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Journal of Physics B Atomic Molecular and Optical Physics

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

Brian C Holloway, Gavin Michael Chase, Lee E. Harrell, David Hutchinson, William K. North, Tyler C. Catapano, Christian Francis Custodio, Simon Kirschenbaum, Michael Charles Speer, David O. Kashinski

Published Feb 2, 2026• 0 citations
Publisher

Abstract

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.

DOI
10.1088/1361-6455/ae407f

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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.
Abstract We utilize an electromagnetically induced transparency (EIT) of a three-level cascade system involving Rydberg state in a room-temperature cell, formed with a cesium 6S1/2–6P3/2–66S1/2 scheme, to investigate the Autler–Townes (AT) splitting resulting from a 15.21-GHz radio-frequency (RF) field that couples the | 66 S 1 / 2 〉 → | 65 P 1 / 2 〉 Rydberg transition. The radio-frequency electric field induced AT splitting, γ AT, is defined as the peak-to-peak distance of an EIT-AT spectrum. The dependence of AT splitting γ AT on the probe and coupling Rabi frequency, Ωp and Ωc, is investigated. It is found that the EIT-AT splitting strongly depends on the EIT linewidth that is related to the probe and coupling Rabi frequency in a weak RF-field regime. Using a narrow linewidth EIT spectrum would decrease the uncertainty of the RF field measurements. This work provides new experimental evidence for the theoretical framework in [J. Appl. Phys. 121, 233106 (2017)].
We investigate electromagnetically induced transparency (EIT) and Autler-Townes splitting in Rydberg rubidium atoms for a six-level excitation scheme. In this six-level system, one radio-frequency field simultaneously couples to two high-laying Rydberg states and results in interesting atomic spectra observed in the EIT lines. We present experimental results for several excitation parameters. We also present two theoretical models for this atomic system, where these two models capture different aspects of the observed spectra. One is a six-level model used to predict dominant spectral features and the other a more complex eight-level model used to predict the full characteristics of this system. Both models shows very good agreement with the experimental data.
Abstract In this paper, the physical origin of interferences has been explored in a four-level cascade rubidium atom by simultaneous interaction with three energies; two optical fields and one radio frequency (RF) field. The atomic system is investigated by a combination of the analytical method introduced by Zhu et al (2010 Phys. Rev. A 81 053836) and resonant pole method introduced by Anisimov (2008 J. Mod. Opt. 55 ). A substantial amount of variation in the probe absorption has been observed in various regimes. The transition from electromagnetically induced transparency (EIT) to Autler–Townes spitting (ATS) is observed. It is found that a definite threshold value exists governing the crossover from EIT to ATS. The applied analytical method gives a clear insight into the nature of interferences; one may observe EIT as a consequence of destructive interference, whereas ATS is a consequence of constructive interference. Furthermore, a transition from single EIT to double electromagnetically induced transparency has been detected when the system is illuminated by RF-driving field in weak control regime. Further, transition from ATS to double Autler–Townes splitting has been observed in the strong control regime.
We investigate the relationship between the Rabi frequency (ΩRF, related to the applied electric field) and Autler-Townes (AT) splitting, when performing atom-based radio-frequency (RF) electric (E) field strength measurements using Rydberg states and electromagnetically induced transparency (EIT) in an atomic vapor. The AT splitting satisfies, under certain conditions, a well-defined linear relationship with the applied RF field amplitude. The EIT/AT-based E-field measurement approach derived from these principles is currently being investigated by several groups around the world as a means to develop a new SI-traceable RF E-field measurement technique. We establish conditions under which the measured AT-splitting is an approximately linear function of the RF electric field. A quantitative description of systematic deviations from the linear relationship is key to exploiting EIT/AT-based atomic-vapor spectroscopy for SI-traceable field measurement. We show that the linear relationship is valid and can be used to determine the E-field strength, with minimal error, as long as the EIT linewidth is small compared to the AT-splitting. We also discuss interesting aspects of the thermal dependence (i.e., hot- versus cold-atom) of this EIT-AT technique. An analysis of the transition from cold- to hot-atom EIT in a Doppler-mismatched cascade system reveals a significant change of the dependence of the EIT linewidth on the optical Rabi frequencies and of the AT-splitting on ΩRF.
Electromagnetically induced transparency (EIT) and Autler-Townes splitting (ATS) are two similar quantum coherent phenomena but have different mechanisms and applications. Akaike information criteria (AIC), an objective method to discriminate EIT and ATS from an experimental viewpoint, has been employed in a variety of systems. Here we use AIC method to quantitively discriminate a series of spectra of cold atoms in a Rydberg-involved upper-driving ladder-type. The derived weights of EIT and ATS reflect that our spectra change from EIT-ATS intermediate region to ATS-dominated region along Rabi frequency of coupling field increases. We find that there are two factors affecting EIT-ATS weights in a Rydberg-involved three-level system: dephasing rate, induced by the interactions among Rydberg atoms, makes the EIT-ATS crossover move to the direction of low Rabi frequency of coupling field and the experimental noise makes the difference between EIT and ATS weights reduce at elsewhere. Our investigation could provide a meaningful reference for the observations and applications of Rydberg-involved quantum coherent spectroscopy.
Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in an atomic vapor cell can be used as novel methods for electric-magnetic field detection. Here we make use of 3 infrared lasers to realize a Rydberg EIT system in a thermal rubidium vapor cell. With the AT splitting induced by the THz radiation, we observe a linear trend between THz field amplitude and the frequency splitting of the absorption dips and EIT transmission peaks. Due to the well-known atomic transition dipole moment of the Rydberg state, the THz electric field can be calibrated from the frequency splitting, making this Rydberg atomic measurement system a practical tool for THz field detection.