  We report on the experimental implementation of tunable occupation-dependent
tunneling in a Bose-Hubbard system of ultracold atoms via time-periodic
modulation of the on-site interaction energy. The tunneling rate is inferred
from a time-resolved measurement of the lattice site occupation after a quantum
quench. We demonstrate coherent control of the tunneling dynamics in the
correlated many-body system, including full suppression of tunneling as
predicted within the framework of Floquet theory. We find that the tunneling
rate explicitly depends on the atom number difference in neighboring lattice
sites. Our results may open up ways to realize artificial gauge fields that
feature density dependence with ultracold atoms.
