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Vercruyssen, N., Verhagen, T. G. A., Flokstra, M. G., Pekola, J. P., & Klapwijk, T. M. (2012). Evanescent states and nonequilibrium in driven superconducting nanowires. Phys. Rev. B, 85, 224503(1–10).
Abstract: We study the nonlinear response of current transport in a superconducting diffusive nanowire between normal reservoirs. We demonstrate theoretically and experimentally the existence of two different superconducting states appearing when the wire is driven out of equilibrium by an applied bias, called the global and bimodal superconducting states. The different states are identified by using two-probe measurements of the wire, and measurements of the local density of states with tunneling probes. The analysis is performed within the framework of the quasiclassical kinetic equations for diffusive superconductors.
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Semenov, A. D., Nebosis, R. S., Gousev, Y. P., Heusinger, M. A., & Renk, K. F. (1995). Analysis of the nonequilibrium photoresponse of superconducting films to pulsed radiation by use of a two-temperature model. Phys. Rev. B, 52(1), 581–590.
Abstract: Photoresponse of a superconducting film in the resistive state to pulsed radiation has been studied in the framework of a model assuming that two different effective temperatures can be assigned to the quasiparticle and phonon nonequilibrium distributions. The coupled electron-phonon-substrate system is described by a system of time-dependent energy-balance differential equations for effective temperatures. An analytical solution of the system is given and calculated voltage transients are compared with experimental photoresponse signals taking into account the radiation pulse shape and the time resolution of the readout electronics. It is supposed that a resistive state (vortices, fluxons, network of intergrain junctions, hot spots, phase slip centers) provides an ultrafast connection between electron temperature changes and changes of the film resistance and thus plays a minor role in the temporal evolution of the response. In accordance with experimental observations a two-component response was revealed from simulations. The slower component corresponds to a bolometric mechanism while the fast component is connected with the relaxation of the electron temperature. Calculated photoresponse transients are presented for different ratios of the electron and phonon specific heat, radiation pulse durations and fluences, and frequency band passes of registration electronics. From the amplitude of the bolometric component we determine the radiation energy absorbed in a film. This enables us to reveal an intrinsic electron-phonon scattering time even if it is much shorter than the time resolution of readout electronics. We analyze experimental voltage transients for NbN, YBa2Cu3O7, and TlBa2Ca2Cu3O9 superconducting films and find the electron-phonon interaction times at the transition temperatures of 17, 2.5, and 1.8 ps, respectively. The values are in reasonable agreement with data of other experiments.
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Pekker, D., Shah, N., Sahu, M., Bezryadin, A., & Goldbart, P. M. (2009). Stochastic dynamics of phase-slip trains and superconductive-resistive switching in current-biased nanowires. Phys. Rev. B, 80, 214525 (1 to 17).
Abstract: Superconducting nanowires fabricated via carbon-nanotube templating can be used to realize and study quasi-one-dimensional superconductors. However, measurement of the linear resistance of these nanowires have been inconclusive in determining the low-temperature behavior of phase-slip fluctuations, both quantal and thermal. Thus, we are motivated to study the nonlinear current-voltage characteristics in current-biased nanowires and the stochastic dynamics of superconductive-resistive switching, as a way of probing phase-slip events. In particular, we address the question: can a single phase-slip event occurring somewhere along the wire—during which the order-parameter fluctuates to zero—induce switching, via the local heating it causes? We explore this and related issues by constructing a stochastic model for the time evolution of the temperature in a nanowire whose ends are maintained at a fixed temperature. We derive the corresponding master equation as a tool for evaluating and analyzing the mean switching time at a given value of current (smaller than the depairing critical current). The model indicates that although, in general, several phase-slip events are necessary to induce switching via a thermal runaway, there is indeed a regime of temperatures and currents in which a single event is sufficient. We carry out a detailed comparison of the results of the model with experimental measurements of the distribution of switching currents, and provide an explanation for the rather counterintuitive broadening of the distribution width that is observed upon lowering the temperature. Moreover, we identify a regime in which the experiments are probing individual phase-slip events, and thus offer a way of unearthing and exploring the physics of nanoscale quantum tunneling of the one-dimensional collective quantum field associated with the superconducting order parameter.
