Structural and photophysical characterization of multichromophoric pyridylporphyrin-rhenium(i) conjugates

Four porphyrin-Re(I) conjugates, in which a pyridylporphyrin chromophore is directly coordinated to the electron-acceptor fragment [ fac-Re(CO) 3(bipy)] (+), were prepared: the dimeric and pentameric compounds [ fac-Re(CO) 3(bipy)(4'MPyP)](CF 3SO 3) ( 1) (4'MPyP = 4'-monopyridylporphyrin) and [ fac-{Re(CO) 3(bipy)} 4(mu-4'TPyP)](CF 3SO 3) 4 ( 2) (4'TPyP = 4'-tetrapyridylporphyrin), and the corresponding compounds with 3' rather than 4' porphyrins, [ fac-Re(CO) 3(bipy)(3'MPyP)](CF 3SO 3) ( 3) and [ fac-{Re(CO) 3(bipy)} 4(mu-3'TPyP)](CF 3SO 3) 4 ( 4). These adducts proved to be very stable in solution and were also structurally characterized in the solid state by X-ray crystallography. A detailed photophysical study was performed on the zincated adducts of the conjugates 1- 3, labeled 5, 6, and 7, respectively. In all adducts the typical fluorescence of the zinc-porphyrin unit was reduced in intensity and lifetime by the presence of the peripheral rhenium-bipy fragment(s) (heavy-atom effect). For the dyads 5 and 7 the photoinduced charge transfer process from the zinc-porphyrin to the Re(I)-bipy unit is only slightly exoergonic. Ultrafast spectroscopy experiments showed no evidence for electron transfer quenching in the dyads as such, whereas the addition of pyridine (that binds axially to zinc and thus affects the porphyrin redox potential) led to a moderately efficient photoinduced electron transfer process. In perspective, an appropriate functionalization of the bipy ligand and/or of the porphyrin chromophore might improve the thermodynamics and, thus the efficiency, of the photoinduced electron transfer process.     

Spectral multipliers on 2-step groups: topological versus homogeneous dimension

Let G be a 2-step stratified group of topological dimension d and homogeneous dimension Q. Let \({\mathcal{L}}\) be a homogeneous sub-Laplacian on G. By a theorem due to Christ and to Mauceri and Meda, an operator of the form \({F(\mathcal{L})}\) is of weak type (1, 1) and bounded on L ^p (G) for all p ∈ (1, ∞) whenever the multiplier F satisfies a scale-invariant smoothness condition of order s > Q/2. It is known that, for several 2-step groups and sub-Laplacians, the threshold Q/2 in the smoothness condition is not sharp and in many cases it is possible to push it down to d/2. Here we show that, for all 2-step groups and sub-Laplacians, the sharp threshold is strictly less than Q/2, but not less than d/2.     

Nonlocal Tug‐of‐War and the Infinity Fractional Laplacian

Motivated by the “tug‐of‐war” game studied by Peres et al. in 2009, we consider a nonlocal version of the game that goes as follows: at every step two players pick, respectively, a direction and then, instead of flipping a coin in order to decide which direction to choose and then moving a fixed amount ϵ > 0 (as is done in the classical case), it is an s‐stable Levy process that chooses at the same time both the direction and the distance to travel. Starting from this game, we heuristically derive a deterministic nonlocal integrodifferential equation that we call the “infinity fractional Laplacian.” We study existence, uniqueness, and regularity, both for the Dirichlet problem and for a double‐obstacle problem, both problems having a natural interpretation as tug‐of‐war games. © 2011 Wiley Periodicals, Inc.     

Distributed quantum computation via optical fibers

We investigate the possibility of realizing effective quantum gates between two atoms in distant cavities coupled by an optical fiber. We show that highly reliable swap and entangling gates are achievable. We exactly study the stability of these gates in the presence of imperfections in coupling strengths and interaction times and prove them to be robust. Moreover, we analyze the effect of spontaneous emission and losses and show that such gates are very promising in view of the high level of coherent control currently achievable in optical cavities.     

Continuity of optimal transport maps and convexity of injectivity domains on small deformations of 𝕊2

Given a compact Riemannian manifold, we study the regularity of the optimal transport map between two probability measures with cost given by the squared Riemannian distance. Our strategy is to define a new form of the so‐called Ma‐Trudinger‐Wang condition and to show that this condition, together with the strict convexity on the nonfocal domains, implies the continuity of the optimal transport map. Moreover, our new condition, again combined with the strict convexity of the nonfocal domains, allows us to prove that all injectivity domains are strictly convex too. These results apply, for instance, on any small C⁴‐deformation of the 2‐sphere. © 2009 Wiley Periodicals, Inc.     

Generalization of thermodynamic potentials including information

In this work we analyze the connection between information theory and thermodynamics. Three different potentials are presented, all related to the Kullback–Leibler divergence. These potentials represent three different conditions of energy and information exchange between a reservoir and a subsystem. The first potential describes a situation where the two systems are exchanging energy without any external control. The second potential considers the situation where the reservoir can get information through the state of another secondary system about the internal state of the subsystem. This information can then be used by a Maxwell demon to increase the free energy of the subsystem. In this second scenario it is assumed that the energy cost of the information probe and the Maxwell demon are at the expense of the reservoir. Finally, a third case is considered where the information obtained through the secondary system is used not only to manipulate an internal Maxwell demon, but to perform directly work over the subsystem. This last case involves a direct modification of the Hamiltonian of the subsystem.     

Direct measurement of the formation length of photons

We report the first observation of a shoulder in the radiation spectrum from GeV electrons in a structured target consisting of two thin and closely spaced foils. The position of the shoulder depends on the target spacing and is directly connected to the finite formation length of a low-energy photon emitted by an ultrarelativistic electron. With the present setup it is possible to control the separation of the foils on a μm scale and hence measure interference effects caused by the macroscopic dimensions of the formation length. Several theoretical groups have predicted this effect using different methods. Our observations have a preference for the modified theory by Blankenbecler but disagree with the results of Baier and Katkov.     

Compact fibre-based coherent anti-Stokes Raman scattering spectroscopy and interferometric coherent anti-Stokes Raman scattering from a single femtosecond fibre-laser oscillator

We demonstrate a new approach to CARS spectroscopy by efficiently synthesizing synchronized narrow-bandwidth (less than 10 cm⁻¹) pump and Stokes pulses (frequency difference continuously tunable upto ≈3000 cm⁻¹) based on spectral compression together with second harmonic generation (in periodically-poled nonlinear crystals) of femtosecond pulses emitted by a single compact Er-fibre oscillator. For a far better signal to non-resonant background contrast, interferometric CARS (I-CARS) is demonstrated and CARS signal enhancement upto three orders of magnitude is achieved by constructive interference with an auxiliary local oscillator at anti-Stokes field, also synthesized by spectral compression of pulses emitted from the same fibre oscillator.