Thermal magnetic noise in rf SQUIDS coupled to ferromagnetic cores

We present a simple model for the thermal magnetic noise in a rf SQUID coupled to a ferromagnetic core via a superconducting dc flux transformer. We show that, under conditions that are almost always fulfilled in practice, the coupling to the core can be described in terms of a SQUID frequency-dependent complex inductance Ls (ω). This inductance reduces to an ordinary, frequency-independent real value above a roll-off frequency ωc . To this inductance, a Nyquist flux noise generator is associated, with spectral density S′2φi(ω) =−4kBT Im[Ls(ω)]/ ω, where kB is the Boltzmann constant, T the temperature, and Im[Ls (ω)] the imaginary part of Ls (ω). If ωc ≪ωrf , with ωrf the frequency of the rf pump, then the response of the SQUID to low-frequency signals is not modified by the coupling to the core, while the above Nyquist noise acts as an additive input noise. We experimentally demonstrate the model for a SQUID coupled to a toroidal core.