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

We develop a systematic analytical approach on linear and nonlinear pulse propagations in an open Lambda-type molecular system with Doppler broadening. In linear case, by using residue theorem and a spectrum decomposition method, we prove that there exists a crossover from electromagnetically induced transparency (EIT) to Autler-Townes splitting (ATS) for co-propagating configuration of probe and control fields. However, there is no EIT and hence no EIT-ATS crossover for counter-propagating configuration. We give various explicit formulas, including probe-field spectrum decomposition, EIT condition, width of 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 A. Lazoudis et al. [Phys. Rev.A82, 023812 (2010)]. In nonlinear case, by 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.