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

Mean-field Dynamics and Fisher Information in matterwave Interferometry