  Experimental evidence of the Higgs mode in strongly interacting superfluid
Fermi gases had not been observed until recently [Behrle et al., Nat. Phys. 14,
781 (2018)]. Due to the coupling with other collective modes and quasiparticle
excitations, generating stable Higgs-mode oscillations is challenging. We study
how to excite long-lived Higgs-mode oscillations in a homogeneous superfluid
Fermi gas in the BCS-BEC crossover. We find that the Higgs mode can be excited
by time-periodically modulating the scattering length at an appropriate
amplitude and frequency. However, even for a modulation frequency below twice
the pairing-gap energy, quasiparticles are still excited through the generation
of higher harmonics due to nonlinearity in the superfluid. More importantly, we
find that persistent Higgs-mode oscillations with almost constant amplitude can
be produced by removing particles at an appropriate momentum, and the
oscillation amplitude can be controlled by the number of removed particles.
Finally, we propose two ways to experimentally realize particle removal.
