Addressing the impact of magnetic field fluctuations on the critical dressing mode of nEDM@SNS

The neutron electric dipole moment experiment at the Spallation Neutron Source (nEDM@SNS) proposes to measure the nEDM using the spin-dependent capture cross section of neutrons on helium-3. The critical dressing mode of this experiment uses an oscillating magnetic field to dress the gyromagnetic ratios of neutrons and helium-3 to the same effective value. While this technique grants increased sensitivity to the nEDM by improving the signal-to-noise ratio, randomly fluctuating magnetic fields and magnetic field gradients can cause the spins of the neutrons and helium-3 atoms to drift apart over time, potentially erasing these gains. Here we use second-order time-dependent perturbation theory to estimate the relaxation and frequency shifts due to magnetic field instabilities in terms of the noise power spectrum and compare these calculations to numerical solutions obtained by integrating the Bloch equations. We then investigate several mitigation strategies for this type of noise. In particular, we demonstrate that modulating the dressing field can reduce the impact of magnetic field fluctuations.