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Journal of Experimental and Theoretical Physics Letters

Theoretical analysis of the operation of the kinetic inductance-based superconducting microwave detector

Alexander V. Semenov, Igor A. Devyatov, M. Yu. Kupriyanov

Published Dec 1, 2008• 6 citations
Publisher

Abstract

Nonequilibrium quasiparticle distribution functions that appear in a current-biased thin narrow diffuse superconducting strip under microwave irradiation at a low temperature have been calculated. A change in the kinetic inductance of the strip due to irradiation has been determined. The application of the strip as a microwave detector has been considered and the influence of the nonlinear phonon subsystem of the strip on the magnitude of the response has been found.

DOI
10.1134/s0021364008190077

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arXiv:2005.08765•AIP Advances•Sep 1, 2020•2 citations
Nonequilibrium quasiparticle distribution functions that appear in a current-biased thin narrow diffuse superconducting strip under microwave irradiation at a low temperature have been calculated. A change in the kinetic inductance of the strip due to irradiation has been determined. The application of the strip as a microwave detector has been considered and the influence of the nonlinear phonon subsystem of the strip on the magnitude of the response has been found.
While experimental studies of kinetic-inductance sensors have been limited so far by the temperature range near the superconducting transition, these detectors can be very sensitivity at temperatures well below the transition, where the number of equilibrium quasiparticles is exponentially small. In this regime, a shift of the quasiparticle chemical potential under radiation results in the change of the kinetic inductance, which can be measured by a sensitive SQUID readout. We modeled the kinetic inductance response of detectors made from disordered superconducting Nb, NbC, and MoRe films. Low phonon transparency of the interface between the superconductor and the substrate causes substantial re-trapping of phonons providing high quantum efficiency and the operating time of approximately 1 ms at 1 K. Due to the small number of quasiparticles, the noise equivalent power of the detector determined by the quasiparticle generation-recombination noise can be as small as approximately 10(exp -19) W/Hz(exp 1/2) at He4 temperatures.
Superconducting detectors are a modern technology applied in various fields. The microwave kinetic inductance detector (MKID) is one of the cutting-edge superconducting detectors. It is based on the principle of a superconducting resonator circuit. A radiation entering the MKID breaks the Cooper pairs in the superconducting resonator, and the intensity of the radiation is detected as a variation of the resonant condition. Therefore, calibration of the detector responsivity, i.e., the variation of the resonant phase with respect to the number of Cooper-pair breaks (quasiparticles), is important. We propose a method for responsivity calibration. Microwaves used for the detector readout locally raise the temperature in each resonator, which increases the number of quasiparticles. Since the magnitude of the temperature rise depends on the power of readout microwaves, the number of quasiparticles also depends on the power of microwaves. By changing the power of the readout microwaves, we simultaneously measure the phase difference and lifetime of quasiparticles. We calculate the number of quasiparticles from the measured lifetime and by using a theoretical formula. This measurement yields a relation between the phase responses as a function of the number of quasiparticles. We demonstrate this responsivity calibration using the MKID maintained at 285 mK. We also confirm the consistency between the results obtained using this method and conventional calibration methods in terms of the accuracy.
We analyse theoretically the influence of inelastic processes on coherent excited states of a superconductor generated by the application of microwaves. These states were identified recently [Phys. Rev. Lett. 117, 047002 (2016)] as the source of resonance frequency shift in microwave superconducting micro-resonators at low temperatures where the quasiparticle density is negligible. As a convenient model we use a thin dirty superconducting strip in contact with a diffuse normal metallic reservoir through an opaque tunnel junction and calculate analytically both the spectral functions and the non-equilibrium distribution function in the presence of a monochromatic microwave signal. We demonstrate that in the quantum mode of depairing, when the frequency of the microwave signal is much larger than the normalised signal amplitude, but much less than the modulus of a superconductor order parameter, the change of the kinetic inductance is determined primarily by the change of the spectral functions. We propose an experimental system to measure the spectral functions as well as the non-equilibrium distribution function using a non-invasive tunnel-junction on a microwave-driven superconducting wire.
A microwave kinetic inductance detector (MKID) is a cutting-edge superconducting detector, and its principle is based on a superconducting resonator circuit. The superconducting transition temperature (Tc) of the MKID is an important parameter because various MKID characterization parameters depend on it. In this paper, we propose a method to measure the Tc of the MKID by changing the applied power of the readout microwaves. A small fraction of the readout power is deposited on the MKID, and the number of quasiparticles in the MKID increases with this power. Furthermore, the quasiparticle lifetime decreases with the number of quasiparticles. Therefore, we can measure the relation between the quasiparticle lifetime and the detector response by rapidly varying the readout power. From this relation, we evaluate the intrinsic quasiparticle lifetime. This lifetime is theoretically modeled by Tc, the physical temperature of the MKID device, and other known parameters. We obtain Tc by comparing the measured lifetime with that acquired using the theoretical model. Using an MKID fabricated with aluminum, we demonstrate this method at a 0.3 K operation. The results are consistent with those obtained by Tc measured by monitoring the transmittance of the readout microwaves with the variation in the device temperature. The method proposed in this paper is applicable to other types, such as a hybrid-type MKID.