Part 1: Three-wave-mixing scanning RF-SQUID magnetometer: low-noise and wide-bandwidth imaging of thin NbN films

Here we introduce radio frequency (RF) scanning SQUIDs that function as resonant, low-dissipation magnetic scanning sensors with tunable frequency ranges of 2 to 12 GHz. The RF SQUID is operated entirely within the superconducting state of the SQUID and we use the intrinsic nonlinearity of the Josephson junction to achieve three-wave mixing processes. We analyze the RF SQUID Hamiltonian to locate the Kerr-free point where unwanted frequency shifts of the mode are reduced, and here achieve parametric gain up to 20 dB. At these sweet spots we obtain enhanced signal-to-noise ratio with measured flux noise of ~300 nΦ₀/ √Hz at 10 mK with an average pickup loop size of ~1 µm.  In part 2, we discuss how to apply these techniques to measure low superfluid density samples, including niobium nitride films tuned near their superconductor-insulator transition. We further discuss applying this sensor to measure vortex dynamics and noise in the vicinity of the Berenzinskii-Kosterlitz-Thouless transition.