  We investigate the response to superlattice modulation of a bosonic quantum
gas confined to arrays of tubes emulating the one-dimensional Bose-Hubbard
model. We demonstrate, using both time-dependent density matrix renormalization
group and linear response theory, that such a superlattice modulation gives
access to the excitation spectrum of the Bose-Hubbard model at finite momenta.
Deep in the Mott-insulator, the response is characterized by a narrow energy
absorption peak at a frequency approximately corresponding to the onsite
interaction strength between bosons. This spectroscopic technique thus allows
for an accurate measurement of the effective value of the interaction strength.
On the superfluid side, we show that the response depends on the lattice
filling. The system can either respond at infinitely small values of the
modulation frequency or only above a frequency threshold. We discuss our
numerical findings in light of analytical results obtained for the Lieb-Liniger
model. In particular, for this continuum model, bosonization predicts power-law
onsets for both responses.
