Correlations and counting statistics of an atom laser

We demonstrate time-resolved counting of single atoms extracted from a weakly interacting Bose-Einstein condensate of 87Rb atoms. The atoms are detected with a high-finesse optical cavity and single atom transits are identified. An atom laser beam is formed by continuously output coupling atoms from the Bose-Einstein condensate. We investigate the full counting statistics of this beam and measure its second order correlation function g((2))(tau) in a Hanbury Brown-Twiss type experiment. For the monoenergetic atom laser we observe a constant correlation function g((2))(tau)=1.00 +/- 0.01 and an atom number distribution close to a Poissonian statistics. A pseudothermal atomic beam shows a bunching behavior and a Bose distributed counting statistics.     

Real-Time Detection of Polymerase Activity Using Supercritical Angle Fluorescence

We investigated the incorporation efficiencies of different fluorescently labelled dNTPs with polymerases by complementary strand synthesis. For this reason single stranded DNA was immobilized on a coverslip and the increase of fluorescence due to the synthesis of the corresponding strand with tagged dNTPs was detected with a supercritical angle fluorescence biosensor in real-time. By comparison of the observed signal intensities it was possible to conclude that the system Cy5-dCTP-Klenow (exonuclease free) fragment gives the best incorporation yield of the investigated enzymes and dNTPs.     

Interface profiles near three-phase contact lines in electric fields

Long-range electrostatic fields deform the surface profile of a conductive liquid in the vicinity of the contact line. We have investigated the equilibrium profiles by balancing electrostatic and capillary forces locally at the liquid vapor interface. Numerical results show that the contact angle at the contact line approaches Young's angle. Simultaneously, the local curvature displays a weak algebraic divergence. Furthermore, we present an asymptotic analytical model, which confirms these results and elucidates the scaling behavior of the profile close to the contact line.     

Laser-induced temperature jump electrochemistry on gold nanoparticle-coated electrodes

Laser-induced temperature jumps (LITJs) at gold nanoparticle-coated indium tin oxide (ITO) electrodes in contact with electrolyte solutions have been measured using temperature-sensitive redox probes and an infrared charge-coupled device. Upon irradiation with 532 nm light, interfacial temperature changes of ca. 20 degrees C were recorded for particle coverages of ca. 1 x 1010 cm-2. In the presence of a redox molecule, LITJ yields open-circuit photovoltages and photocurrents that are proportional to the number of particles on the surface. When ssDNA was used to chemisorb nanoparticles to the ITO surface, solution concentrations as low as 100 fM of target ssDNA-modified nanoparticles could be detected at the electrode surface.     

Experimental investigation and analytical description of a vibro-impact NES coupled to a single-degree-of-freedom linear oscillator harmonically forced

In this paper, the dynamics of a system composed of a harmonically forced single-degree-of-freedom linear oscillator coupled to a vibro-impact nonlinear energy sink (VI-NES) is experimentally investigated. The mass ratio between the VI-NES and the primary system is about \(1\%\). Depending on the external force’s amplitude and frequency, either a strongly modulated response (SMR) or a constant amplitude response (CAR) is observed. In both cases, an irreversible transfer of energy occurs from the linear oscillator toward the VI-NES: process known in the literature as passive targeted energy transfer. Furthermore, the problem is analytically studied by using the method of multiple scales. The obtained slow invariant manifold shows the existence of a stable and of an unstable branch of solutions, as well as of an energy threshold (a saddle-node bifurcation) for the solutions to appear. Subsequently, the fixed points of the problem are calculated. When a stable fixed point is reached, the system is naturally drawn to it and a CAR is established, whereas when no stable point is attained, the system exhibits a SMR regime. Finally, a good correlation between the experimental and the analytical results is presented.     

Degenerations of ideal hyperbolic triangulations

Let M be a cusped 3-manifold, and let ${\mathcal{T}}$ be an ideal triangulation of M. The deformation variety ${\mathfrak{D}(\mathcal{T})}$ , a subset of which parameterises (incomplete) hyperbolic structures obtained on M using ${\mathcal{T}}$ , is defined and compactified by adding certain projective classes of transversely measured singular codimension-one foliations of M. This leads to a combinatorial and geometric variant of well-known constructions by Culler, Morgan and Shalen concerning the character variety of a 3-manifold.     

Computational Prediction of 1H and 13C NMR Chemical Shifts for Protonated Alkylpyrroles: Electron Correlation and Not Solvation is the Salvation

Prediction of chemical shifts in organic cations is known to be a challenge. In this article we meet this challenge for α-protonated alkylpyrroles, a class of compounds not yet studied in this context, and present a combined experimental and theoretical study of the ¹³C and ¹H chemical shifts in three selected pyrroles. We have investigated the importance of the solvation model, basis set, and quantum chemical method with the goal of developing a simple computational protocol, which allows prediction of ¹³C and ¹H chemical shifts with sufficient accuracy for identifying such compounds in mixtures. We find that density functional theory with the B3LYP functional is not sufficient for reproducing all ¹³C chemical shifts, whereas already the simplest correlated wave function model, Møller–Plesset perturbation theory (MP2), leads to almost perfect agreement with the experimental data. Treatment of solvent effects generally improves the agreement with experiment to some extent and can in most cases be accomplished by a simple polarizable continuum model. The only exception is the NH proton, which requires inclusion of explicit solvent molecules in the calculation.     

Quantification of "fuzzy" chemical concepts: a computational perspective

Chemists recurrently utilize "fuzzy" chemical concepts (e.g. atomic charges, the chemical bond, strain, aromaticity, branching, etc.), which lack unique quantitative assessments but, nonetheless, are frequently employed as tools for understanding the intricacies of chemical behaviour. This tutorial review provides an overview of the computational schemes specifically developed to quantify four of the most commonly employed, yet debated, chemical concepts: the chemical bond, atomic charges, (hyper)conjugation, and molecular strain. The enhanced knowledge gained from these schemes not only helps in the depiction of molecules with unique properties, but also provides breadth to our fundamental understanding of chemistry. Nevertheless, the numerous existing methodologies often result in different interpretations that culminate in discrepancies. Through recent examples in the literature, guidelines are provided which illustrate the strengths and weaknesses of various schemes for each individual concept.