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We study the Higgs mode of superfluid Bose gases in a three dimensionaloptical lattice, which emerges near the quantum phase transition to the Mottinsulator at commensurate fillings. Specifically, we consider responses of theHiggs mode to temporal modulations of the onsite interaction and the hoppingenergy. In order to calculate the response functions including the effects ofquantum and thermal fluctuations, we map the Bose-Hubbard model onto aneffective pseudospin-one model and use a perturbative expansion based on theimaginary-time Green's function theory. We also include the effects of aninhomogeneous trapping potential by means of a local density approximation. Wefind that the response function for the hopping modulation is equal to that forthe interaction modulation within our approximation. At the unit filling rateand in the absence of a trapping potential, we show that the Higgs mode canexist as a sharp resonance peak in the dynamical susceptibilities at typicaltemperatures. However, the resonance peak is significantly broadened due to thetrapping potential when the modulations are applied globally to the entiresystem. We suggest that the Higgs mode can be detected as a sharp resonancepeak by partial modulations around the trap center.

Response of the Higgs amplitude mode of superfluid Bose gases in a three dimensional optical lattice