Analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening

Abstract

We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Λ-type molecular system with Doppler broadening. In the linear case, using a residue theorem and a spectrum decomposition method, we prove that a crossover from electromagnetically induced transparency (EIT) to Autler–Townes splitting (ATS) exists for a co-propagating configuration of probe and control fields. However, there is no EIT and hence no EIT–ATS crossover for a counter-propagating configuration. We give various explicit formulas, including probe-field spectrum decomposition, the EIT condition, the width of the EIT transparency window, as well as a comparison with the result of cold molecules. Our analytical result agrees well with the experimental one reported recently by Lazoudis et al (2010 Phys. Rev. A 82 023812). In the nonlinear case, using the method of multiple scales, we derive a nonlinear envelope equation for probe-field propagation. We show that stable ultraslow solitons can be realized in the open molecular system.