Theory of the adiabatic passage in two-level quantum systems with superpositional initial states

An analytic theory of the adiabatic passage (AP) regime of interaction of short frequency chirped laser pulses with a two-lever quantum system (QS) being initially in the superpositional quantum state is presented. We show that the initial value of the non-diagonal elements of the density matrix can influence the dynamics of the population transfer during the action of the laser pulse, but do not influence essentially the final populations of the states of the QS obtained at the end of the interaction near the AP regime. A novel solution to the Bloch equations is obtained in the form of a converging power series generalizing the ordinary AP solution.