By numerically solving the density matrix equations, we show that the laser frequency ramping method by means of position-dependent Zeeman splitting can efficiently polarize nuclear spin of atoms/ions in an accelerator beamline. This minimizes a quantum phenomenon, coherent population trapping, which limits the optical pumping efficiency in the polarized beamline for radioactive nuclear spin polarization. We consider the atomic system interacting with two circularly polarized laser beams in the presence of time-dependent magnetic field. From numerical results, we find that optimum frequency ramping allows efficient optical pumping for a short interaction time, e.g., 2 μs.
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