  The time it takes a quantum system to complete a tunneling event (which in
the case of cross-barrier tunneling can be viewed as the time spent in a
classically forbidden area) is related to the time required for a state to
evolve to an orthogonal state, and an observation, i.e., a quantum mechanical
projection on a particular basis, is required to distinguish one state from
another. We have performed time-resolved measurements of Landau-Zener tunneling
of Bose-Einstein condensates in accelerated optical lattices, clearly resolving
the steplike time dependence of the band populations. The use of different
protocols enabled us to access the tunneling probability, 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
freeparticle momentum eigenstates. Our findings pave the way towards more
quantitative studies of the tunneling time for LZ transitions, which are of
current interest in the context of optimal quantum control and the quantum
speed limit.
