Mean-field Dynamics and Fisher Information in matterwave Interferometry

TL;DR

This paper adapts Fisher information tools to evaluate the sensitivity of matterwave interferometry schemes dominated by mean-field dynamics, comparing four gyroscope proposals and emphasizing the importance of classical Fisher information.

Contribution

It introduces a method to assess metrological sensitivity in mean-field dominated matterwave interferometry using classical and quantum Fisher information.

Findings

Quantum Fisher information varies among schemes but aligns with Sagnac phase shift.

Classical Fisher information differs significantly between schemes.

The paper demonstrates the importance of classical Fisher information for sensitivity assessment.

Abstract

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.