In situ measurement of the permittivity of helium using microwave NbN resonators

By measuring the electrical transport properties of superconducting NbN quarter-wave resonators in direct contact with a helium bath, we have demonstrated a high-speed and spatially sensitive sensor for the permittivity of helium. In our implementation an ∼10−3mm3 sensing volume is measured with a bandwidth of 300kHz in the temperature range of 1.8–8.8K. The minimum detectable change in the permittivity of helium is calculated to be ∼6×10−11ϵ0∕Hz1∕2 with a sensitivity of the order of 10−13ϵ0∕Hz1∕2 easily achievable. Potential applications include operation as a fast, localized helium thermometer and as a transducer in superfluid hydrodynamic experiments.