Angular momentum sensitivity of a MEMS gyroscope for condensed matter systems

The angular momentum carries crucial information on the physical nature of quantum matter. We propose and analyze MEMS gyroscope techniques suitable for measuring the angular momentum of mesoscopic quantum matter specimens at low temperatures. We bear in mind that it is not always possible to implement mode-matched gyroscopes, which we will refer to as degenerate gyroscopes, for the maximal signal sensitivity for these applications due to the constraints given by the cryogenic environment and the types of samples available for experiments. Because the analysis of non-degenerate gyroscopes in the literature is somewhat limited, we analyze and compare the ultimate angular momentum sensitivity of both degenerate and non-degenerate gyroscopes under amplitude and frequency modulation operation. Calculation based on our prototype device shows that the frequency modulation extends the operational range and improves sensitivity at low temperatures.