The response of RF superconducting quantum interferometers, particularly those containing resistive sections, to magnetic flux modulation

The response of a double hole RF SQUID to modulation by magnetic flux phi e introduced into one of the holes is first considered. The output voltage v0 is a periodic function of phi e but it is shown that one would expect the period not to be equal to the flux quantum phi 0 itself but to some multiple of it. The flux in either hole of the SQUID may be calculated by imagining the weak link broken and the RF drive removed: one period of the v0 variation is produced by a change in phi e sufficient to change the flux in either hole (averaged over one RF cycle), due both to current in the coil and to current induced on the inside wall of the SQUID, by phi 0. This principle is applied to a double hole SQUID modified by the replacement of part of one wall by a block of normal metal (an R SQUID). Explicit expressions for the response to modulation, which is frequency dependent, are derived in the limit of low frequency, and more generally, at any frequency, for an R SQUID in which both the holes and the modulation coil are long in comparison with their diameter. The size of the superconducting screen which must surround the R SQUID, if only to avoid interference from other magnetic fields in the laboratory, is shown to play an important part in determining the response at low frequencies. The spectrum of noise currents is also calculated.