Measuring weak microwave signals via current-biased Josephson Junctions II: Arriving at single-photon detection sensitivity

TL;DR

This work tackles the challenge of detecting single microwave photons with current-biased Josephson junctions by leveraging non-equilibrium dynamics induced by rapid bias-current sweeps. The core idea is to operate the JTD in a non-adiabatic regime where the phase evolution becomes highly sensitive to the initial phase $\varphi_0$ while becoming effectively immune to thermal noise, enabling detection at the single-photon energy scale $E_\text{ph}=\hbar\omega$. The authors quantify detection performance using switching-current distributions and ROC-based metrics (AUC), showing that non-equilibrium JTDs yield pronounced fingerprints that distinguish signal from noise, with bandwidth around $\Delta\omega\approx\beta\omega_J$ and dynamic range supporting photon-number resolution up to tens of photons in simulations. They demonstrate, via numerical simulations for both continuous-wave and pulsed signals, that optimized parameters $(\kappa,\varphi_0)$ can approach single-photon sensitivity and even realize practical lower bounds on detectable power $P_{\min}$ on the order of $10^{-23}$ W for nanoampere-scale critical currents. While not yielding single-shot detection, the approach provides a pathway to broadband, high-sensitivity, photon-number-resolving microwave detection, potentially enhanced by machine-learning classification of multi-peak SCD fingerprints.

Abstract

It is well known that the current-biased Josephson junction (CBJJ) can serve as a Josephson threshold detector (JTD) for the sensitive detection of weak microwave signals. Based on the recent work (PRB {\bf 111}, 024501 (2025)) on the detection sensitive limit of the usual equilibrium JTD, here we numerically demonstrate that a non-equilibrium JTD can be alternatively utilized to implement the higher sensitive detection of a weak microwave signal, arriving at its energy quantum limit. In the presence of thermal noise, we numerically simulate the phase dynamics for the CBJJ in the JTD with the different sweep rates of the biased currents, and find that the SCDs of the JTD with and without the microwave signal input show different behaviors. It is demonstrated that, depending on how high the sweep rate of the biased current being applied, the JTD can be operated in either the equilibrium- or the non-equilibrium state. Specifically, under the rapidly non-adiabatic driving, the SCDs of the JTD are obviously insensitive to the thermal noises, which means that the non-equilibrium JTD can possess a higher achievable detection sensitivity, compared with its equilibrium state counterpart. Consequently, the non-equilibrium JTD can be utilized to implement the desired single microwave-photon detection. Also, some of the achievable performance indexes, such as the dynamic range, detection bandwidth, and the photon-number resolvability, etc., of the non-equilibrium JTD have been estimated, when it serves as a wideband microwave single-photon detector.

Figures (17)

• Figure 1: A schematic diagram for a phase particle dynamics described by the equation \ref{['eq:potential']}. Here, the gray ball represents the phase particle trapped in a potential well with the height of $\Delta U$, while the pink ball refers to the phase particle that has escaped from the trapped potential well and moves freely.
• Figure 2: The phase-time curves obtained by numerically solving Eq. \ref{['eq:RCSJ1']} five times. Here, the relevant parameters are set as $\varphi_0=0.1$, $\dot{\varphi_0}=0$, $\beta=10^{-4}$, $v=1\times10^{-5}$ and $2\beta k_BT/E_{J0}=10^{-7}$ (typical thermal noise intensity for a microampere-level JJ at 50 mK with a GHz plasma frequency), respectively.
• Figure 3: The initial phase dependence of the switch currents for the JTD driven by the biased currents with different sweep rates, in the absence of thermal noise. It is noted that the three orange lines are numerically identical. For clearer visualization, they have been vertically offset by 0.03, 0.02, and 0.01 (from top to bottom), respectively. The other parameters are set the same as in Fig. \ref{['FF2']}.
• Figure 4: Numerical simulations of the SCDs for a JTD driven by the biased currents with the typical sweep rates. The other parameters are set the same as in Fig. \ref{['FF2']}.
• Figure 5: The numerical simulation results of JTD's SCD for different initial phases. The parameters are set as $\kappa=5$ and the other parameters are set the same as in Fig. \ref{['FF2']}. The initial phase is set to $\varphi_0=\pm0.1$ in (a) and (c), and to $\varphi_0=\pm 0.2$ in (b) and (d). In the figure, (a) and (b) show the statistical distribution from 10,000 simulation runs, while (c) and (d) correspond to 50000 simulation runs.