Effects of neighboring transitions on the mechanisms of electromagnetically induced absorption and transparency in an open degenerate multilevel system

In this study, optical Bloch equations with and without neighboring hyperfine states near the degenerate two-level system (DTLS) in the challenging case of 85\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$^{85}$$\end{document}Rb D2 transition, which involves the Doppler broadening effect, are solved. The calculated spectra agree well with the experimental results obtained based on the coupling-probe scheme with orthogonal linear polarizations of the coupling and probe fields. The mechanisms of electromagnetically induced absorption (electromagnetically induced transparency) for the open Fg=3→Fe=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_g=3 \rightarrow F_e=2$$\end{document} and 3 transitions (open Fg=2→Fe=2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_g=2 \rightarrow F_e=2$$\end{document} and 3 transitions) are determined to be the effect of the strong closed Fg=3→Fe=4\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_g=3 \rightarrow F_e=4$$\end{document} transition line (strong closed Fg=2→Fe=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_g=2 \rightarrow F_e=1$$\end{document} transition line); this finding is based on a comparison between the calculated absorption profiles of the DTLS without neighboring states and those of all levels with neighboring states, depending on the coupling and probe power ratios. Furthermore, based on the aforementioned comparison, the crucial factors that enhance or reduce the coherence effects and lead to the transformation between electromagnetically induced absorption and electromagnetically induced transparency, are (1) the power ratios between the coupling and probe beams, (2) the openness of the excited state, and (3) effects of the neighboring states due to Doppler broadening in a real atomic system.