On Bargmann Representations of Wigner Function

By using the localized character of canonical coherent states, we give a straightforward derivation of the Bargmann integral representation of Wigner function (W). A non-integral representation is presented in terms of a quadratic form V*FV, where F is a self-adjoint matrix whose entries are tabulated functions and V is a vector depending in a simple recursive way on the derivatives of the Bargmann function. Such a representation may be of use in numerical computations. We discuss a relation involving the geometry of Wigner function and the spacial uncertainty of the coherent state basis we use to represent it.Comment: accepted for publication in J. Phys. A: Math. and Theo

Properties of Squeezed-State Excitations

The photon distribution function of a discrete series of excitations of squeezed coherent states is given explicitly in terms of Hermite polynomials of two variables. The Wigner and the coherent-state quasiprobabilities are also presented in closed form through the Hermite polynomials and their limiting cases. Expectation values of photon numbers and their dispersion are calculated. Some three-dimensional plots of photon distributions for different squeezing parameters demonstrating oscillatory behaviour are given.Comment: Latex,35 pages,submitted to Quant.Semiclassical Op

A random laser as a dynamical network

The mode dynamics of a random laser is investigated in experiment and theory. The laser consists of a ZnCdO/ZnO multiple quantum well with air-holes that provide the necessary feedback. Time-resolved measurements reveal multi-mode spectra with individually developing features but no variation from shot to shot. These findings are qualitatively reproduced with a model that exploits the specifics of a dilute system of weak scatterers and can be interpreted in terms of a lasing network. Introducing the phase-sensitive node coherence reveals new aspects of the self-organization of the laser field. Lasing is carried by connected links between a subset of scatterers, the fields on which are oscillating coherently in phase. In addition, perturbing feedback with possibly unfitting phases from frustrated other scatterers is suppressed by destructive superposition. We believe that our findings are representative at least for weakly scattering random lasers. A generalization to random laser with dense and strong scatterers seems to be possible when using a more complex scattering theory for this case.Peer Reviewe

Radon transform and pattern functions in quantum tomography

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.Comment: To appear on Journal of Modern Optics.Submitted t

Lorentz Beams

A new kind of tridimensional scalar optical beams is introduced. These beams are called Lorentz beams because the form of their transverse pattern in the source plane is the product of two independent Lorentz functions. Closed-form expression of free-space propagation under paraxial limit is derived and pseudo non-diffracting features pointed out. Moreover, as the slowly varying part of these fields fulfils the scalar paraxial wave equation, it follows that there exist also Lorentz-Gauss beams, i.e. beams obtained by multipying the original Lorentz beam to a Gaussian apodization function. Although the existence of Lorentz-Gauss beams can be shown by using two different and independent ways obtained recently from Kiselev [Opt. Spectr. 96, 4 (2004)] and Gutierrez-Vega et al. [JOSA A 22, 289-298, (2005)], here we have followed a third different approach, which makes use of Lie's group theory, and which possesses the merit to put into evidence the symmetries present in paraxial Optics.Comment: 11 pages, 1 figure, submitted to Journal of Optics

Wigner function evolution in self-Kerr Medium derived by Entangled state representation

By introducing the thermo entangled state representation, we convert the calculation of Wigner function (WF) of density operator to an overlap between "two pure" states in a two-mode enlarged Fock space. Furthermore, we derive a new WF evolution formula of any initial state in self-Kerr Medium with photon loss and find that the photon number distribution for any initial state is independent of the coupling factor with Kerr Medium, where the number state is not affected by the Kerr nonlinearity and evolves into a density operator of binomial distribution.Comment: 9 pages, 1 figur

Effect of soil fertilization on the incidence of berry shrivel and the quality of resulting wine

Berry shrivel is becoming an increasing concern for winegrowers all over the world. Until today, no single factor causing this physiological disorder has been determined. Studies concerning berry shrivel conducted in Austria have shown that an unbalanced ratio of K and Mg in the soil is a likely factor contributing to the disorder. The aims of the present study were to establish a better understanding of the causes and consequences of berry shrivel and observe the effects of K and Mg fertilization via the soil on the incidence of berry shrivel, the mineral composition of affected berries and the resulting wine quality. A two-year fertilization trial was conducted on two sites located within southern Germany with the varieties 'Zweigelt' and 'Pinot Blanc'. Different amounts of K and Mg were applied each year at both locations in order to generate different ratios of K and Mg in the soil. Before harvest, the incidences of berry shrivel of the different treatments were determined. In addition, macronutrients including K, Mg and Ca that were translocated in healthy berries and berries affected by berry shrivel were determined at harvest. To compare the quality of wine influenced by berry shrivel, different wines were produced consisting of shrivelled berries, berries affected by bunch stem necrosis and healthy berries. In the soil fertilization trials, no significant differences in the incidences of berry shrivel were observed in relation to the soil fertilization. Major differences were found in the wine qualities of the different wines. Wines produced from healthy berries were always rated as the best wines, whereas wines produced from shrivelled berries were always rated as the lowest quality. The low quality parameters found in the must did not improve in the wine making process. Wines produced from berries affected by bunch stem necrosis were rated better than berry-shrivel-wines, however, rated less than the wine produced from healthy berries. The determinations of macronutrients’ level in the berries showed significant differences regarding the concentration of Ca. In the variety 'Zweigelt' in 2009, an average of 36 mg∙L-1 of Ca were found in healthy berries and 107 mg∙L-1 in berries affected by berry shrivel. In 'Pinot Blanc' in 2010, the average of Ca in healthy berries was 46 mg∙L-1 and 70 mg∙L-1 in berries affected by berry shrivel. No significant differences were found for K and Mg in the berries.

Effect of the Microstructure of Copper Films on the Damping of Oscillating Quartz Resonators*

An electrochemical procedure is described which allows the preparation of copper films of various crystallinity. Impedance spectra recorded for copper loaded quartz resonators were analysed in terms oft he lumped-element circuit of the Butterworth-Van Dyke type to obtain their electrical and mechanical properties. Plots of the damping resistance versus film thickness indicate that the film's dissipation factor is significantly smaller in the case of disordered films with a finer crystallinity (10—100nm) than in the case of more ordered structures having a grain size between 600—1500nm. This observations states, that the finely structured copper phase behaves more rigid than the coarse material. The suggested explanation relates this effect to energy losses which occur during oscillation at the phase boundary of the grains by wearless internal friction. No contributions to the damping from surface roughness were observed for films thicker 0.5pm. Thus, the damping of the quartz oscillator caused by different degrees of surface roughness of the generated copper films was of secondary importance, compared with the effect of the crystallinity

Energy-Sensitive and "Classical-like" Distances Between Quantum States

We introduce the concept of the ``polarized'' distance, which distinguishes the orthogonal states with different energies. We also give new inequalities for the known Hilbert-Schmidt distance between neighbouring states and express this distance in terms of the quasiprobability distributions and the normally ordered moments. Besides, we discuss the distance problem in the framework of the recently proposed ``classical-like'' formulation of quantum mechanics, based on the symplectic tomography scheme. The examples of the Fock, coherent, ``Schroedinger cats,'' squeezed, phase, and thermal states are considered.Comment: 23 pages, LaTex, 2 eps figures, to appear in Physica Script