Static characteristics of Josephson interferometers

TLDR: In this paper, the authors investigated the range in operating currents for which a Josephson interferometer, sometimes referred to as Superconducting QUantum Interference Device (SQUID), may remain in the zero-voltage Josephson condition.

Abstract: This investigation deals with the range in operating currents for which a Josephson interferometer, sometimes also referred to as Superconducting QUantum Interference Device (SQUID), may remain in the zero-voltage Josephson condition. An interferometer consists of one or more inductive loops each of which contains two Josephson junctions or other weak links. Two types of current are considered. Gate currentIgpasses the junctions in parallel. Control currentIcgenerates magnetic flux via inductive coupling in the loops. Zero-voltage operation is possible within certain areas of theIg,Icplane. These areas are manifestations of flux-quantum states and their boundary lines are referred to as static characteristics. In view of the nonlinearity of the constituting equations, not all their formal solutions are physically realizable. A stability analysis yields criteria which permit the identification of realizable operating conditions. The static characteristics comprise operating conditions where the limit of stability is reached. To obtain the static characteristics, linearized equations may be utilized if theLIo product, a measure for the size of an interferometer, is large compared to the flux quantumΦ0, whereL is the inductance per loop, andIo 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 theIg,Icplane. 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.