The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, which is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer-Rao theoretical bound. Applications might be found, for example, in some astronomical detection problems (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).The measurement of the escape time of a Josephson junction might be used to detect the presence of a sinusoidal signal embedded in noise when use of standard signal processing tools can be prohibitive due to the extreme weakness of the source or to the huge amount of data. In this paper we show that the prescriptions for the experimental setup and some physical behaviors depend on the detection strategy. More specifically, by exploitation of the sample mean of escape times to perform detection, two resonant regions are identified. At low frequencies there is a stochastic resonance or activation phenomenon, while near the plasma frequency a geometric resonance appears. Furthermore, detection performance in the geometric resonance region is maximized at the prescribed value of the bias current. The naive sample mean detector is outperformed, in terms of error probability, by the optimal likelihood ratio test. The latter exhibits only geometric resonance, showing monotonically increasing performance as the bias current approaches the junction critical current. In this regime the escape times are vanishingly small and therefore performance is essentially limited by measurement electronics. The behavior of the likelihood ratio and sample mean detector for different values of incoming signal to noise ratio is discussed, and a relationship with the error probability is found. Detectors based on the likelihood ratio test could be employed also to estimate unknown parameters in the applied input signal. As a prototypical example we study the phase estimation problem of a sinusoidal current, which is accomplished by using the filter bank approach. Finally we show that for a physically feasible detector the performances are found to be very close to the Cramer-Rao theoretical bound. Applications might be found, for example, in some astronomical detection problems (where the all-sky gravitational and/or radio wave search for pulsars requires the analysis of nearly sinusoidal long-lived waveforms at very low signal-to-noise ratio) or to analyze weak signals in the subterahertz range (where the traditional electronics counterpart is difficult to implement).

arXiv:1112.0435Physical Review EJan 11, 201253 citations

Measuring weak microwave signals via current-biased Josephson junctions: Approaching the quantum limit of energy detection

Y. Q. Chai, S. N. Wang, P. H. Ouyang +1 more

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 ${d}_{\mathrm{KC}}$ 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.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 ${d}_{\mathrm{KC}}$ 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.

arXiv:2410.23947Physical review. B./Physical review. BJan 2, 20256 citations

Traversal Time in Josephson Junctions

Pasquale Fabeni, Daniela Mugnai, Gian Paolo Pazzi +5 more

Journal of SuperconductivityDec 1, 19999 citations

{d}_{\mathrm{KC}}

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.