Higgs mode in fermionic condensates with the BCS pairing
interaction describes the dynamics of the pairing amplitude. I show that the
existence and properties of this mode are sensitive to the energy dispersion of the interaction. Specifically, when the pairing is suppressed at the
Fermi level, the Higgs mode may become unphysical (virtual) state or a resonance with finite lifetime, depending on the details of interaction.
Conversely, the Higgs mode is discrete for the pairing interaction enhanced at the Fermi level. The dynamics may be probed by pairing perturbation in
the regimes of linear and non-linear responses. For the latter, coupled dynamics of the collective BCS mode and individual fermion pair states can
exhibit either synchronization or Landau dephasing, depending on the details of perturbation. I will illustrate these results with numerical simulations
of the pairing dynamics.