Joint estimation of phase and uncorrelated dephasing in a differential quantum interferometer

Precise measurements in optical and atomic systems often rely on differential interferometry. This method allows to handle large and correlated phase noise contributions -- such as environmental vibrations, thermal fluctuations, or instrumental drifts -- preventing them from blurring the signal. To date, this approach has primarily focused on extracting the differential phase shift. However, valuable information about the system is also contained in the width of uncorrelated phase fluctuations. In this work, we present a maximum likelihood approach for the simultaneous estimation of both the differential phase shift and the width of uncorrelated phase noise. Unlike conventional methods, our technique explicitly accounts for the data spreading and outperforms traditional ellipse fitting in terms of both precision and accuracy. We demonstrate our methodology using a quantum mechanical model of coupled interferometers, where uncorrelated dephasing arises from projection noise and interparticle interactions. Our results establish a novel approach to data analysis in differential interferometry that is readily applicable to current experiments.