  We investigate order parameter fluctuations in the Hubbard model within a
time-dependent Gutzwiller approach. While in the weak coupling limit we find
that the amplitude fluctuations are short-lived due to a degeneracy with the
energy of the edge of the quasiparticle continua (and in agreement with
Hartree-Fock + RPA theory), these are shifted below the edge upon increasing
the interaction. Our calculations therefore predict undamped amplitude (Higgs)
oscillations of the order parameter in strongly coupled superconductors, cold
atomic fermion condensates and in strongly interacting charge- and spin-density
wave systems. We propose an experimental realization for the detection of the
spin-type Higgs mode in undoped cuprates and related materials where, due to
the Dzyaloshinsky-Moriya interaction, it can couple to an out-of plane
ferromagnetic excitation which is visible via the Faraday effect.
