Mean-field Dynamics and Fisher Information in matterwave Interferometry

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.