  We report the first detection of the Higgs-type amplitude mode using Bragg
spectroscopy in a strongly interacting condensate of ultracold atoms in an
optical lattice. By the comparison of our experimental data with a spatially
resolved, time-dependent dynamic Gutzwiller calculation, we obtain good
quantitative agreement. This allows for a clear identification of the amplitude
mode, showing that it can be detected with full momentum resolution by going
beyond the linear response regime. A systematic shift of the sound and
amplitude modes' resonance frequencies due to the finite Bragg beam intensity
is observed.
