Crossover from Electromagnetically Induced Transparency to Autler-Townes Splitting in Open Ladder Systems with Doppler Broadening

We propose a general theoretical scheme to investigate the crossover from electromagnetically induced transparency (EIT) to Autler-Townes splitting (ATS) in open ladder-type atomic and molecular systems with Doppler broadening. We show that when the wavenumber ratio $k_c/k_p\approx -1$, EIT, ATS, and EIT-ATS crossover exist for both ladder-I and ladder-II systems, where $k_c$ ($k_p$) is the wavenumber of control (probe) field. Furthermore, when $k_c/k_p$ is far from $-1$ EIT can occur but ATS is destroyed if the upper state of the ladder-I system is a Rydberg state. In addition, ATS exists but EIT is not possible if the control field used to couple the two lower states of the ladder-II system is a microwave field. The theoretical scheme developed here can be applied to atoms, molecules, and other systems (including Na$_2$ molecules, and Rydberg atoms), and the results obtained may have practical applications in optical information processing and transformation.