Periodic motion around the crossing point in a two‐level system

We study a two‐level system described by a Hamiltonian which exhibits a time‐periodic variation of its diagonal matrix elements in the small coupling regime. We investigate the transition probability, the Bloch–Siegert shift, and the Rabi frequency of the multiquantum transition as functions of the amplitude and frequency of the oscillations. These quantities all exhibit a very distinct behavior depending upon whether or not the amplitude of the oscillations allows for the crossing of the levels. This behavior is monotonic for small amplitudes while it presents oscillations as a function of the frequency for larger amplitudes. These oscillations are unambiguously attributed to the Landau–Zener–Stueckelberg interference effects between the crossing point and the turning point. A discussion of the relevance of these oscillations to possible experimental observations, notably in electron‐transfer reactions, is presented.