We demonstrate a straightforward optoelectronic fiber alignment technique for super- conducting nanowire single-photon detectors (SNSPDs) that exploits the temperature- dependent resistance of the nanowire under optical absorption. The target nanowire is illuminated via the fiber, and the local absorption of light heats the wire, causing a change in its resistivity. Scanning the fiber over the nanowire, the change in its resistivity is moni- tored by lock-in amplifier, mapping the spatial photothermal response correlated to absorp- tion and coupling efficiency. The maximum of the response corresponds to optimal fiber- SNSPD alignment. This method allows for aligning the fiber to the center of the meander with sub-micron precision. The response is robust to variations in the angle and height of the fiber, providing an alternative or complement to fiber-to-chip alignment methods based on the back-reflection or transmission measurement.

The technique of non-contact broadband transmission line flip-chip spectroscopy is utilized to probe resonances of mm-sized square resonators fabricated from strongly disordered molybdenum carbide films in the GHz frequency range. The temperature dependence of the resonances was modeled by the surface impedance of the thin films via the complex conductivity of disordered superconductors, which reflects the Dynes superconducting density of states of these superconductors. The obtained Dynes broadening parameters relate reasonably well to those known from scanning tunneling spectroscopy measurements. The eigenmodes of the 2D resonator were visualized by EM model in Sonnet software.

The optical properties of disordered ultra-thin NbTiN films are studied by means of spectroscopic ellipsometry. Drude-Lorentz model modified by quantum corrections describes the obtained optical conductivities well, including double plasmon behaviour and their transport properties.

High gain and large bandwidth of traveling-wave parametric amplifier exploiting the nonlinearity of Josephson Junctions can be achieved by fulfilling the so-called phase-matching condition. This condition is usually addressed by placing resonant structures along the waveguide or by periodic modulations of its parameters, creating gaps in the waveguide's dispersion. Here, we propose to employ the Josephson junctions, which constitute the centerline of the amplifier, as resonant elements for phase matching. By numerical simulations in JoSIM (and WRspice) software, we show that Josephson plasma oscillations can be utilized to create wave vector mismatch sufficient for phase matching as well as to prevent the conversion of the pump energy to higher harmonics. The proposed traveling wave parametric amplifier design has a gain of 15 dB and a 3 GHz bandwidth, which is comparable to the state-of-the-art TWPAs.

The requirements and details of designing a measuring cell and low-back-action deeply-cooled amplifier for quantum measurements at 10 mK are discussed. This equipment is a part of a microwave single-photon counter based on a superconducting flux qubit. The high electron mobility transistors (HEMTs) in the amplifier operate in unsaturated microcurrent regime and dissipate only 1 microwatt of dc power per transistor. Simulated amplifier gain is 15 dB at 450 MHz with a high-impedance ( 5 kOhm signal source and standard 50-Ohm output.

Highly disordered NbN thin films exhibit promising superconducting and optical properties. Despite extensive study, discrepancies in its basic electronic properties persist. Analysis of the optical conductivity of disordered ultrathin NbN films, obtained from spectroscopic ellipsometry by the standard Drude-Lorentz model, provides inconsistent parameters. We argue that this discrepancy arises from neglecting the presence of quantum corrections to conductivity in the IR range. To resolve this matter, we suggest a modification to the Drude-Lorentz model, incorporating quantum corrections. The parameters obtained from the modified model are consistent with transport and superconducting measurements. The revisited values describing conduction electrons, which differ significantly from commonly adopted ones, are the electron relaxation rate F 1.8 eV/h, the Fermi velocity v F 0.7 x 106 ms-1, and the electron density of states N ( E F ) = 2 states of both spins/eV/Vf.u..

Superconducting nanowire single-photon detectors are widely used in various fields of physics and technology, due to their high efficiency and timing precision. Although, in principle, their detection mechanism offers broadband operation, their wavelength range has to be optimized by the optical cavity parameters for a specific task. We present a study of the optical absorption of a superconducting nanowire single photon detector (SNSPD) with an optical cavity. The optical properties of the niobium nitride films, measured by spectroscopic ellipsometry, were modelled using the Drude-Lorentz model with quantum corrections. The numerical simulations of the optical response of the detectors show that the wavelength range of the detector is not solely determined by its geometry, but the optical conductivity of the disordered thin metallic films contributes considerably. This contribution can be conveniently expressed by the ratio of imaginary and real parts of the optical conductivity. This knowledge can be utilized in detector design.

Based on analysis of current-voltage characteristics and imaging of the resistive state of thin-film tin strips using low-temperature laser scanning microscopy (LTLSM), the process of destruction of superconductivity by current and microwave irradiation with the formation and spatial rearrangement of the order parameter phase slip lines, and their transformation into discrete localized normal domains are shown. The prospects of LTLSM are considered from the point of view of the study of the high-frequency properties of superconducting structures and spatial characteristics in the pre-critical state for instrumental applications.

