Characterization of the Escape Times of Josephson Junctions for Signal Detection

We propose to characterize underdamped Josephson Junctions (JJ) as threshold detectors with signal analysis theory. In this perspective signal detection is based on the analysis of the noise induced escapes of a Josephson junction from the zero voltage state, for threshold detection is based on the possibility to reveal a signal via the transition from a stable state to another. Thus, the essential ingredients are: i) a two-state detector,ii) a signal conveyed to the detector as a perturbation capable to induce a switch from a state to the other, iii) the possibility to detect the transition from a state to other when the detector passes a threshold, hence the name. In this sense the noise-induced activation of a finite voltage ina JJ can be interpreted as a detector that converts the noise-signal mixtures in a series of escape (orresident) times. The analysis of the electrical response, the voltage associated to the escape in an underdamped JJ can be used to decide about the presence of a signal embedded in the noise. JJ as threshold detectors have been employed to characterize (up to higher order moments) weak fluctuations close to the quantum limit [1-3]. It is precisely the possibility to employ JJ in a regime where noise is close to the quantum limit [4] that makes them appealing for the detection of weak signals corrupted by noise [5], for it is possible in principle to exploit a device, the JJ, that adds aslittle noise as possible. A straightforward evaluation of the detector performances has been performed through the average escape times has shown some interesting regions for signal detection[5]. A more sophisticated analysis based on maximum likelihood estimators [6] significantly improves the performances of the detector and reveals that stochastic resonance is the result of a suboptimal detection strategy [7].