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

TL;DR

This paper presents a high-speed, sensitive in-situ sensor using superconducting NbN resonators to measure helium's permittivity, with potential applications in thermometry and superfluid experiments.

Contribution

The authors demonstrate a novel microwave resonator-based sensor capable of rapid, localized permittivity measurements of helium with high sensitivity.

Findings

Achieved a measurement bandwidth of 300 kHz.

Demonstrated a minimum detectable permittivity change of ~6×10^{-11} ε₀/Hz^{1/2}.

Sensor volume of approximately 10^{-3} mm³.

Abstract

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 a $\sim10^{-3}$ mm$^3$ sensing volume is measured with a bandwidth of 300 kHz in the temperature range 1.8 to 8.8 K. The minimum detectable change of the permittivity of helium is calculated to be $\sim6\times$$10^{-11}$ $\epsilon_0$/Hz$^{1/2}$ with a sensitivity of order $10^{-13}$ $\epsilon_0$/Hz$^{1/2}$ easily achievable. Potential applications include operation as a fast, localized helium thermometer and as a transducer in superfluid hydrodynamic experiments.