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 i
ntroduced 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.
We report time-resolved measurements of Landau-Zener tunneling of Bose-Einstein condensates in accelerated optical lattices, clearly resolving the step-like time dependence of the band populations. Using different experimental protocols we were able
to measure the tunneling probability both in the adiabatic and in the diabatic bases of the system. We also experimentally determine the contribution of the momentum width of the Bose condensates to the width of the tunneling steps and discuss the implications for measuring the jump time in the Landau-Zener problem.
