled ½ spins interacting with a common spin ½ bath, is analyzed.

Starting from a factorized condition, the possibility of controlling the generation of only classical or also quantum correlations is brought to light examining the time evolution of two functions of physical interest.

An approach to the problem of the Casimir force on magnetodielectric bodies is outlined, which is based on the calculation of the ground-state Lorentz force acting on the polarization and magnetization charges and currents that constitute the bodies within the framework of linear, macroscopic electrodynamics. As an application, planar structures are considered and a correct generalization of Casimir's original formula to the case where the two highly reflecting plates are embedded in a medium is given.

Quantum optics experiments contribute to a deeper understanding of quantum theory. Neutron phase-echo and spin rotation experiments have shown that, in all cases of an interaction, parasitic beams are produced which cannot be recombined with the original beam in an ideal way. This means that a complete reconstruction of the original state would, in principle, be impossible. Thus a kind of intrinsic irreversibility occurs, even when the original quantum state survives to a very high extent. When plane waves are used, completely reversible situations can be constructed in certain cases, but in any physical situation, wave packets have to be used which do not permit complete reversibility. Even small interaction potentials can have huge effects when they are arranged periodically and resonance effects appear. This gives various constraints for repetitive measurements and prevents a complete freezing of a quantum state in Zeno-like experiments. Additionally, a spectral change occurs, due to the dispersive action of the interaction, which has to be taken into account when many repetitive measurements are considered. A dedicated proposal for a repetitive neutron spin rotation experiment within a perfect crystal resonator will be analyzed in detail. Unavoidable losses due to quantum phenomena can be separated from losses caused by experimental imperfections.

Unpolarized light is invariant with respect to any SU(2) polarization transformation. Since this fully characterizes the set of density matrices representing unpolarized states, we introduce the degree of polarization of a quantum state as its distance to the set of unpolarized states. We discuss different candidates of distance, and show that they induce fundamentally different degrees of polarization.

A brief review of nonclassicality conditions in terms of moments of the creation and annihilation operators is given. By introducing k-th power amplitude squeezing, the notions of ordinary quadrature squeezing and amplitude-squared squeezing are generalized. Minimum uncertainty states are considered as a special class of k-th power amplitude squeezed states. These states can be characterized by a special, rather simple nonclassicality condition.

We derive atomic spin relaxation rates near metallic and superconducting surfaces. Our results are based on a quantum-theoretical treatment of electromagnetic radiation near absorbing bodies. We show that there exists an atom-surface distance for which the expected relaxation rate becomes maximal and we discuss its dependence on the skin depth of the substrate material. In view of this effect we examine the possible use of superconducting materials. Furthermore, we discuss the influence of absorbing materials on spatial coherences in optical lattices.

We study propagation of short laser pulses in a Bose-Einstein condensate taking into account dispersive effects under the conditions for electromagnetically induced transparency. We calculate dispersion coefficients using typical experimental parameters of slow-light schemes in condensates. By numerically propagating the laser pulse, and referring to theoretical estimations, we determine the conditions for which dispersion starts to introduce distortions on the pulse shape.

We investigate the dynamical instability for a two component Bose-Einstein Condensate (BEC) in an optical lattice. We assume that the two components are in sinusoidal potentials with the same period but different phases. We find a swallow-tail type instability near the band edge, however an extra tail is formed due to the inter-component interaction. Depending on the phase difference of the potentials, the instability region may expand or shrink with increasing inter-component interaction.