An Interdisciplinary Journal

* 2013, Vol.16, No.1, pp.86-92*

The general semiclassical time-dependent two-state problem is
considered for a specific field configuration referred to as the
generalized Rosen-Zener model. This is a rich family of pulse
amplitude- and phase-modulation functions describing both
non-crossing and term-crossing models with one or two crossing
points. The model includes the original constant-detuning
non-crossing Rosen-Zener model as a particular case. We show that
the governing system of equations is reduced to a confluent Heun
equation. When inspecting the conditions for returning the system
to the initial state at the end of the interaction with the field,
we reformulate the problem as an eigenvalue problem for the peak
Rabi frequency and apply the Rayleigh-Schrödinger
perturbation theory. Further, we develop a generalized approach
for finding the higher-order approximations, which is applicable
for the whole variation region of the involved input parameters of
the system. We examine the general surface *U _{0n} =U_{0n} (δ_{0} ,δ_{1})*,

*Key words: *
two-state problem, Rosen - Zener model, confluent Heun equation, eigenvalue problem, Rabi frequency

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Last updated: *February 1, 2013*