We prepared a bi-metal Sn/Al thin film bridge of 1 × 5 µm2 in size and exposed it to microwave irradiation in a frequency range of 7 to 40 GHz to explore the Shapiro steps in the current-voltage characteristics, which served as a reliable indicator for assessing current-phase relation (CPR). The measurements were made in the temperature range (0.89 … 0.99)Tc with Tc = 3.66 K. No fractional steps are observed at 10 GHz, while all integer steps are present, and their widths oscillate with microwave field amplitude, which suggests a non-skewed quasi-sine CPR. Therefore, the normal-metal covering alters the resistive state of the long thin-film strip containing phase-slip centers so that the bi-metallic long bridge exhibits characteristics similar to a Josephson weak link. Considering a simple fabrication procedure, it may be utilized in making Josephson-effect-based devices such as DC and RF SQUIDs, especially in low-budget projects. Additional small-scale oscillations of the step widths found between the main peaks and the missing first step at a higher frequency of 20 GHz near Tc may be associated with Landau–Zener transitions between Andreev states and require further detailed study.

Light-matter interaction and understanding the fundamental physics behind is essential for emerging quantum technologies. Solid-state devices may explore new regimes where coupling strengths are "ultrastrong", i.e., comparable to the energies of the subsystems. New exotic phenomena occur the common root of many of them being the fact that the entangled vacuum contains virtual photons. They herald the lack of conservation of the number of excitations which is the witness of ultrastrong coupling breaking the U(1) symmetry. Despite more than a decade of research, the detection of ground-state virtual photons still awaits demonstration. In this work, we recognize the "conspiring" set of experimental challenges and show how to overcome them, thus providing a solution to this long-standing problem. We find that combining a superinductor-based unconventional "light fluxonium" qudit and coherent control yields a highly efficient, faithful, and selective conversion of virtual photons into real ones. This enables their detection with resources available to present-day quantum technologies.

The operating principle of traveling-wave parametric amplifiers is typically understood in terms of the standard coupled mode theory, which describes the evolution of forward propagating waves without any reflections, i.e. for perfect impedance matching. However, in practice, superconducting microwave amplifiers are unmatched nonlinear finite-length devices, where the reflecting waves undergo complex parametric processes, not described by the standard coupled mode theory. Here, we present an analytical solution for the TWPA gain, which includes the interaction of reflected waves. These reflections result in corrections to the well-known results of the standard coupled mode theory, which are obtained for both 3-wave and 4-wave mixing processes. Due to these reflections, gain is enhanced and unwanted nonlinear phase modulations are suppressed. Predictions of the model are experimentally demonstrated on two types of unmatched TWPA, based on coplanar waveguides with a central wire consisting of i) a high kinetic inductance superconductor, and ii) an array of 2000 Josephson junctions.

Joule heat generated by resistive elements of cryogenic micro- and nanodevices often originates boiling of the cooling cryogenic liquids (helium, nitrogen). The article proposes an experimental method to explore the dynamics of the formation and development of a single vapor bubble in cryogenic liquid by sensing the temperature change of a superconducting thin-film microbridge being in the resistive state with single phase slip center or line. It serves both the source of heat for generating single bubbles and the surface temperature sensor due to its temperature-dependent excess current. The average bubble detachment rate and the average single bubble volume were experimentally determined for nucleate helium boiling. The obtained values are in good agreement with the data of other authors found in literature.

Waveguides with superconducting Josephson junction-based metamaterial are widely used as parametric amplifiers. However, the precise estimation of power entering the device is crucial for the estimation of gain and noise temperature. This is nontrivial when the measurement tract is not symmetrical. We present a basic framework for the analysis of properties of such nonlinear systems and calibration of the input power. Utilizing measurements with varied temperature and power of the input signal, we estimate additional attenuation of the input line. We demonstrate a precise calibration procedure of a Josephson junction metamaterial.

A set of 5nm thick molybdenum carbide films were deposited by reactive magnetron sputtering on sapphire substrates. Changing the deposition parameters, the sheet resistance of the films was varied in the range from 390 to 3900 Omega/square at room temperature. The sheet resistance is enhanced by intrinsic disorder in the metallic films. Starting from room temperature, the DC conductivity of the samples decreases with decreasing temperature, following T(1/2 )dependence due to quantum corrections to the conductivity. Furthermore, we extended the studied range of the conductivity by optical spectroscopic ellipsometry, which enables to evaluate both the real and the imaginary part of the frequency-dependent complex conductivity. The real part of the conductivity further follows the root mean square corrections in the frequency domain and smoothly merges with the Drude response at the scale of the Drude relaxation time Gamma, which is approximately 3000 THz for our films. The dependences are analyzed by a simple formula, which allows us to determine the absolute measure of the strength of the quantum corrections on an extended scale. The strength of the quantum corrections increases with the disorder, and they significantly alter the optical conductivity from the Drude response up to the ultraviolet region. Moreover, we employ a numerical extrapolation method for complex conductivity of disordered metals, which enables us to extrapolate the conductivity from the visible frequency range down to far-infrared and up to the ultraviolet region.