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Huard, B., Pothier, H., Esteve, D., & Nagaev, K. E. (2007). Electron heating in metallic resistors at sub-Kelvin temperature. Phys. Rev. B, 76, 165426(1–9).
Abstract: In the presence of Joule heating, the electronic temperature in a metallic resistor placed at sub-Kelvin temperatures can significantly exceed the phonon temperature. Electron cooling proceeds mainly through two processes: electronic diffusion to and from the connecting wires and electron-phonon coupling. The goal of this paper is to present a general solution of the problem in a form that can easily be used in practical situations. As an application, we compute two quantities that depend on the electronic temperature profile: the second and the third cumulant of the current noise at zero frequency, as a function of the voltage across the resistor. We also consider time-dependent heating, an issue relevant for experiments in which current pulses are used, for instance, in time-resolved calorimetry experiments.
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Sidorova, M., Semenov, A. D., Hübers, H. - W., Ilin, K., Siegel, M., Charaev, I., et al. (2020). Electron energy relaxation in disordered superconducting NbN films. Phys. Rev. B, 102(5), 054501 (1 to 15).
Abstract: We report on the inelastic-scattering rate of electrons on phonons and relaxation of electron energy studied by means of magnetoconductance, and photoresponse, respectively, in a series of strongly disordered superconducting NbN films. The studied films with thicknesses in the range from 3 to 33 nm are characterized by different Ioffe-Regel parameters but an almost constant product qTl (qT is the wave vector of thermal phonons and l is the elastic mean free path of electrons). In the temperature range 14–30 K, the electron-phonon scattering rates obey temperature dependencies close to the power law 1/τe−ph∼Tn with the exponents n≈3.2–3.8. We found that in this temperature range τe−ph and n of studied films vary weakly with the thickness and square resistance. At 10 K electron-phonon scattering times are in the range 11.9–17.5 ps. The data extracted from magnetoconductance measurements were used to describe the experimental photoresponse with the two-temperature model. For thick films, the photoresponse is reasonably well described without fitting parameters, however, for thinner films, the fit requires a smaller heat capacity of phonons. We attribute this finding to the reduced density of phonon states in thin films at low temperatures. We also show that the estimated Debye temperature in the studied NbN films is noticeably smaller than in bulk material.
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Bardeen, J., & Mattis, D. C. (1958). Theory of the anomalous skin effect in normal and superconducting metals. Phys. Rev., 111(2), 412–417.
Abstract: Chambers' expression for the current density in a normal metal in which the electric field varies over a mean free path is derived from a quantum approach in which use is made of the density matrix in the presence of scattering centers but in the absence of the field. An approximate expression used for the latter is shown to reduce to one derived by Kohn and Luttinger for the case of weak scattering. A general space-and time-varying electromagnetic interaction is treated by first-order perturbation theory. The method is applied to superconductors, and a general expression derived for the kernel of the Pippard integral for fields of arbitrary frequency. The expressions derived can also be used to discuss absorption of electromagnetic radiation in thin superconducting films.
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Zhang, W., Miao, W., Yao, Q. J., Lin, Z. H., Shi, S. C., Gao, J. R., et al. (2012). Spectral response and noise temperature of a 2.5 THz spiral antenna coupled NbN HEB mixer. Phys. Procedia, 36, 334–337.
Abstract: We report on a 2.5 THz spiral antenna coupled NbN hot electron bolometer (HEB) mixers, fabricated with in-situ process. The receiver noise temperature with lowest value of 1180 K is in good agreement with calculated quantum efficiency factor as a function of bias voltage. In addition, the measured spectral response of the spiral antenna coupled NbN HEB mixer shows broad frequency coverage of 0.8-3 THz, and corrected response for optical losses, FTS, and coupling efficiency between antenna and bolometer falls with frequency due to diffraction-limited beam of lens/antenna combination.
