We theoretically show that the use of chirped laser pulses with an appropriate bandwidth is more favorable in achieving a higher degree of nuclear-spin polarization of atoms/ions. The physical origin of this is identified as multiple pump-dump processes during the single chirped laser pulse. As a specific example, we consider the case of muonium (, lifetime 2.2 μs). By numerically solving a set of density matrix equations, we find that a chirped 1 ns pulse with a narrow bandwidth instead of a broad bandwidth efficiently induces a resonant pump and following dump processes within a single laser pulse, thereby transferring the angular momentum of the circularly polarized pump pulse to the atoms, which leads to the higher degree of nuclear-spin polarization. For muoniums at rest, a single chirped 1 ns pulse with a 4 GHz bandwidth and peak intensity of leads to 43% of nuclear-spin polarization, which is to be compared with 33% of nuclear-spin polarization by the transform-limited 1 ps pulse or chirped 1 ns pulse with a 400 GHz bandwidth for both. We also find that an introduction of the chirp does not help in the presence of significant Doppler broadening. This means that the use of chirped laser pulses is beneficial for the atomic beam at the cross-beam geometry, where the influence of Doppler broadening is negligible, and similarly, if a slow muonium beam is realized in the future to nearly eliminate Doppler broadening, then chirped laser pulses would be useful to attain a higher degree of nuclear-spin polarization.
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