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The effect of Johnson noise generated by normal metal in an otherwise superconducting SQUID gradiometer circuit is investigated theoretically. The generalized Nyquist theorem is applied to develop a simple method for computing the noise at frequencies less than the inverse of the normal metal's magnetic flux diffusion time. For gradiometers prepared using printed-circuit-board technology (superconducting lines deposited on copper substrate lines) the Johnson noise is predicted to generate white current noise at low frequencies. Since the power spectrum is proportional to the cube of the normal-metal thickness, the current noise can be of nearly the same order of magnitude as that which would be generated by the bare normal metal when the normal metal is sufficiently thick. The method also can be used to compute the Johnson noise generated by normal metal at solder joints, as well as by any normal metal in the vicinity of the SQUID input circuit, whether in electrical contact or not. The theoretical results indicate that, to limit the amount of Johnson noise generated by a SQUID gradiometer, one should avoid placing excessive quantities of normal metal close by.
John R. Clem (Sun,) studied this question.