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Semenov, A. D., Hübers, H. - W., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2002). 2.5 THz heterodyne receiver with NbN hot-electron-bolometer mixer. Phys. C: Supercond., 372-376, 448–453.
Abstract: We describe a 2.5 THz heterodyne receiver for applications in astronomy and atmospheric research. The receiver employs a superconducting NbN phonon-cooled hot-electron-bolometer mixer and an optically pumped far-infrared gas laser as local oscillator. 2200 K double sideband mixer noise temperature was measured at 2.5 THz across a 1 GHz intermediate frequency bandwidth centred at 1.5 GHz. The total conversion losses were 17 dB. The mixer response was linear at load temperatures smaller than 400 K. The receiver was tested in the laboratory environment by measuring the methanol line in emission. Observed pressure broadening confirms the true heterodyne detection regime of the mixer.
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Cherednichenko, S., Kroug, M., Merkel, H., Khosropanah, P., Adam, A., Kollberg, E., et al. (2002). 1.6 THz heterodyne receiver for the far infrared space telescope. Phys. C: Supercond., 372-376, 427–431.
Abstract: A low noise heterodyne receiver is being developed for the terahertz range using a phonon-cooled hot-electron bolometric mixer based on 3.5 nm thick superconducting NbN film. In the 1–2 GHz intermediate frequency band the double-sideband receiver noise temperature was 450 K at 0.6 THz, 700 K at 1.6 THz and 1100 K at 2.5 THz. In the 3–8 GHz IF band the lowest receiver noise temperature was 700 K at 0.6 THz, 1500 K at 1.6 THz and 3000 K at 2.5 THz while it increased by a factor of 3 towards 8 GHz.
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Cherednichenko, S., Rönnung, F., Gol'tsman, G., Kollberg, E., & Winkler, D. (2000). YBa2Cu3O7−δ hot-electron bolometer mixer. Phys. C: Supercond., 341-348, 2653–2654.
Abstract: We present an investigation of hot-electron bolometric mixer based on YBa2Cu3O7−δ (YBCO) superconducting thin film. Mixer conversion loss, absorbed local oscillator power and intermediate frequency bandwidth was measured at the local oscillator frequency 600 GHz. The fabrication technique for nanoscale YBCO hot-electron bolometer (HEB) mixer integrated into planar antenna structure is described.
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Huebers, H. - W., Pavlov, S., Semenov, A., Köhler, R., Mahler, L., Tredicucci, A., et al. (2005). Terahertz quantum cascade laser as local oscillator in a heterodyne receiver. Optics Express, 13(15), 5890–5896.
Abstract: Terahertz quantum cascade lasers have been investigated with respect to their performance as a local oscillator in a heterodyne receiver. The beam profile has been measured and transformed in to a close to Gaussian profile resulting in a good matching between the field patterns of the quantum cascade laser and the antenna of a superconducting hot electron bolometric mixer. Noise temperature measurements with the hot electron bolometer and a 2.5 THz quantum cascade laser yielded the same result as with a gas laser as local oscillator.
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Rabanus, D., Graf, U. U., Philipp, M., Ricken, O., Stutzki, J., Vowinkel, B., et al. (2009). Phase locking of a 1.5 terahertz quantum cascade laser and use as a local oscillator in a heterodyne HEB receiver. Optics Express, 17(3), 1159–1168.
