A centimeter-sized gas pressure sensor for high-vacuum measurements at cryogenic temperatures

Gas pressure sensors based on nanomechanical membranes have recently demonstrated an ultra-wide ten-decade measurement range, a gas-type-independent response, and a self-calibrating operation with uncertainties of approximately $1\,\%$. The readout relied on tabletop free-space laser interferometers. Here we present a centimeter-sized, portable implementation in which a square Si$_3$N$_4$ membrane is read out via a fiber-based laser interferometer. We perform pressure measurements between $5\times10^{-5}$ and $10^{-1}$~mbar in a confined $0.7$~L volume cooled to $78$~K. Because no suitable commercial pressure sensor exists for direct cryogenic comparison, we benchmark our device against room-temperature commercial gauges connected to the cold volume through a pipe of limited conductance. The measured relationship between the two sensors is compared with models accounting for temperature- and pumping-induced pressure gradients within the measurement chamber. These models agree with the measurements to within $