Cancelling the geometric phase in the nEDM@SNS experiment

A non-zero neutron electric dipole moment (EDM) produces a tiny precession frequency shift proportional to the strength and direction of the electric field. The nEDM@SNS experiment uses Helium-3 as a comagnetometer. Three frequency shifts (“geometric phase”, |E|² and |B|²) all of which depend on the same trajectory correlation functions, are significant at the goal sensitivity (2-3x10^-28 e*cm). These effect both neutrons and comagnetometer in any neutron EDM experiment. Helium-3 has a unique advantage as a comagnetometer in that its trajectory correlation functions, and therefore its frequency shifts, are strongly temperature dependent. This allows the experiment temperature (T) and magnetic field strength (B) to be tuned to cancel the geometric phase. We present a simulation demonstrating how a measurement of the |E|² frequency shift can be used to experimentally determine values for B and T where the geometric phase is effectively cancelled and place a limit on this key systematic error.