Microwave Circulation in an Extended Josephson Junction Ring

TL;DR

This work proposes a DC-controlled, on-chip microwave circulator based on an extended annular long Josephson junction with moving fluxons acting as a synthetic moving medium to break time-reversal symmetry. By formulating a sine-Gordon model for the LJJ and coupling it to external waveguides through galvanic or capacitive schemes, the authors predict a resonant three-port circulator with a bandwidth of approximately 210 MHz and low dissipation under realistic Nb–AlOx–Nb parameters. They validate full SG simulations against a temporally coupled-mode model, identify optimal fluxon number and bias current (e.g., $n=8$, $i_b\approx 3\times 10^{-4}$) and show tunability of the resonance via fluxon count. The analysis includes the impact of internal losses ($g$) and surface losses ($p$) on circulation and demonstrates a practical, fabrication-friendly path toward integrated superconducting circulators for quantum technologies, with a 1-dB compression point around $-90$ dBm and saturation well above single-photon levels at GHz frequencies. The results underscore the viability of synthetic-motion nonreciprocity in compact, on-chip devices and offer guidance for experimental implementation leveraging standard LJJ fabrication techniques and fluxon-insertion methods.

Abstract

Circulators are nonreciprocal devices that enable directional signal routing. Nonreciprocity, which requires time-reversal symmetry breaking, can be produced in waveguides in which the propagation medium moves relative to the waveguide at a moderate fraction of the wave speed. Motivated by this effect, here we propose a design for nonreciprocal microwave transmission based on an extended, annular Josephson junction, in which the propagation medium consists of a train of moving fluxons. We show how to harness this to build a high-quality resonant microwave circulator, and we theoretically evaluate the anticipated performance of such a device.

Figures (9)

• Figure 1: (a) Cartoon of an annular LJJ (not to scale), consisting of two superconducting rings (blue) formed from evaporated aluminium films, and separated by a tunnel-barrier junction (yellow), and coupled to three external ports, depicting the central conductors of the port waveguides as cylinders. The $n=8$ 'wagon wheels' represent the current density loops associated to localised fluxons (pink). Vertical arrows indicate a current bias $i_b$ through the junction to induce fluxon motion. (b) Dimensionless DC I-V response of an annular LJJ for different numbers of fluxons $n$, with system parameters $\textsf{L}=15$ and $\textsf{g}=0.02$. Dashed lines represent the asymptotic voltage $\textsf{V}=2\pi n/\textsf{L}$, determined by the Swihart velocity.
• Figure 2: (a) Pairwise-degenerate fluxon-mode frequencies $\omega_1,\omega_{n-1}$ and $\omega_2,\omega_{n-2}$ (markers) versus the fluxon number $n$, with the asymptote (dashed), shown for $\textsf{i}_b=0$, $\textsf{L}=15$. (b) The degeneracy of the counter-rotating modes $\omega_1$ and $\omega_{n-1}$ is lifted for non-zero current bias $\textsf{i}_b$, shown for $n=8$, $\textsf{g}=0.02$.
• Figure 3: (a) $|S_{j1}|$ dependence on the dimensionless current bias $\textsf{i}_b$ at the resonant frequency $\omega_d/(2\pi) = 7.53 \, \mathrm{GHz}$; $|S_{21}|$ is maximised at $\textsf{i}_b = 3 \times 10^{-4}$. Solid lines are from numerical solutions of the input-output SG \ref{['eq:SGEquation']}, and markers are from the temporal coupled-mode (TCM) model. (b) $|S_{j1}|$ dependence on the drive frequency $\omega_d$ at $\textsf{i}_b = 3 \times 10^{-4}$ at $n=8$ (solid lines). Also shown is $|S_{21}|$ for $n=7,9$ (dashed and dotted lines). In both panels $\textsf{L}=26$.
• Figure 4: (a) Dependence of $S$-matrix elements on the dimensionless quasiparticle loss, $\textsf{g}$, computed numerically from the SG \ref{['eq:SGEquation']} (solid lines), and TCM (markers). (b) Dependence of $S_{j1}$ on the dimensionless surface loss, $\textsf{p}$. In both panels, the external coupling is $\Gamma_{\rm x}=0.002$.
• Figure 5: Input power dependence of the $S$-matrix elements $|S_{j1}|$, showing the reduction in circulation performance with increasing power. The 1-dB power compression point occurs at $P_{\mathrm{{1\,dB}}} = -90 \, \mathrm{dBm}$. Parameters are as in \ref{['fig:SmatrixAnalysis']}.