Nonperiodic flux to voltage conversion of series arrays of dc superconducting quantum interference devices

We present a theoretical study on the voltage response function [V] of series arrays of dc; superconducting quantum interference devices (SQUIDs) for which the elementary de SQUID loops vary in size and, possibly, in orientation. If the distribution of the array loop sizes is chosen according to an arithmetic relation, [V] is not a Phi (0)-periodic function of the strength of external magnetic field B. For arithmetic arrays the periodicity of [V] is controlled by the geometry of the array alone and does not depend on spreads in the array junction parameters. If small fluctuations are added to the loop size distribution, [V] becomes a unique function around a global minimum at B=0 without possessing significant additional minima for finite B. This filter property does not apply for conventional SQUIDs and series arrays of identical or nearly identical SQUID loops. Applications of arithmetic series arrays include the design of current amplifiers and novel quantum interference filters, which possess large Voltage swing and low noise level. In particular, quantum interference filters should provide a rather simple and extremely sensitive measurement of the absolute strength of magnetic fields. (C) 2001 American Institute of Physics.