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In quantum many-body systems with spontaneous breaking of continuoussymmetries, Higgs modes emerge as collective amplitude oscillations of orderparameters. Recently, Higgs mode has been observed in the ultracold Fermi gas.In the present paper, we use the time-dependent Bogoliubov-de Gennes equationsto investigate Higgs amplitude oscillations of the superfluid order parameterin a Fermi gas induced by a rapid change of the ${\it s}$-wave scatteringlength. In particular, we investigate the Higgs mode with different values ofthe initial scattering length. We find that the energy of the Higgs modecoincides with the threshold energy of the pair-breaking excitation, andexponent of the power-low decay of the Higgs mode $\gamma$ continuously changesbetween $\gamma=-1/2$ and $\gamma=-3/2$ through theBardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover.Moreover, we propose the optimal ramp speed of the scattering length forobserving the clearest Higgs oscillations.

Excitation of the Higgs Mode in a Superfluid Fermi Gas in the BCS-BEC Crossover