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

In quantum many-body systems with spontaneous breaking of continuous symmetries, Higgs modes emerge as collective amplitude oscillations of order parameters. Recently, Higgs mode has been observed in the ultracold Fermi gas. In the present paper, we use the time-dependent Bogoliubov-de Gennes equations to investigate Higgs amplitude oscillations of the superfluid order parameter in a Fermi gas induced by a rapid change of the ${\it s}$-wave scattering length. In particular, we investigate the Higgs mode with different values of the initial scattering length. We find that the energy of the Higgs mode coincides with the threshold energy of the pair-breaking excitation, and exponent of the power-low decay of the Higgs mode $\gamma$ continuously changes between $\gamma=-1/2$ and $\gamma=-3/2$ through the Bardeen-Cooper-Schrieffer-Bose-Einstein condensation (BCS-BEC) crossover. Moreover, we propose the optimal ramp speed of the scattering length for observing the clearest Higgs oscillations.