Semiclassical Floquet-Markov master equation for Monte Carlo spin integration
Abstract
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.
Copyright and License
©2025 American Physical Society.
Acknowledgement
The author would like to thank Brad Filippone, Robert Golub, David Davis, and the nEDM@SNS publications committee for their helpful input and review of the paper. The author would also like to thank Matthew Morano and David Mathews for their work in designing the GPU-based particle tracking software on which this work is based. This work was funded by the National Science Foundation (NSF) Grants No. 2110898 and 1822515. This research was supported in part through research cyberinfrastructure resources and services provided by the Partnership for an Advanced Computing Environment (PACE) at the Georgia Institute of Technology, Atlanta. This research was supported in part through research infrastructure and services provided by the Rogues Gallery testbed hosted by the Center for Research into Novel Computing Hierarchies (CRNCH) at Georgia Tech. The Rogues Gallery testbed is primarily supported by the National Science Foundation (NSF) under NSF Award No. 2016701. Any opinions, findings and conclusions, or recommendations expressed in this material are those of the author, and do not necessarily reflect those of the NSF.
Data Availability
The data that support the findings of this article are openly available:
- R. Tat, “Simulated spin tracking data used to compute frequency shifts (2025)” [Data set], CaltechDATA, https://doi.org/10.22002/nmnfa-zwq61.
- R. Tat, Spin-tracking (2024), https://github.com/rtat-caltech/Spin-tracking/tree/floquet-fft.
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Additional details
Funding
- National Science Foundation
- 2110898
- National Science Foundation
- 1822515
- National Science Foundation
- 2016701
- Georgia Institute of Technology
Dates
- Available
-
2025-07-11Published online