Experimentally estimating of physical parameters of the fabricated superconducting Josephson junctions

Abstract

Superconducting Josephson junctions are the key devices for superconducting quantum computation and microwave single photon detection. It is important to fabricate the Josephson junctions with designable parameters. Different from the typical methods to calibrate the parameters of the Josephson junctions,, e.g., by using the microwave drivings and measuring the ratio of hysteresis current to critical one, in this paper we achieve the calibrations with the low frequency current biases. First, we measure the <i>I</i>-<i>V</i> characteristic curves of the fabricated Al/AlO<i>_x</i>/Al junctions. Second, we measure the statistical distributions of the jump currents of the Josephson junction samples driven by the low frequency (@71.3 Hz) biased currents at an extremely low temperature of 50 mK. These two sets of experimental data are utilized to estimate the typical parameters of the Josephson junction, i.e., junction capacitance, critical current, and the damping coefficient, which are difficult to be directly measured in the usual experiments. The critical current and capacitance of the Josephson junction are estimated by fitting the statistical distribution of the measured jump currents with the relevant theoretical model of the "particle" escape from the potential driven by the thermal excitations and quantum tunnelings. With the calibrated critical current of the junction, the relation between <inline-formula><tex-math id="M3">\begin{document}$I/I_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M3.png"/></alternatives></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}${\rm{d}}\varphi/{\rm{d}}\tau,\,\tau=\omega_{\rm{c}}t$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M4.png"/></alternatives></inline-formula> (with <inline-formula><tex-math id="M5">\begin{document}$\omega_{\rm{c}}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M5.png"/></alternatives></inline-formula> being the plasmon frequency) is obtained from the measured <inline-formula><tex-math id="M6">\begin{document}$I\text-V$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M6.png"/></alternatives></inline-formula> curve. Using the standard resistively capacitance shunted junction model to fit such a relation, the damping coefficient of the junction can be estimated. With the estimated critical current, capacitance, and damping coefficient, the resistance <inline-formula><tex-math id="M7">\begin{document}$R_n$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M7.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="17-20210393_M7.png"/></alternatives></inline-formula> of the junction at the working temperature is calibrated consequently. It is shown that our estimated results are in good agreement with that predicted by the famous Ambgaokar-Baratoff formula. Physically, the method demonstrated here possesses two advantages. First, it is relatively insensitive to the noise during the measurement of the junction's <i>I</i>-<i>V</i> characteristic curve, compared with the usual method to calibrate damping coefficient by measuring the ratio of hysteresis current to critical current. Second, only the low frequency driving is required to measure the jump current of the junction for estimating the damping coefficient. The microwave driving is not necessary. Hopefully, the present work is useful for the on-demand designs of the Josephson junctions for various applications.