Identify and Quantify Various Dissipation Mechanisms of Josephson Junction in Superconducting Circuits

TL;DR

The paper addresses dissipation in Josephson junctions used in superconducting circuits. It introduces a junction-embedded resonator (JER), a $\tfrac{1}{2}\lambda$ open-circuit transmission-line resonator with a JJ in the middle, and leverages the $1^{\mathrm{st}}$ and $2^{\mathrm{nd}}$ harmonics to create distinct boundary conditions that isolate internal vs external dissipation. By varying the junction area $A_{\mathrm{TJ}}$ and the number of junctions, the study extracts the dissipation rates $\Gamma_{\mathrm{TJ,1H}}$ and $\Gamma_{\mathrm{TJ,2H}}$, finding that internal dissipation scales with area while external dissipation remains nearly constant: $\Gamma_{\mathrm{TJ,1H}}/A_{\mathrm{TJ}} \approx 1.61\times10^{-8}\ \mathrm{s^{-1}\,\mu m^{-2}}$ and $\Gamma_{\mathrm{TJ,2H}} \approx 1.61\times10^{-6}\ \mathrm{s^{-1}}$ (averaged). This separation enables quantitative benchmarking of junction-related losses, providing clear guidance for optimizing JJs in different circuit regimes (e.g., transmon vs fluxonium) and establishing the JER as a versatile platform for dissipation characterization in superconducting devices.

Abstract

Pinpointing the dissipation mechanisms and evaluating their impacts to the performance of Josephson junction (JJ) are crucial for its application in superconducting circuits. In this work, we demonstrate the junction-embedded resonator (JER) as a platform which enables us to identify and quantify various dissipation mechanisms of JJ. JER is constructed by embedding JJ in the middle of an open-circuit, 1/2 λ transmission-line resonator. When the 1st and 2nd harmonics of JER are excited, JJ experiences different boundary conditions, and is dominated by internal and external dissipations, respectively. We systematically study these 2 dissipation mechanisms of JJ by varying the JJ area and number. Our results unveil the completely different behaviors of these 2 dissipation mechanisms, and quantitatively characterize their contributions, shedding a light on the direction of JJ optimization in various applications.

Figures (4)

• Figure 1: (a) The schematic of the . The top panel shows the structure of . The coaxial line represents the transmission-line structure. The "x" mark in the middle is the embedded . The middle and bottom panels demonstrate the voltage (orange curve) and current (blue curve) distributions of the 1st and 2nd harmonics along the transmission line of . Note that the embedded in the middle (i.e., $1/4 \, \lambda$ position) experiences different boundary conditions in the 1st and 2nd harmonics. (b) The optical microscope image of the , where the scale bar indicates 400 $\mathrm{\mu}$m. The insets on the right show the zoom-in images of the dummy (top) and 2 s in series (bottom), where the scale bar indicates 50 $\mathrm{\mu}$m.
• Figure 2: $\Delta$ (defined as $1/2 \, f_{\mathrm{2H}} - f_{\mathrm{1H}}$) of all the resonators on sample A. About the x-axis, Ctrl. 1 and 2 represent 2 controlled devices which are normal resonators; Dummy-JJ, L-JJ, M-JJ, and S-JJ are the s containing dummy, large-area, medium-area, and small-area s, which are in the ascending order of . The inset shows the extracted total of s ($L_{\mathrm{TJ}}$) depending on the total junction area ($A_{\mathrm{TJ}}$).
• Figure 3: (a) Dependences of on of typical devices on sample A. The blue and orange circles represent data points of the 1st harmonics of Ctrl. 1 resonator and L-JJ , respectively. The curves in different colors are the fitting results of \ref{['eq:power_dep']} on the corresponding data points. (b) and (c) $\Gamma_{\mathrm{LP}}$ of all the devices on sample A and B. The blue and orange circles represent the data points of the 1st and 2nd harmonics. In (c), we are not able to acquire the data points of the 6-JJ because of its malfunction.
• Figure 4: Dependence of $\Gamma_{\mathrm{TJ}}$ on $A_{\mathrm{TJ}}$. The blue and orange colors represent the data points of the 1st and 2nd harmonics. The circle and square marks indicate the data points of sample A and B, respectively. The blue line is the linear fitting result of the 1st-harmonic $\Gamma_{\mathrm{TJ}}$ ($\Gamma_{\mathrm{TJ, 1H}}$). The orange horizontal line is the averaged value of all the 2nd-harmonic $\Gamma_{\mathrm{TJ}}$ ($\Gamma_{\mathrm{TJ, 2H}}$).