Theory of signal and noise performance of superconducting quantum interferometers with two quantization loops

The superconducting quantum interferometer with two quantization loops, the so-called double SQUID, or D-SQUID, is a modification of the well-known rf SQUID. The modification consists of a replacement of the one junction of the rf SQUID by a superconducting loop with two Josephson junctions. This device can be used to transform the weak magnetic flux applied to the loop with junctions to a voltage across the tank circuit inductively coupled to the other loop. As has previously been shown in experiments [G. S. Krivoy and H. Koch, J. Appl. Phys. 74, 2925 (1993)], D-SQUIDs have an extremely large output signal swing up to 1 mV and a transfer function of several mV/(h/2e). In this paper, a D-SQUID theory using a numerical and an analytical approach is developed. The theoretical results are compared with the above-mentioned experiments.