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Optical and transport properties of a series of ultrathin NbN films with different thickness grown on sapphire have been evaluated by means of spectral ellipsometry and dc measurements of superconducting critical parameters. The growth process and thus the nitrogen content have been optimized for each film in the series to achieve the highest superconducting transition temperature, which however increases with the film thickness. Optical and transport measurements agree in slowly increasing disorder while the electron density of states at the Fermi level shows a twofold decrease when the film thickness drops from 14 to 3 nm. Nearinfrared extinction spectra of nanowire gratings from our films are well described by the scattering matrix method that uses optical parameters of nonstructured films and the grating geometry. The technique provides an attractive tool for analyzing various devices for nanophotonics.

We have studied supercurrent-assisted formation of the resistive state in nano-structured Nb and NbN superconducting films after absorption of a single photon. In amorphous narrow NbN strips the probability of the resistive state formation has a pronounced spectral cut-off. The corresponding threshold photon energy decreases with the bias current. Analysis of the experimental data in the framework of the generalized hot-spot model suggests that the quantum yield for near-infrared photons increases faster than the photon energy. Relaxation of the resistive state depends on the photon energy making the phenomenon feasible for the development of energy resolving singlephoton detectors.

We present results from an extensive study of fluctuation phenomena in superconducting nanowires made from sputtered NbN. Nanoscale wires were fabricated in form of a meander and operated at a constant temperature ) 0 ( 4 . 0 c T T ≈ . The superconducting state is driven close to the electronic phase transition by a high bias current near the critical one.Fluctuations of sufficient strength temporarily drive a section of the meander structure into the normal conducting state, which can be registered as a voltage pulse of nanosecond duration.We considered three different models (vortex-antivortex pairs, vortex edge barriers and phase slip centers) to explain the experimental data. Only thermally excited vortices, either via unbinding of vortex-antivortex pairs or vortices overcoming the edge barrier, lead to a satisfactory and consistent description for all measurements. c T . At lower temperatures the probability of thermodynamic fluctuations drops exponentially so that they are experimentally no longer observable far below the transition temperature. However, the freezing-out of thermal fluctuations opens up the possibility to observe quantum fluctuations that prevail in the limit 0 = T , for example quantum phase-slips [16].Although well-defined one-and two-dimensional systems have been studied in great detail, the cross-over region between these limiting cases is less understood. This situation is just beginning to change as the size of superconducting conduction paths of devices such as SQUIDs or quantum detectors is continually decreasing, and therefore a better understanding of superconducting structures that are in between the limiting dimensions is required.I and are sensitive in the visible and near-infrared spectral range (3.1 -0.4 eV). It is generally believed that fluctuations are the major source of dark-count events in these detectors [22][23][24]. Measuring the dark-count rate thus gives us direct information about the fluctuation rates in a part of the superconducting phase diagram that is otherwise not easily accessible. The commonly used approach [23] to measure the DC resistance that is then used to infer the fluctuation rate is not appropriate at large bias currents close to the experimental critical current c,e I , since the Joule heating cannot be eliminated. By contrast, Joule heating may influence the amplitude and duration of individual voltage transients in our time-resolved measurements, but it does not superconducting systems [5]

Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 or level 2.5 large deviation functional characterizing the empirical density and current of the underlying stochastic process. For Langevin systems obeying detailed balance, the explicit form of the level 2 functional has been known ever since the mathematical work of Donsker and Varadhan. We rederive the Donsker-Varadhan result using stochastic path-integrals. We than generalize the derivation to level 2.5 large deviation functionals for non-equilibrium steady states and elucidate the relation between the large deviation functionals and different notions of entropy production in stochastic thermodynamics. Finally, we discuss some aspects of the contractions to level 1 large deviation functions and illustrate our findings with examples. T TIf the limit exists, the random variable a T is said to satisfy a large deviation principle [5]. The large deviation function ( ) J a contains the desired information about the statistics of a T . First of all, consistency requires á ñ = ( ) J a 0 st and ( )  J a 0 for all a. Taylor expansion around the minimum of ( ) J a up to second order yields a Gaussian probability distribution generalizing Einsteins theory of equilibrium fluctuations[ 7]. In addition, the complete function ( ) J a characterizes the statistics of exponentially rare realizations a T that deviate substantially from á ñ a st . Recent applications of large deviation functions to describe rare events in statistical mechanics can be found in [8][9][10][11][12][13][14].Different Brownian functionals deriving from the same stochastic process ( ) x t have different large deviation functions. On the other hand, we may rewrite (1.1) as New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al New J. Phys. 18 (2016) 083010 J Hoppenau et al