Superconducting detectors are a modern technology applied in various fields. The microwave kinetic inductance detector (MKID) is one of cutting-edge superconducting detector. 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 response as a function of the number of quasiparticles. We demonstrate this responsivity calibration using the MKID maintained at 285mK. We also confirm consistency between the results obtained using this method and conventional calibration methods in terms of the accuracy.
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