  A non-perturbative treatment, the Dirac-Frenkel time-dependent variation is
employed to examine dynamics of the Landau-Zener model with both diagonal and
off-diagonal qubit-bath coupling using the multiple Davydov trial states. It is
shown that steady-state transition probabilities agree with analytical
predictions at long times. Landau-Zener dynamics at intermediate times is
little affected by diagonal coupling, and is found to be determined by
off-diagonal coupling and tunneling strength between two diabatic states. We
investigate effects of bath spectral densities, coupling strengths and
interaction angles on Laudau-Zener dynamics. Thanks to the multiple Davydov
trial states, detailed boson dynamics can also be analyzed in Landau-Zener
transitions. Results presented here may help provide guiding principles to
manipulate the Laudau-Zener transitions in circuit QED architectures by tuning
off-diagonal coupling and tunneling strength.
