Analytical model for transient evolution of an EIT-AT spectrum with Rydberg atoms

An analytical model of an electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting spectrum with a four-level Rydberg atom was presented, and equations were derived to explain the dependence of the transient absorption for a probe laser on light and microwave (MW) fields. The analytical solution of absorption for the probe laser <i>Im</i>[<i>χ</i>(<i>t</i>)] shows that it depends on the spontaneous decay rate from level |2〉 to level |1〉, Rabi frequencies of the control and MW fields. For ⁸⁷<i>Rb</i> atoms, a stronger control laser shortens the steady-state time window and a stronger MW field will lead to a higher oscillation frequency shown in analytical and numerical results. The time-dependent EIT-AT splitting spectrum is also investigated, and the stable splitting distance shows a linear dependence on the continuous MW E-field strength.