Dark-state evolution and self-phase modulation in a<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>Λ</mml:mi></mml:math>medium

Abstract

We consider the propagation of two laser pulses in a medium of three-level $\ensuremath{\Lambda}$ atoms with nonvanishing two-photon detuning and different oscillator strengths of the transitions. We show that the two-photon detuning and the derivative of the mixing angle are described by one and the same equation. We analyze the solution of this equation and its physical consequences. In particular, we obtain the conditions and the distance where the nonadiabaticity and the two-photon detuning may be reduced. We derive a simple expression for the maximum length to which excitation in the medium may reach.