Optimizing Spin Dressing Sensitivity for the nEDMSF Experiment

Abstract

nEDMSF aims to measure the neutron electric dipole moment (\(d_n\)) with unprecedented precision. In this paper we explore the experiment's sensitivity when operating with an implementation of the critical dressing method in which the angle between the neutron and Helium-3 spins (\(\phi_{3n}\)) is subjected to a square modulation by an amount \(\phi_d\) (the "dressing angle"). Several parameters can be tuned to optimize sensitivity. We find roughly 10% improvement over a previous estimate, resulting primarily from the addition of a waiting period between the \(\pi/2\) pulse that initiates \(d_n\)-driven \(\phi_{3n}\) growth and the start of \(\phi_{3n}\) modulation. We find negligible further improvement by allowing \(\phi_d\) to vary continuously over the course of a run, and no degradation resulting from the addition of an in situ background measurement into each \(\phi_{3n}\) modulation sequence. A complete simulation confirms a 300 live-day sensitivity of \(\sigma = 1.45\times10^{-28}\,e \cdot \rm{cm}\). At this level of sensitivity, \(\sigma_{\phi_{3n0}} = 1\,{\rm mrad}\) precision on the initial \(n/^3{\rm He}\) angle difference is not negligible.