We propose a scheme for the detection of microwave-induced photons through a current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero-voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the signal-to-noise ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.
We propose a scheme for the detection of microwave-induced photons through a current-biased Josephson junction, from the point of view of the statistical decision theory. Our analysis is based on the numerical study of the zero-voltage lifetime distribution in response to a periodic train of pulses, that mimics the absorption of photons. The statistical properties of the detection are retrieved comparing the thermally induced transitions with the distribution of the switchings to the finite voltage state due to the joint action of thermal noise and of the incident pulses. The capability to discriminate the photon arrival can be quantified through the Kumar-Caroll index, which is a good indicator of the signal-to-noise ratio. The index can be exploited to identify the system parameters best suited for the detection of weak microwave photons.
This work deals with the numerical analysis of the zero-voltage state lifetimes distribution of an underdamped Josephson junction used for the detection of single microwave photons in the presence of thermal noise. The analysis considers the switching probabilities of a JJ subjected to a train of current pulses, which simulates a weak photon field. To characterize the detection, we take advantage of a statistic tool, the Kumar-Carroll (KC) index, which is a good proxy of the signal-to-noise-ratio. It can be, therefore, exploited to identify the proper device fabrication parameters and the optimal operation point of the junction.
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.
The performances of a Josephson junction employed to reveal a train of pulses (a rough model for single photon detection) are analyzed with a theoretical estimate that exploits an index employed in statistical decision theory, the Kumar–Carroll index. The approximate analysis compares the numerically simulated performances of the device through the receiver operating characteristics, that offer an overview of the rate of false detection, as well as the probability to miss a signal (in this case, a pulse train). It is thus demonstrated the usefulness and the limits of the succinct Kumar–Carroll parameter. On the first side, it is proven that an increase of the parameter corresponds to an improvement of the detection. However, on the side of the limitations, the expected performances are not quite accurate, for the actual performances are systematically worse than the theoretical estimates. The results may be relevant to characterize Josephson junctions as detectors of weak signals, as those stemming from axions.
In this Letter, we experimentally demonstrated that Josephson threshold detectors (JTDs) could be developed to implement the sensitive detection of broadband microwave photons. Beginning with the numerical simulations of the damped dynamics for the macroscopic phase particle generated by a Josephson junction (JJ), we showed that the time-domain threshold voltage state switched measurements of the JJ driven by a low-frequency triangular wave current, which could be utilized to implement the sensitive microwave photons detection. The detectable signal power can be determined by using the Kumar–Caroll index to quantify the distinguishability between two statistical distributions on the measured threshold switched durations of the JJ with and without the signal input. Experimentally, we fabricated the Al/AlOx/Al JJ and measured its threshold responses, at 50 mK temperature, to the input microwave photons at the frequency of ∼5 GHz. The experimental results indicated that the weak microwave signals, which are phenomenologically threatened by the additional thermal noise that modifies the damped phase dynamics of the JJ, can be detected by the fabricated JTD. The detectable power of the microwave signals demonstrated here was calibrated as about −92 dBm (corresponding to the photons rate of ∼2×108 photons/ms). Based on the numerical simulations for optimizing the relevant performance indicators of the detectors, we further argue that the JTDs could be utilized to achieve the sensitive detection of broadband microwave photons at the single-photon level.
Single-photon detection is an energy quantum limit detection (EQLD) of extremely weak electromagnetic waves. Given that the sensitivity of the conventional electromagnetic induction microwave receiver working at room temperature is very limited, as a result of the significantly strong thermal noise, here we analyze the possibility of approaching the EQLD of the weak microwave signal by using a current-biased Josephson junction (CBJJ) detector. By numerically simulating the dynamics for the phase particle of the CBJJ, we propose an approach to describe the discriminability between the probabilistically escaped events of the phase particle with and without the microwave current driving, by measuring the minimum dKC index. Our predictions indicate that the experimentally demonstrated CBJJ detector possesses the ability to resolve about a dozen photons. Furthermore, with the minimum detectable signal strength and the saturation threshold, we discuss how to determine the dynamic range of the proposed CBJJ detector. The feasibility of using the proposed CBJJ detector to achieve the EQLD in a microwave band is also discussed.
Thermal noise is one of the physical obstacles that constrain the achievable detection sensitivities of various detectors. Indeed, as we showed in a recent paper (PRB 111, 024501 (2025)), the usual Josephson threshold detector (JTD) operated in an equilibrium state can be utilized to implement a weak microwave signal, just approaching (but not arriving at) its energy quantum limit, even though its physical parameters have been optimized. In this letter, we further demonstrate numerically that the phase dynamics of a current-biased Josephson junction (CBJJ) can be insensitive to the always-on thermal noise if the sweep rate of the biased current is significantly high. As a consequence, the JTD can be operated alternatively in a non-equilibrium state. Based on the statistical binary detection criterion, we demonstrate how such a non-equilibrium JTD (NEJTD) can be utilized to implement the weak microwave signal, arriving at its energy quantum limit level. The dynamic range and photon-number resolvability of the proposed NEJTD are also discussed when it serves as a broadband single microwave-photon detector.