Observation of spatial quantum correlations induced by multiple scattering of non-classical light

We present the experimental realization of spatial quantum correlations of photons that are induced by multiple scattering of squeezed light. The quantum correlation relates photons propagating along two different light trajectories through the random medium and is infinite in range. Both positive and negative spatial quantum correlations are observed when varying the quantum state incident to the multiple scattering medium, and the magnitude of the correlations is controlled by the number of photons. The experimental results are in excellent agreement with recent theoretical proposals by implementing the full quantum model of multiple scattering

Entropy and diffraction of the kk-free points in nn-dimensional lattices

We consider the $k$th-power-free points in $n$-dimensional lattices and explicitly calculate their entropies and diffraction spectra. This is of particular interest since these sets have holes of unbounded inradius.Comment: 27 pages, 2 figures; revised version with new references [7,8,23]; latest version with new Theorem 6 and updated reference [7

Experimental measurement of the Melnikov function

International audienceWe study the transport properties of a genuine two-dimensional flow with a large mean velocity perturbed periodically in time by means of an original experimental technique. The flow, generated by the co-rotation of two cylinders is both stratified with a linear density gradient using salted water, and viscous in order to prevent Ekman pumping and centrifugal instabilities. Thus, the mean flow contains a hy-perbolic point with a homoclinic streamline, which we perturb periodically by an extra oscillation. A blob of scalar injected close to the stagnation point contracts on the stable manifold, and stretches in the unstable direction. The distance between the stable and the unstable manifolds is measured as the distance between the maximum and the minimum of the dye undulating pattern, and is recorded as a function of the perturbation frequency. This distance, also called the Melnikov function, presents a maximum when the residence time of a fluid particle in the mean flow is about half a perturbation period. This resonance criterion is recovered with good quantitative agreement by the theoretical prediction of the Melnikov function computed for this flow

L’Euphraise nordique (Euphrasia frigida) en Hesse

Der Nordische Augentrost (Euphrasia frigida) ist eine boreal-montane Art, die einige vom Hauptareal abgesetzte Vorposten in deutschen Mittelgebirgen besitzt, wo sie extensiv genutztes, in der Regel ungedüngtes Grünland besiedelt. Aus den hessischen Mittelgebirgen lagen neuere Nachweise nur aus dem nördlichen Spessart vor (vier Populationen). Im Rahmen des Artenhilfsprogramms (und außerdem bei zwei FFH-Grunddatenerfassungen) konnten sechs weitere Spessart-Vorkommen festgestellt werden. Hinweise auf ein kleines Vorkommen im Hochtaunus (Neufund für den Naturraum) konnten bestätigt werden. Die Nachsuche an ehemaligen Wuchsorten im Vogelsberg, wo die Art bis in die 1970er Jahre vorkam, verlief hingegen durchweg erfolglos; allerdings gelang auch hier der Neufund einer kleinen Population. Auch im hessischen Teil der Hohen Rhön gelang inzwischen ein Erstnachweis (siehe Barth 2008). Insgesamt liegt mehr als die Hälfte aller bekannten deutschen Fundorte in Hessen. Dem Land kommt daher eine besondere Verantwortung für die Erhaltung der Art zu. Hauptgefährdungsursachen für die Art sind Nutzungsintensivierung (Düngung, zu früher Mahdtermin) und Nutzungsaufgabe sowie die Aufforstung von Grenzertragsgrünland. Die Erhaltung der Art ist am besten durch vertraglich vereinbarte extensive Grünlandnutzung (Verzicht auf Düngung, Mahd nicht vor Anfang Juli) zu gewährleisten.The Cold Eyebright (Euphrasia frigida) has a boreo-montane distribution in Europe, Asia, and North America. However, this species also occurs in the German uplands away from these main habitats, where it inhabits poorly used grasslands that generally remain unfertilised. In Hesse, only four populations in the northern Spessart area were known at the onset of a recovery programme for this species in 2003. Six new populations were found in the course of this programme. As a new record, a small population was found in the Upper Taunus region. All previously known populations in the Vogelsberg region, where this species occurred up until the 1970s, could no longer be found, but one new, small population was found. Lately, the species was also recorded in the Hessian part of the Rhön region (Barth 2008). More than half the sites where the Cold Eyebright occurs in Germany are located in Hesse, which therefore has a prominent role in the conservation of this species. It is endangered by intensification of land use (use of fertilizers, early mowing) and abandonment and forestation of low-production meadows in upland areas. The best strategy for conserving this species is to contractually ensure that farmers maintain the traditional use of meadows.Euphrasia frigida est une espèce boréo-montagnarde avec quelques stations disjointes dans les moyennes montagnes en Allemagne où elle occupe des prairies utilisées de façon extensive et en général sans engrais. Dans les montagnes de la Hesse, des spécimens récents n’ont pu être prouvés que dans le Nord du Spessart (4 en tout). Dans le cadre d’un programme d’aide à la conservation des espèces (ainsi que dans 2 investigations de FFH), on a pu constater 6 autres populations. L’indication d’une population dans le Haut-Taunus a pu être vérifiée positivement (nouvelle présence dans cette région). Les recherches dans le Vogelsberg entreprises sur les stations où l’espèce était autrefois présente jusque dans les années 70 ont été quasi négatives, mais par contre une nouvelle petite population y a été découverte. De même, l’espèce a été découverte pour la première fois dans la partie hessoise du Haut-Rhön (cf. Barth 2008). Dans l’ensemble, plus de la moitié des stations connues en Allemagne se trouvent en Hesse. Pour cette raison, le Land porte une responsabilité particulière quant à la conservation de l’espèce. Les sources principales des menaces pesant sur l’espèce sont l’utilisation intensive (emploi d’engrais et fauche trop précoce) et l’abandon de pratiques agropastorales ainsi que le reboisement des prairies à rendement limité. La garantie optimale de la conservation de l’espèce doit être obtenue par une convention portant sur l’utilisation extensive des prairies (renoncement à l’engrais, fauche après juin)

