High-fidelity simulation and reduced-order modeling of optical pumping in quantum devices
Spatially resolved modeling of optically pumped alkali-metal vapors requires the solution of a high-dimensional nonlinear diffusive quantum master equation (DQME) coupled to state-dependent light propagation. We develop a structure-preserving computational framework for this coupled three-dimensional system in the high-pressure limit. The high-fidelity solver combines second-order finite differences, explicit pseudo-time marching, and an exponential-integrator discretization of the light-propagation equation. The scheme preserves the density-matrix trace, while a derived global pseudo-time-step restriction guarantees nonnegative, bound-preserving population updates and frozen-coefficient $1$-norm stability. In the absence of a closed-form solution for the general coupled problem, the solver is verified against complementary analytical reductions, pumping-rate asymptotics, and a light-propagation invariant, all of which are accurately recovered. Tensorized GPU implementation reduces the per-iteration cost by more than two orders of magnitude relative to a single-core CPU. For repeated parameter queries, we further construct an intrusive POD--Galerkin reduced-order model. The quadratic spin-exchange term is treated by an exact nonlinear quadratic expansion, whereas the nonpolynomial and nonlocal optical-pumping term is hyper-reduced using the discrete empirical interpolation method. At out-of-sample parameter points, the reduced model closely reproduces the full-order population and polarization fields while achieving speedup of more than \(7\times10^3\) relative to the single-core CPU full-order solver. The resulting hierarchy connects verified high-fidelity simulation with efficient reduced-order prediction for spatially resolved alkali-metal spin dynamics.