Abstract
In this paper we describe how quantum coherence of superfluid helium provides a mechanism by which very small rotations can substantially modify the flow in a toroidal container. The specific modifications to that flow are discussed. For $^{4}\mathrm{He}$, we explain how the rotationally induced flow can be detected by monitoring the apparent phase-slip critical current. The rotational resolution is limited by stochastic processes related to the nucleation of phase slips. This type of superfluid-helium gyroscope (SHEG) is an analog of the rf superconducting quantum interference device (SQUID). We also show how the large coherence length of $^{3}\mathrm{He}$ can be utilized to lead to a rotationally induced interference pattern. Changes in this pattern can permit the detection of very small rotational motion. This type of SHEG is analogous to the dc SQUID. In appendixes, electrical circuits equivalent to the SHEG are described, as are certain constraints on rotational sensitivity imposed by external measuring devices.
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