Autler–Townes splitting in Rydberg atoms: transition dipole matrix element extraction and field efficiency analysis

Abstract We report the observation and quantitative analysis of Autler–Townes splitting in rubidium atoms excited to Rydberg states using a four-level ladder-type electromagnetically induced transparency (EIT) scheme and resonant radio-frequency (RF) fields. By fitting the EIT spectra to Voigt profiles and calibrating the frequency axis with a semi-empirical Rydberg–Ritz model, we extracted transition dipole matrix elements (TDMEs) for the n D 5 / 2 → ( n + 1 ) P 3 / 2 transitions across five principal quantum numbers: n = 53, 55, 68, 75, and 85. Comparison with theoretical predictions revealed systematic deviations in the Rabi frequencies, attributed to RF delivery inefficiencies and standing-wave enhancement within the vapor cell. To address these effects, we developed two complementary approaches: an empirical quartic fit to measured efficiencies and a physics-based model, capturing both transverse radial variation and dominant longitudinal interference along the cell axis. These models explain the observed scaling behavior, predict an efficiency peak near n ≈ 60, and reduce TDME discrepancies to less than 5% at the validation point. Our analysis highlights the influence of spatial field distribution and cell geometry on precision atom–field interaction measurements and establishes a robust experimental framework for TDME extraction in ladder-type EIT systems.