In conducting an experiment to measure a neutron electric dipole moment (nEDM), it is often necessary to determine the behavior of an ensemble of spins under time-dependent and randomly fluctuating magnetic fields. This is particularly relevant for experiments which utilize dressing magnetic fields to modify the effective Larmor frequency of the neutrons under study. In this work, we investigate a new technique to calculate the frequency shifts arising from magnetic field inhomogeneities and motional magnetic fields, particularly in the case where the spins in question are subjected to a time-periodic magnetic field. The method is based on Floquet theory, a general framework for analyzing periodic linear differential equations, and Redfield theory, which governs the time evolution of the density matrix in the presence of weak couplings to an environment. We benchmark this method against the analytical results derived both with and without dressing field, as well as against the results of a conventional Runge-Kutta integrator, and find agreement in all cases. We further study the performance of the method, and find order-of-magnitude improvements in runtime over the conventional integrator.

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• Neutron physics
• Tests of fundamental symmetries
• Direct numerical simulations