Continuous-wave spatial quantum correlations of light induced by multiple scattering

We present theoretical and experimental results on spatial quantum correlations induced by multiple scattering of nonclassical light. A continuous mode quantum theory is derived that enables determining the spatial quantum correlation function from the fluctuations of the total transmittance and reflectance. Utilizing frequency-resolved quantum noise measurements, we observe that the strength of the spatial quantum correlation function can be controlled by changing the quantum state of an incident bright squeezed-light source. Our results are found to be in excellent agreement with the developed theory and form a basis for future research on, e.g., quantum interference of multiple quantum states in a multiple scattering medium.Comment: 8 pages, 6 figure

Columnar structure formation of a dilute suspension of settling spherical particles in a quiescent fluid

The settling of heavy spherical particles in a column of quiescent fluid is investigated. The performed experiments cover a range of Galileo numbers ($110 \leq \text{Ga} \leq 310$) for a fixed density ratio of $\Gamma = \rho_p/\rho_f = 2.5$. In this regime the particles are known (M. Jenny, J. Du\v{s}ek and G. Bouchet, Journal of Fluid Mechanics 508, 201 (2004).) to show a variety of motions. It is known that the wake undergoes several transitions for increasing $\text{Ga}$ resulting in particle motions that are successively: vertical, oblique, oblique oscillating, and finally chaotic. Not only does this change the trajectory of single, isolated, settling particles, but it also changes the dynamics of a swarm of particles as collective effects become important even for dilute suspensions, with volume fraction up to $\Phi_V = \mathcal{O}\left(10^{-3}\right)$, which are investigated in this work. Multi-camera recordings of settling particles are recorded and tracked over time in 3 dimensions. A variety of analysis are performed and show a strong clustering behavior. The distribution of the cell areas of the Vorono\"i tessellation in the horizontal plane are compared to that of a random distribution of particles and shows clear clustering. Moreover, a negative correlation was found between the Vorono\"i area and the particle velocity; clustered particles fall faster. In addition, the angle between two adjacent particles and the vertical is calculated and compared to a homogeneous distribution of particles, clear evidence of vertical alignment of particles is found. The experimental findings are compared to simulations.Comment: 8 pages, 6 figure