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

Due to their high quality-factors and ease of fabrication, superconducting microwave resonators are increasingly being recognized as ideal sensors in ultra-sensitive, low-temperature measurements. In this talk, we will discuss the design and characterization of superconducting NbN quarter-wave resonators implemented as a high-speed and spatially-sensitive detector for the permittivity of a surrounding helium bath. Measurements of a device with a $\sim$10$^{-3}$ mm$^3$ spatial resolution, a $\sim$6$\times$$10^{-11}$ $\epsilon_0$/Hz$^{1/2}$ sensitivity to changes in the permittivity of helium, and a bandwidth of 300 kHz will be presented in the temperature range from 1.8 to 8.8 K. Potential applications, including operation as a fast, localized helium thermometer and as a transducer in superfluid hydrodynamic experiments, will be discussed.