Quantum key distribution session with 16-dimensional photonic states

The secure transfer of information is an important problem in modern telecommunications. Quantum key distribution (QKD) provides a solution to this problem by using individual quantum systems to generate correlated bits between remote parties, that can be used to extract a secret key. QKD with D-dimensional quantum channels provides security advantages that grow with increasing D. However, the vast majority of QKD implementations has been restricted to two dimensions. Here we demonstrate the feasibility of using higher dimensions for real-world quantum cryptography by performing, for the first time, a fully automated QKD session based on the BB84 protocol with 16-dimensional quantum states. Information is encoded in the single-photon transverse momentum and the required states are dynamically generated with programmable spatial light modulators. Our setup paves the way for future developments in the field of experimental high-dimensional QKD.Comment: 8 pages, 3 figure

Generation of maximally entangled states of qudits using twin photons

We report an experiment to generate maximally entangled states of D-dimensional quantum systems, qudits, by using transverse spatial correlations of two parametric down-converted photons. Apertures with D-slits in the arms of the twin fotons define the qudit space. By manipulating the pump beam correctly the twin photons will pass only by symmetrically opposite slits, generating entangled states between these differents paths. Experimental results for qudits with D=4 and D=8 are shown. We demonstrate that the generated states are entangled states.Comment: 04 pages, 04 figure

Form factors of radiative pion decays in nonlocal chiral quark models

We study the radiative pion decay pi+ -> e+ nu_e gamma within nonlocal chiral quark models that include wave function renormalization. In this framework we analyze the momentum dependence of the vector form factor F_V(q^2), and the slope of the axial-vector form factor F_A(q^2) at threshold. Our results are compared with available experimental information and with the predictions given by the NJL model. In addition we calculate the low energy constants l_5 and l_6, comparing our results with the values obtained in chiral perturbation theory.Comment: 22 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:1011.640

Exceptional orthogonal polynomials and the Darboux transformation

We adapt the notion of the Darboux transformation to the context of polynomial Sturm-Liouville problems. As an application, we characterize the recently described $X_m$ Laguerre polynomials in terms of an isospectral Darboux transformation. We also show that the shape-invariance of these new polynomial families is a direct consequence of the permutability property of the Darboux-Crum transformation.Comment: corrected abstract, added references, minor correction

A Motivating Exploration on Lunar Craters and Low-Energy Dynamics in the Earth -- Moon System

It is known that most of the craters on the surface of the Moon were created by the collision of minor bodies of the Solar System. Main Belt Asteroids, which can approach the terrestrial planets as a consequence of different types of resonance, are actually the main responsible for this phenomenon. Our aim is to investigate the impact distributions on the lunar surface that low-energy dynamics can provide. As a first approximation, we exploit the hyberbolic invariant manifolds associated with the central invariant manifold around the equilibrium point L_2 of the Earth - Moon system within the framework of the Circular Restricted Three - Body Problem. Taking transit trajectories at several energy levels, we look for orbits intersecting the surface of the Moon and we attempt to define a relationship between longitude and latitude of arrival and lunar craters density. Then, we add the gravitational effect of the Sun by considering the Bicircular Restricted Four - Body Problem. As further exploration, we assume an uniform density of impact on the lunar surface, looking for the regions in the Earth - Moon neighbourhood these colliding trajectories have to come from. It turns out that low-energy ejecta originated from high-energy impacts are also responsible of the phenomenon we are considering.Comment: The paper is being published in Celestial Mechanics and Dynamical Astronomy, vol. 107 (2010

Invariant Manifolds, the Spatial Three-Body Problem and Space Mission Design

The invariant manifold structures of the collinear libration points for the spatial restricted three-body problem provide the framework for understanding complex dynamical phenomena from a geometric point of view. In particular, the stable and unstable invariant manifold \tubes" associated to libration point orbits are the phase space structures that provide a conduit for orbits between primary bodies for separate three-body systems. These invariant manifold tubes can be used to construct new spacecraft trajectories, such as a \Petit Grand Tour" of the moons of Jupiter. Previous work focused on the planar circular restricted three-body problem. The current work extends the results to the spatial case

CFD and aeroelastic analysis of the MEXICO wind turbine

This paper presents an aerodynamic and aeroelastic analysis of the MEXICO wind turbine, using the compressible HMB solver of Liverpool. The aeroelasticity of the blade, as well as the effect of a low-Mach scheme were studied for the zero-yaw 15m/s wind case and steady- state computations. The wake developed behind the rotor was also extracted and compared with the experimental data, using the compressible solver and a low-Mach scheme. It was found that the loads were not sensitive to the Mach number effects, although the low-Mach scheme improved the wake predictions. The sensitivity of the results to the blade structural properties was also highlighted