Abstract: We demonstrate for the first time the closure of an electronic phase lock loop for a continuous–wave quantum cascade laser (QCL) at 1.5 THz. The QCL is operated in a closed cycle cryo cooler. We achieved a frequency stability of better than 100 Hz, limited by the resolution bandwidth of the spectrum analyser. The PLL electronics make use of the intermediate frequency (IF) obtained from a hot electron bolometer (HEB) which is downconverted to a PLL IF of 125 MHz. The coarse selection of the longitudinal mode and the fine tuning is achieved via the bias voltage of the QCL. Within a QCL cavity mode, the free-running QCL shows frequency fluctuations of about 5 MHz, which the PLL circuit is able to control via the Stark–shift of the QCL gain material. Temperature dependent tuning is shown to be nonlinear, and of the order of -16 MHz/K. Additionally we have used the QCL as local oscillator (LO) to pump an HEB and perform, again for the first time at 1.5 THz, a heterodyne experiment, and obtain a receiver noise temperature of 1741 K.
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Lobanov, Y. V., Vakhtomin, Y. B., Pentin, I. V., Rosental, V. A., Smirnov, K. V., Goltsman, G. N., et al. (2021). Time-resolved measurements of light–current characteristic and mode competition in pulsed THz quantum cascade laser. Optical Engineering, 60(8), 1–8.
Abstract: Quantum cascade lasers (QCL) are widely adopted as prominent and easy-to-use solid-state sources of terahertz radiation. Yet some applications require generation and detection of very sharp and narrow terahertz-range pulses with a specific spectral composition. We have studied time-resolved light-current (L–I) characteristics of multimode THz QCL operated with a fast ramp of the injection current. Detection of THz pulses was carried out using an NbN superconducting hot-electron bolometer with the time constant of the order of 1 ns while the laser bias current was swept during a single driving pulse. A nonmonotonic behavior of the L–I characteristic with several visually separated subpeaks was found. This behavior is associated with the mode competition in THz QCL cavity, which we confirm by L–I measurements with use of an external Fabry–Perot interferometer for a discrete mode selection. We also have demonstrated the possibility to control the L–I shape with suppression of one of the subpeaks by simply adjusting the off-axis parabolic mirror for optimal optical alignment for one of the laser modes. The developed technique paves the way for rapid characterization of pulsed THz QCLs for further studies of the possibilities of using this approach in remote sensing.
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Lobanov, Y., Shcherbatenko, M., Shurakov, A., Rodin, A. V., Klimchuk, A., Nadezhdinsky, A. I., et al. (2014). Heterodyne detection at near-infrared wavelengths with a superconducting NbN hot-electron bolometer mixer. Opt. Lett., 39(6), 1429–1432.
Abstract: We report on the development of a highly sensitive optical receiver for heterodyne IR spectroscopy at the communication wavelength of 1.5 μm (200 THz) by use of a superconducting hot-electron bolometer. The results are important for the resolution of narrow spectral molecular lines in the near-IR range for the study of astronomical objects, as well as for quantum optical tomography and fiber-optic sensing. Receiver configuration as well as fiber-to-detector light coupling designs are discussed. Light absorption of the superconducting detectors was enhanced by nano-optical antennas, which were coupled to optical fibers. An intermediate frequency (IF) bandwidth of about 3 GHz was found in agreement with measurements at 300 GHz, and a noise figure of about 25 dB was obtained that was only 10 dB above the quantum limit.
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Kitaeva, G. K., Kornienko, V. V., Kuznetsov, K. A., Pentin, I. V., Smirnov, K. V., & Vakhtomin, Y. B. (2019). Direct detection of the idler THz radiation generated by spontaneous parametric down-conversion. Opt. Lett., 44(5), 1198–1201.
Abstract: We study parametric down-conversion (PDC) of optical laser radiation in the strongly frequency non-degenerate regime which is promising for the generation of quantum-correlated pairs of extremely different spectral ranges, the optical and the terahertz (THz) ones. The possibility to detect tenuous THz-frequency photon fluxes generated under low-gain spontaneous PDC is demonstrated using a hot electron bolometer. Then experimental dependences of the THz radiation power on the detection angle and on the pump intensity are analyzed.
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