Shape dependence and anisotropic finite-size scaling of the phase coherence of three-dimensional Bose-Einstein condensed gases

We investigate the equilibrium phase-coherence properties of Bose-condensed particle systems, focusing on their shape dependence and finite-size scaling (FSS). We consider three-dimensional (3D) homogeneous systems confined to anisotropic L x L x L_a boxes, below the BEC transition temperature $T_c$. We show that the phase correlations develop peculiar anisotropic FSS for any $T<T_c$, in the large-$L$ limit keeping the ratio \lambda = L_a/L^2 fixed. This phenomenon is effectively described by the 3D spin-wave (SW) theory. Its universality is confirmed by quantum Monte Carlo simulations of the 3D Bose-Hubbard model in the BEC phase. The phase-coherence properties of very elongated BEC systems, \lambda>>1, are characterized by a coherence length \xi_a \sim A_t \rho_s/T where A_t is the transverse area and \rho_s is the superfluid density.Comment: 7 page

Hyperentanglement witness

A new criterium to detect the entanglement present in a {\it hyperentangled state}, based on the evaluation of an entanglement witness, is presented. We show how some witnesses recently introduced for graph states, measured by only two local settings, can be used in this case. We also define a new witness $W_3$ that improves the resistance to noise by increasing the number of local measurements.Comment: 6 pages, 2 figures, RevTex. v2: new title, minor changes in the explanation of the witness for hyperentangled states, more comments in the conclusions sectio

Hyperentanglement of two photons in three degrees of freedom

A 6-qubit hyperentangled state has been realized by entangling two photons in three degrees of freedom. These correspond to the polarization, the longitudinal momentum and the indistinguishable emission produced by a 2-crystal system operating with Type I phase matching in the spontaneous parametric down conversion regime. The state has been characterized by a chained interferometric apparatus and its complete entangled nature has been tested by a novel witness criterium specifically introduced for hyperentangled states. The experiment represents the first realization of a genuine hyperentangled state with the maximum entanglement between the two particles allowed in the given Hilbert space.Comment: 4 pages, 2 figures, Revtex

San Martino in Soverzano, da insediamento fortificato a villa rinascimentale

Some of the most important country residences of the Bolognese nobility, which can be found in the area between Bologna, theriver Reno and the province of Ferrara, often evolved in the 15th century from previous small fortified settlements. In EgnazioDanti’s book of drawings, which he produced in 1578 for what was later to become the Gallery of Maps of the Vatican, what isstriking is the permanence of the fortified nature of the settlements, something that had, however, already been considered asindispensable for life in a villa by Pier de’ Crescenzi in the early 14th century. The disappearance of many of the buildings hasnot allowed as yet the writing of a satisfactory history of the original pre-renaissance villa settlements, nor the carrying out of aproper census of them in the region. From this point of view, the complex at San Martino in Soverzano represents a particularlysignificant case for establishing a first well-documented interpretative framework on the phenomenon of pre-renaissance countrymanors in the province of Bologna

First measurement of the 14N/15N ratio in the analogue of the Sun progenitor OMC-2 FIR4

We present a complete census of the 14N/15N isotopic ratio in the most abundant N-bearing molecules towards the cold envelope of the protocluster OMC-2 FIR4, the best known Sun progenitor. To this scope, we analysed the unbiased spectral survey obtained with the IRAM-30m telescope at 3mm, 2mm and 1mm. We detected several lines of CN, HCN, HNC, HC3N, N2H+, and their respective 13C and 15N isotopologues. The lines relative fluxes are compatible with LTE conditions and moderate line opacities have been corrected via a Population Diagram method or theoretical relative intensity ratios of the hyperfine structures. The five species lead to very similar 14N/15N isotopic ratios, without any systematic difference between amine and nitrile bearing species as previously found in other protostellar sources. The weighted average of the 14N/15N isotopic ratio is 270 +/- 30. This 14N/15N value is remarkably consistent with the [250-350] range measured for the local galactic ratio but significantly differs from the ratio measured in comets (around 140). High-angular resolution observations are needed to examine whether this discrepancy is maintained at smaller scales. In addition, using the CN, HCN and HC3N lines, we derived a 12C/13C isotopic ratio of 50 +/- 5.Comment: Accepted for publication in ApJ ; 19 pages, 5 tables, 12 figure