  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.
