  We study the excitation spectrum of strongly correlated lattice bosons for
the Mott-insulating phase and for the superfluid phase close to localization.
Within a Schwinger-boson mean-field approach we find two gapped modes in the
Mott insulator and the combination of a sound mode (Goldstone) and a gapped
(Higgs) mode in the superfluid. To make our findings comparable with
experimental results, we calculate the dynamic structure factor as well as the
linear response to the optical lattice modulation introduced by Stoeferle et
al. [Phys. Rev. Lett. 92, 130403 (2004)]. We find that the puzzling finite
frequency absorption observed in the superfluid phase could be explained via
the excitation of the gapped (Higgs) mode. We check the consistency of our
results with an adapted f-sum-rule and propose an extension of the experimental
technique by Stoeferle et al. to further verify our findings.
