Landau-Zener transitions in qubits controlled by electromagnetic fields

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 classic problems come together in this model: the Landau-Zener (LZ) and the Rabi problem. The probability of LZ 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. We discuss physical realizations in microwave optics, quantum dots and molecular nanomagnets.