Synchronization in Serial DC SQUID Arrays

The study of superconducting devices such as SQUIDs (Superconducting Quantum Interference Devices) leads to improved magnetic field detectors in numerous technologies such as MRI machines, scanning SQUID microscopes, gravity wave detectors, etc. One interesting question that arises is if multiple SQUIDs are connected in a serial array will synchronized voltage outputs across them result in a more sensitive/accurate device? The first step is understanding the synchronization behavior of SQUIDs when in a serial array. We studied the voltages across the SQUIDs numerically for the cases of one and two SQUID systems, and we observed synchronization behavior within the two SQUID serial arrays, in which both SQUIDS oscillate with the same average voltage. We were able to obtain both numerical and approximate analytical solutions for the boundary of the synchronization region in a two-SQUID serial array as a function of applied bias current and magnetic field. We also have preliminary code for studying the voltages in a serial array with arbitrary number N of SQUIDs.