In permalloy, the hyperfine field distribution ranges from 26 to 31 T with a peak at about 28 T. The accelerated decay of the nuclear exciton cannot be explained by the width of the hyperfine field distribution, which contributes only marginally to the decay rate. The quantum phase shift will be different for various hyperfine field values due to different reductions ΔBhf for each hyperfine field value. Thus, the transition dipole oscillation frequencies will also differ. However, this does not influence the temporal shift measured in the quantum beat. From the model of the hyperfine field reduction by the magnon (13), we conclude that the influence of the magnon is a relative reduction in the hyperfine field that scales with the precession angle of the magnetization, which is uniform over the sample. The ratio ΔBhf/Bhf in Eq. S8 leads to a temporal shift that is the same for every hyperfine field. Thus, the hyperfine field distribution does not influence the time delay. The different beat frequencies encountered for the various hyperfine field values normalize the different phase shifts to the same temporal shift in the quantum beat. This is the reason why no blurring effects are observed due to the hyperfine field distribution in the phase-shifted quantum beats.

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