  We perform precision measurements on a Mott-insulator quantum state of
ultracold atoms with tunable interactions. We probe the dependence of the
superfluid-to-Mott-insulator transition on the interaction strength and explore
the limits of the standard Bose-Hubbard model description. By tuning the
on-site interaction energies to values comparable to the interband separation,
we are able to quantitatively measure number-dependent shifts in the excitation
spectrum caused by effective multi-body interactions.
