Static characteristics of Josephson interferometers

This investigation deals with the range in operating currents for which a Josephson interferometer (SQUID) may remain in the zero-voltage Josephson condition. Two types of current are considered. Gate current Isub(g) passes the junctions in parallel. Control current Isub(c) generates magnetic flux via inductive coupling in the loops. Zero-voltage operation is possible within certain areas of the Isub(g), Isub(c) plane. These areas are manifestations of flux-quantum states and their boundary lines are referred to as static characteristics. To obtain the static characteristics, linearized equations may be utilized if the LIsub(o) product, a measure for the size of an interferometer, is large compared to the flux quantum PHIsub(o), where L is the inductance per loop, and Isub(o) the maximum Josephson current per junction. As a general method of solving system of transcendental equations, continuation is discussed. The utilization of continuation for obtaining interferometer characteristics is explained. It is shown that some changes in the gate-current feed arrangement are equivalent to shearing the characteristics in the Isub(g), Isub(c) plane. Analytical results are given on extrema, inflexion points, and singularities in the shape of cusps which conceptually relate to the existence and connectivity of flux-quantum states. Experimental static characteristics are presented on two- and four junction interferometers. They are in agreement with characteristics computed on the basis of simple lumped circuit models. Relevant circuit parameters are obtained from the experimental characteristics. (orig.)