Detection of noise-corrupted sinusoidal signals with Josephson junctions

Abstract

We investigate the possibility of exploiting the speed and low noise features of Josephson junctions for detecting sinusoidal signals masked by Gaussian noise. We show that the escape time from the static locked state of a Josephson junction is very sensitive to a small periodic signal embedded in the noise, and therefore the analysis of the escape times can be employed to reveal the presence of the sinusoidal component. We propose and characterize two detection strategies: in the first the initial phase is supposedly unknown (incoherent strategy), while in the second the signal phase remains unknown but is fixed (coherent strategy). Our proposals are both suboptimal, with the linear filter being the optimal detection strategy, but they present some remarkable features, such as resonant activation, that make detection through Josephson junctions appealing in some special cases.

Escape Time of Josephson Junctions for Signal Detection

“…5), where another resonance appears at a frequency that can be also much smaller than the geometric resonance. The position of this resonance dip depends upon the phase and signal temperature [23], so it can be considered a stochastic resonance [8,26,27,44] or resonant activation [19,21,57]. In Ref.…”

“…The SM strategy, analyzed in detail in [23], has the great advantage of simplicity, but it is obviously suboptimal. Indeed in the coherent and the incoherent (with instantaneous signal reset) acquisition strategies escape time PDFs exhibit oscillations (see Fig.…”

“…In particular, the initial phase is a crucial parameter because the signal to noise mixture can be applied to the JJ in different ways [23,56] to acquire the escape time sequence s ¼ fs i g…”

“…First, a real junction is also characterized by a resistance and a capacitance, second the JJ is dc and ac biased, and third the environment at finite temperature disturbs the junction with noise. The resulting Langevin model equation of a JJ biased with a sinusoidal signal corrupted by additive noise nðtÞ and subject to thermal fluctuations nðtÞ reads [23]:…”

“…A Josephson Junction (JJ) can be used as a threshold detector [13,46], i.e. as a device capable to discriminate a signal with a sharp transition from a state to another [1,23]. Threshold detection is a suboptimal tool in signal processing, because in typical applications the optimal choice is linear matched filtering.…”