  A comprehensive study of the tunneling dynamics of a Bose--Einstein
condensate in a tilted periodic potential is presented. We report numerical and
experimental results on time-resolved measurements of the Landau--Zener
tunneling of ultracold atoms introduced by the tilt, which experimentally is
realized by accelerating the lattice. The use of different protocols enables us
to access the tunneling probability, numerically as well as experimentally, in
two different bases, namely, the adiabatic basis and the diabatic basis. The
adiabatic basis corresponds to the eigenstates of the lattice, and the diabatic
one to the free-particle momentum eigenstates. Our numerical and experimental
results are compared with existing two-state Landau--Zener models.
