Coherent control of a quantum transition by a phase jump

We present an analytically exactly soluble two-state model, in which a hyperbolic-secant-shaped pulsed interaction has a phase jump of φ at the time of its maximum. The detuning has a constant part and a hyperbolic-tangent chirp term. For φ=0, this model reduces to the Demkov-Kunike model, which in turn contains as particular cases three other well-known models: the Rosen-Zener, Allen-Eberly, and Bambini-Berman models. A nonzero φ induces dramatic changes in the transition probability, ranging from complete population inversion to complete population return. The analytic results are particularly instructive in the adiabatic limit and demonstrate that complete population inversion can always occur for a suitable choice of φ. The jump phase φ can therefore be used as a control parameter for the two-state transition probability.