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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Prober, D. E. (1993). Superconducting terahertz mixer using a transition-edge microbolometer. Appl. Phys. Lett., 62(17), 2119–2121.
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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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Phillips, T. G., & Jefferts, K. B. (1973). A low temperature bolometer heterodyne receiver for Millimeter wave astronomy. Rev. Sci. Instrum., 44(8), 1009–1014.
Abstract: Liquid helium cooled InSb hot electronbolometers are used in a balanced mixer configuration as detectors for an imagelessmicrowave receiver. The system is designed for mounting at the prime focus of the National Radio Astronomy Observatory (NRAO) 11 m antenna at Kitt Peak, Arizona, and is suitable for the study of rotational line spectra of interstellar gas molecules. Currently the operating frequency is in the 90–140 GHz band where the double sideband system noise temperature is 250 K.
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Goltsman, G. (2009). Superconducting NbN hot-electron bolometer mixer, direct detector and single-photon counter: from devices to systems.
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Martini, F., Cibella, S., Gaggero, A., Mattioli, F., & Leoni, R. (2021). Waveguide integrated hot electron bolometer for classical and quantum photonics. Opt. Express, 29(6), 7956–7965.
Abstract: The development of performant integrated detectors, which are sensitive to quantum fluctuations of coherent light, are strongly desired to realize a scalable and determinist photonic quantum processor based on continuous variables states of light. Here, we investigate the performance of hot electron bolometers (HEBs) fabricated on top of a silicon-on-insulator (SOI) photonic circuit showing responsivities up to 8600 V/W and a record noise equivalent temperature of 1.1 dB above the quantum limit. Thanks to a detailed analysis of the noise sources of the waveguide integrated HEB, we estimate 14.8 dBV clearance between the shot noise and electrical noise with just 1.1microW of local oscillator power. The full technology compatibility with superconducting nanowire single photon detectors (SNSPDs) opens the possibility of nonclassical state engineering and state tomography performed within the same platform, enabling a new class of optical quantum processors.
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Pentin, I., Vakhtomin, Y., Seleznev, V., & Smirnov, K. (2020). Hot electron energy relaxation time in vanadium nitride superconducting film structures under THz and IR radiation. Sci. Rep., 10(1), 16819.
Abstract: The paper presents the experimental results of studying the dynamics of electron energy relaxation in structures made of thin (d approximately 6 nm) disordered superconducting vanadium nitride (VN) films converted to a resistive state by high-frequency radiation and transport current. Under conditions of quasi-equilibrium superconductivity and temperature range close to critical (~ Tc), a direct measurement of the energy relaxation time of electrons by the beats method arising from two monochromatic sources with close frequencies radiation in sub-THz region (omega approximately 0.140 THz) and sources in the IR region (omega approximately 193 THz) was conducted. The measured time of energy relaxation of electrons in the studied VN structures upon heating of THz and IR radiation completely coincided and amounted to (2.6-2.7) ns. The studied response of VN structures to IR (omega approximately 193 THz) picosecond laser pulses also allowed us to estimate the energy relaxation time in VN structures, which was ~ 2.8 ns and is in good agreement with the result obtained by the mixing method. Also, we present the experimentally measured volt-watt responsivity (S~) within the frequency range omega approximately (0.3-6) THz VN HEB detector. The estimated values of noise equivalent power (NEP) for VN HEB and its minimum energy level (deltaE) reached NEP@1MHz approximately 6.3 x 10(-14) W/ radicalHz and deltaE approximately 8.1 x 10(-18) J, respectively.
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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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Fu, K., Zannoni, R., Chan, C., Adams, S. H., Nicholson, J., Polizzi, E., et al. (2008). Terahertz detection in single wall carbon nanotubes. Appl. Phys. Lett., 92(3), 033105.
Abstract: It is reported that terahertz radiation from 0.69 to 2.54 THz has been sensitively detected in a device consisting of bundles of carbon nanotubes containing single wall metallic carbon nanotubes, quasioptically coupled through a lithographically fabricated antenna, and a silicon lens. The measured data are consistent with a bolometric detection process in the metallic tubes and the devices show promise for operation well above 4.2 K.
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Klapwijk, T. M., Barends, R., Gao, J. R., Hajenius, M., & Baselmans, J. J. A. (2004). Improved superconducting hot-electron bolometer devices for the THz range. In Proc. SPIE (Vol. 5498, pp. 129–139).
Abstract: Improved and reproducible heterodyne mixing (noise temperatures of 950 K at 2.5 THz) has been realized with NbN based hot-electron superconducting devices with low contact resistances. A distributed temperature numerical model of the NbN bridge, based on a local electron and a phonon temperature, has been used to understand the physical conditions during the mixing process. We find that the mixing is predominantly due to the exponential rise of the local resistivity as a function of electron temperature.
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