Speeding up spin dressing calculations for the nEDM@SNS experiment with Magnus integrators

The neutron electric dipole moment experiment at the Spallation Neutron Source (nEDM@SNS) will measure the nEDM by observing the spin-dependent rate of scintillation light produced by neutrons captured on helium-3 within a superfluid helium bath. In the critical dressing mode of this experiment, an oscillating magnetic field will dress the gyromagnetic ratios of neutrons and helium-3 to the same effective value, which will increase sensitivity to the nEDM by improving the signal-to-noise ratio. However, simulating the critical dressing mode is challenging with conventional numerical integration techniques, as the dressing field is both large in magnitude and rapidly varying. This, combined with the requirement that nEDM@SNS simulations be precise at the nanohertz level, leads to prohibitively expensive Monte Carlo simulations using traditional techniques. These simulations can be accelerated using the Magnus expansion to express the propagator over each time step as a product of one or more matrix exponentials. We compare this approach to conventional numerical integration schemes such as DOP853 and find that for certain problems Magnus integration can achieve similar accuracy results with longer step sizes and fewer function evaluations. We additionally investigate techniques to numerically integrate the pseudomagnetic field effect, which couples the helium-3 and neutron spins.