  We investigate the influence of a dipole interaction with a classical
radiation field on a qubit during a continuous change of a control parameter.
In particular, we explore the non-adiabatic transitions that occur when the
qubit is swept with linear speed through resonances with the time-dependent
interaction. Two classical problems come together in this model: the
Landau-Zener and the Rabi problem. The probability of Landau-Zener transitions
now depends sensitively on the amplitude, the frequency and the phase of the
Rabi interaction. The influence of the static phase turns out to be
particularly strong, since this parameter controls the time-reversal symmetry
of the Hamiltonian. In the limits of large and small frequencies, analytical
results obtained within a rotating-wave approximation compare favourably with a
numerically exact solution. Some physical realizations of the model are
discussed, both in microwave optics and in magnetic systems.