Superconducting planar resonators of thin molybdenum carbide (MoC) films were fabricated by optical lithography. The films were deposited via reactive magnetron sputtering and by changing the deposition parameters, the sheet resistance of the films was varied. The microwave properties of the resonators were studied by broadband coplanar waveguide spectroscopy in flip-chip configuration. The kinetic inductance of MoC films governs the high frequency response of the resonators and is determined by the complex conductivity of the superconducting film. Well below the critical temperature of transition, kinetic inductance is proportional to film sheet resistance in normal state. The temperature-dependent resonances in the broadband spectra below critical temperature are described by a lumped LC model, where the inductance consists of geometric and kinetic inductance of the resonator. The temperature and frequency dependent complex conductivity of the superconducting film is calculated by the Dynes model for dirty superconductors. Furthermore, a numerical model of the kinetic planar resonator in Sonnet software is presented, which can be utilized to design resonators with desired properties, based on highly disordered superconductors. An on-chip design of a kinetic planar resonator filter is presented. The high kinetic inductance of the superconducting films allows us to minimize microwave filter dimensions.

Recently, quantum corrections to optical conductivity of disordered metals up to the UV region were observed. Although this increase of conductivity with frequency, also called anti-Drude behavior, should disappear at the electron collision frequency, such transition has never been observed, or described theoretically. Thus the knowledge of optical conductivity in a wide frequency range is of great interest. It is well known that the extrapolation of complex conductivity is ill-posed-a solution of the analytic continuation problem is not unique for data with finite accuracy. However, we show that assuming physically appropriate properties of the searched function a (co), such as symmetry, smoothness, and asymptotic solution for low and high frequencies, one can significantly restrict the set of solutions. We present a simple numerical method utilizing the radial basis function approximation and simulated annealing, which reasonably extrapolates the optical conductivity from visible frequency range down to the far-infrared and up to the ultraviolet region. The method was compared with two widely used analytic continuation techniques and resulting extrapolation obtained on MoC and NbN thin films was checked by transmission measurements across a wide frequency range.

"The non-contact broadband transmission line flip-chip spectroscopy technique is utilized to probe resonances of mm-sized square kinetic planar resonators made from strongly disordered molybdenum carbide films, in the GHz frequency range. The temperature dependence of the resonances was analyzed by the complex conductivity of disordered superconductor, as proposed in Ref. arXiv:1407.2402 , which involves the Dynes superconducting density of states. The obtained Dynes broadening parameters relate reasonably to the ones estimated from scanning tunneling spectroscopy measurements. The eigenmodes of the kinetic planar 2D resonator were visualized by EM model in Sonnet software. The proper understanding of the nature of these resonances can help to eliminate them, or utilize them e.g. as filters."

In this paper, we numerically and experimentally test the exploitability of the broadband non-contact flip-chip transmission line technique in studying the complex conductivity of ultra-thin, highly disordered superconducting films of molybdenum carbide.The complex conductivity of such films with various sheet resistances is calculated in the GHz frequency range by the Mattis-Bardeen model with finite broadening parameter Γ and by the Nam model for Dynes superconductors.The transmission of the line in the vicinity of the superconducting thin film is modeled in electromagnetic simulation software, and is compared to experimental data.Evidence of sharp resonances is reported.

Superconductor insulator transition in transverse magnetic field is studied in the highly disordered MoC film with the product of the Fermi momentum and the mean free path $k_F*l$ close to unity. Surprisingly, the Zeeman paramagnetic effects dominate over orbital coupling on both sides of the transition. In superconducting state it is evidenced by a high upper critical magnetic field $B_{c2}$, by its square root dependence on temperature, as well as by the Zeeman splitting of the quasiparticle density of states (DOS) measured by scanning tunneling microscopy. At $B_{c2}$ a logarithmic anomaly in DOS is observed. This anomaly is further enhanced in increasing magnetic field, which is explained by the Zeeman splitting of the Altshuler-Aronov DOS driving the system into a more insulating or resistive state. Spin dependent Altshuler-Aronov correction is also needed to explain the transport behavior above $B_{c2}$.

It is well known that conductivity of disordered metals is suppressed in the limit of low frequencies and temperatures by quantum corrections. Although predicted by theory to exist up to much higher energies, such corrections have so far been experimentally proven only for $\lesssim$80 meV. Here, by a combination of transport and optical studies, we demonstrate that the quantum corrections are present in strongly disordered conductor MoC up to at least $\sim$4 eV, thereby extending the experimental window where such corrections were found by a factor of 50. The knowledge of both, the real and imaginary parts of conductivity, enables us to identify the microscopic parameters of the conduction electron fluid. We find that the conduction electron density of strongly disordered MoC is surprisingly high and we argue that this should be considered a generic property of metals on the verge of disorder-induced localization transition.