  We theoretically investigate the Higgs oscillation in a one-dimensional
Raman-type spin-orbit-coupled Fermi superfluid with the time-dependent
Bogoliubov-de Gennes equations. By linearly ramping or abruptly changing the
effective Zeeman field in both the Bardeen-Cooper-Schrieffer state and the
topological superfluid state, we find the amplitude of the order parameter
exhibits an oscillating behaviour over time with two different frequencies
(i.e., two Higgs oscillations) in contrast to the single one in a conventional
Fermi superfluid. The observed period of oscillations has a great agreement
with the one calculated using the previous prediction [Volkov and Kogan, J.
Exp. Theor. Phys. 38, 1018 (1974)], where the oscillating periods are now
determined by the minimums of two quasi-particle spectrum in this system. We
further verify the existence of two Higgs oscillations using a periodic ramp
strategy with theoretically calculated driving frequency. Our predictions would
be useful for further theoretical and experimental studies of these Higgs
oscillations in spin-orbit-coupled systems.
