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We show that the analysis of the time evolution of the occupation of site andmomentum modes of harmonically trapped lattice hard-core bosons, under drivendipole oscillations, allows one to determine the energy of the lowestone-particle excitations of the system in equilibrium. The analytic solution ofa single particle in the absence of a lattice is used to identify whichfunction of those time-dependent observables is best fit for the analysis, aswell as to relate the dynamic response of the system to its single-particlespectrum. In the presence of the lattice and of multiple particles, a muchricher and informative dynamical response is observed under the drive.

Driven dipole oscillations and the lowest energy excitations of strongly interacting lattice bosons in a harmonic trap