We investigate the breathing mode of harmonically trapped bosons in an optical lattice at small site occupancies. The Bose-Hubbard model with a trapping potential is used to describe the breathing-mode dynamics initiated through weak quenches of the trap strength. We connect to results for continuum bosons (Lieb-Liniger and Gross-Pitaevskii results) and also present deviations from continuum physics. We take a spectral perspective, identifying the breathing-mode frequency with a particular energy gap in the spectrum of the trapped Bose-Hubbard Hamiltonian. We present the low-energy eigenspectrum of the trapped many-boson system and study overlaps of the initial state with eigenstates of the quenched Hamiltonian. There is an intermediate interaction regime, between a “free-boson” limit and a “free-fermion” limit, in which the Bose-Hubbard breathing-mode frequency approaches the Gross-Pitaevskii prediction. In addition, we present a striking failure of the time-dependent Gutzwiller approximation for describing breathing modes.

• Received 15 October 2013

DOI:https://doi.org/10.1103/PhysRevA.88.063636