Optimizing spin dressing sensitivity for the nEDMSF experiment

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 (ϕ _3n ) is subjected to a square modulation by an amount ϕ _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 π/2 pulse that initiates d_n -driven ϕ _3n growth and the start of ϕ _3n modulation. We find negligible further improvement by allowing ϕ _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 ϕ _3n modulation sequence. A complete simulation confirms a 300 live-day sensitivity of σ = 1.45×10^-28 e ·cm. At this level of sensitivity, σ _{ϕ 3n 0} = 1 mrad precision on the initial n/³He angle difference is not negligible.