Novel measurement method for responsivity of microwave kinetic

Novel measurement method for responsivity of microwave kinetic inductance detector by changing a power of readout microwaves Hiroki Kutsuma (Tohoku University/RIKEN), Makoto Hattori (Tohoku University), Ryo Koyano (Saitama University), Satoru Mima (RIKEN), Shugo Oguri (RIKEN), Chiko Otani (RIKEN), Tohru Taino (Saitama University), Osamu Tajima (Kyoto University) Microwave Kinetic Inductance Detector (MKID) is one of cutting-edge superconducting detectors. In general, changing a physical temperature of a MKID device has been used to derive its responsivity in the calibration. However, the difference between measured temperature and detector temperature causes systematic effect. We propose a novel method for the responsivity calibration to reduce contamination of such systematics. Introduction Microwave Kinetic Inductance Detector [1] is a superconducting detector. Below the critical temperature, a photon with energy hν > 2Δ (Δ : gap energy) breaks Cooper pairs, creates quasiparticles (a), and changes surface impedance (b). Its results in resonance frequency decrease, bandwidth broadening (c) and phase shift (d). Resul t Fig. 1. Detection mechanism of MKID Method In real applications, we have to calibrate the responsivity of the detector, i. e. , dθ/d. Nqp. Changing the physical temperature of a MKID device is the most popular calibration method [1, 2]. However, this method has some issues for consideration. For example, It is difficult to estimate the uncertainty of T, because we cannot directly probe the MKID The number of quasiparticles (Nqp) temperature. depends on the readout power [35], because a loss of readout microwave warms up the devices. The change of the readout power from PH to PL (top), causes the change of the Nqp (middle) and phase response (bottom) with the time constant (τqp). Nqp is deduced from the measured τqp by following formula [6], Fig. 4. Measured phase responses as a function of time after we change the power of typical readout microwaves Fig. 4 shows phase responses as a function of time. We reset the attenuation value at t = 100 μs. We fit the data to Eq (2). We repeat this measurement 40 times for each set of power change. And we get phase response (θH - θL) and τqp and change τqp to Nqp using Eq (1). τ0 : electron phonon interaction time (450 ns for Al) V : volume of the resonator k. B : Boltzmann constant N 0 : single spin density of the states at the Fermi energy (1. 74× 1010 e. V-1/μm 3 for Al) Tc : superconducting transition temperature. (1. 2 K for Al) Fig. 2. Illustrations of the principle to measure the responsivity, dθ/d. Nqp, with By using various sets of readout changing power of the readout power, we obtain phase response microwaves. as a function of Nqp, i. e. , responsivity. Setup We applied this method using hybridtype MKID [7]. The MKID and measurement setup are described in Tab. 1 and Fig. 3. The power is controlled by an input variable attenuator. The microwave power is changed from PH to PL variously. Material Fabrication Volume (Al) Temperature Variable attenuator PL (Attenuation value) PH (Attenuation value) Nb and Al RIKEN 920 μm 3 285 m. K LDA-602 E, Vaunix Co. LTD -17. 5 d. B (~ -70 d. B into the MKID) -11. 0, -12. 0, -13. 0, -14. 0, and -15. 0 d. B Tab. 1. About the MKID and Fig. 3. A diagram of the MKID measurement setup. readout. Fig. 5. The measured relation between the phase response (θL - θH) and the number of quasiparticles (Nqp) base on the proposed method. Fig. 5 shows the relation between the phase response as a function of Nqp. The comparison of results of our method and conventional method is described in Tab. 2. Our method Heater control PSD method [1, 2] [5] dθ/d. Nqp [× 10 -6 rad] 2. 8 ± 0. 4 0. 99 ± 0. 03 2. 4 ± 0. 2 Tab. 2. Comparison of our method and conventional method. We can conclude that our method can be a good new estimator for dθ/d. Nqp. Summar MKID is one of cutting-edge superconducting detector. We proposed a y calibration method, i. e. , simultaneous measurements of the phase difference and the quasiparticle lifetime following the power change of the readout microwaves. The number of quasiparticles was calculated using measured lifetime and volume of the resonator. We demonstrated this method and confirmed its simplicity and ease-of-use. This work will appear in Applied Physics Letters soon (see also ar. Xiv: 1907. 03403). Reference [1] P. K. Day et al. Nature, 425(6960): 817, 2003. [2] J. Gao et. al. Journal of Low Temperature Physics, 151(1 -2): 557– 563, 2008. [3] S. E. Thompson et al. Superconductor Science and Technology, 26(9): 095009, 2013. [4] P. J. de Visser et al. Physical review letters, 112(4): 047004, 2014. [5] P. J. de Visser. Quasiparticle dynamics in aluminium superconducting microwave resonators. Ph. D thesis, Delft University of Technology, Delft, The Netherlands, 2014. [6] S. B. Kaplan et. al. Physical Review B, 14(11): 4854, 1976 [7] T. Nagasaki et. al. Journal of Low Temperature Physics, 193(5 -6): 1066– 1074, 2018. [8] H. Kutsuma et al. , Appl. Phys. Lett. in press (2019) (ar. Xiv: 1907. 03403)