  We discuss how to reveal the massive Goldstone mode, often referred to as the
Higgs amplitude mode, near the Superfluid-to-Insulator quantum critical point
(QCP) in a system of two-dimensional ultracold bosonic atoms in optical
lattices. The spectral function of the amplitude response is obtained by
analytic continuation of the kinetic energy correlation function calculated by
Monte Carlo methods. Our results enable a direct comparison with the recent
experiment [M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schau{\ss}, C.
Gross, E. Demler, S. Kuhr, and I. Bloch, Nature 487, 454-458 (2012)], and
demonstrate a good agreement for temperature shifts induced by lattice
modulation. Based on our numerical analysis, we formulate the necessary
conditions in terms of homogeneity, detuning from the QCP and temperature in
order to reveal the massive Goldstone resonance peak in spectral functions
experimentally. We also propose to apply a local modulation at the trap center
to overcome the inhomogeneous broadening caused by the parabolic trap
confinement.
