  There has been considerable recent interest in the mean-field dynamics of
various atom-interferometry schemes designed for precision sensing. In the
field of quantum metrology, the standard tools for evaluating metrological
sensitivity are the classical- and quantum-Fisher information. In this letter,
we show how these tools can be adapted to evaluate the sensitivity when the
behaviour is dominated by mean-field dynamics. As an example, we compare the
behaviour of four recent theoretical proposals for gyroscopes based on
matterwaves interference in toroidally trapped geometries. We show that while
the quantum Fisher information increases at different rates for the various
schemes considered, in all cases it is consistent with the well-known Sagnac
phase shift after the matterwaves have traversed a closed path. However, we
argue that the relevant metric for quantifying interferometric sensitivity is
the classical Fisher information, which can vary considerably between the
schemes.
