Well characterized photon number resolving detectors are a requirement for many applications ranging from quantum information and quantum metrology to the foundations of quantum mechanics. This prompts the necessity for reliable calibration techniques at the single photon level. In this paper we propose an innovative absolute calibration technique for photon number resolving detectors, using a pulsed heralded photon source based on parametric down conversion. The technique, being absolute, does not require reference standards and is independent upon the performances of the heralding detector. The method provides the results of quantum efficiency for the heralded detector as a function of detected photon numbers. Furthermore, we prove its validity by performing the calibration of a Transition Edge Sensor based detector, a real photon number resolving detector that has recently demonstrated its effectiveness in various quantum information protocols.

Transition Edge Sensors (TESs) are characterized by the intrinsic figures of merit to resolve both the energy and the statistical distribution of the incident photons. These properties lead TES devices to become the best single photon detectors for quantum technology experiments. For a TES based on titanium and gold, has been reached, at telecommunication wavelength, an unprecedented intrinsic energy resolution (0.113 eV). The uncertainty analysis of both energy resolution and photon state assignment has been discussed. The thermal properties of the superconductive device have been studied by fitting the bias curves to evaluate the theoretical limit of the energy resolution.

The influence of dendritic magnetic-flux penetration on the microwave response of superconducting magnesium diboride (MgB2) films is investigated by a coplanar resonator technique. The characteristic feature consists of abrupt jumps in the resonance curves, which are shown to be induced by vortex avalanches freezing magnetic flux inside the resonator. Flux shaking provided by radio frequency currents is the origin of such avalanches, since a mechanism for magnetic instability of the dendrite type is local heating produced from flux motion. Once the external magnetic field has been changed, the interaction between microwave currents and flux lines influences the vortex-relaxation process. As a consequence, the vortex system is maintained close to a nonequilibrium state during the whole frequency sweep (few seconds), resulting in the observation of several events of dendrite nucleation and branching. From the analysis of a robust statistics, it results that avalanche-size distributions before and after flux-pinning tailoring by heavy-ion irradiation are fully consistent with a thermomagnetic model and with molecular dynamics simulations reported in literature.

The microwave properties of polycrystalline $\mathrm{Mg}{\mathrm{B}}_2$ thin films prepared by the so-called in situ method are investigated. The characterization of the films at microwave frequencies was obtained by a coplanar resonator technique. The analysis of the experimental data results in the determination of penetration depth, surface impedance, and complex conductivity. The aim of this work is to set the experimental results in a consistent framework, involving the two-band model in the presence of impurity scattering. The energy gaps are calculated and the contribution of intra- and interband scattering is considered. From the comparison between the calculated gap values and the experimental data it turns out that the temperature dependence of the penetration depth can be accounted for by an effective mean energy gap, in agreement with the predictions of V. G. Kogan and N. V. Zhelezina [Phys. Rev. B 69, 132506 (2004)]. On the other hand, the temperature dependence of the real part of the microwave conductivity and of the surface resistance is accounted for by the single smaller gap, in agreement with the work of B. B. Jin, T. Dahm, A. I. Gubin, E.-M. Choi, H. J. Kim, S.-I. Lee, W. N. Kang, and N. Klein [Phys. Rev. Lett. 91, 127006 (2003)]. Since these findings rely on the same calculated gap structure, the required consistency is fulfilled.