Theory of a Josephson junction parallel array detector sensitive to very weak signals

An array of coupled short junctions (Josephson junction parallel array) is shown to be able to response to ultra-weak signals when it is worked at the onset of nonlinear supratransmission in the hysteresis loop of bistability. The theory is based on the fundamental solutions of the continuous limit (the sine-Gordon equation on the finite interval submitted to Neuman boundary conditions) that result from synchronization and adaptation to the external driving. This provides the solution to a problem that dates back to 1986 [O. H. Olsen and M. R. Samulsen, Phys. Rev. B34, 3510 (1986)], namely the complete analytical understanding of the bistability in a long Josephson junction or in an array of short junctions. The property allows to conceive ultrasensitive detectors or else, by convenient modulation of the seed, efficient digital amplifiers. Numerical simulations reveal that such a bistable behavior occurs also in two-dimensional lattices where no theory is available yet.