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arXiv:2610.04175

Frequency-Axis Calibration via Autler-Townes Splitting in an Electromagnetically Induced Transparency Feature

Stone B. Oliver, Noah Schlossberger, Tate McDonald, Christopher L. Holloway, Nikunjkumar Prajapati

Published Oct 3, 2026• 0 citations
arXivHTMLPDF

Abstract

Rydberg atom-based electrometry is a pivotal technology that enables radio-frequency (rf) field measurements traceable to the International System of Units. This is typically accomplished by converting the direct rf power measurement of classical probes to a frequency measurement referenced to two well-defined spectral features, a commercial wavemeter, or narrow cavity lines produced via clock disciplined electro-optic modulators, although there exist cases where none of these are available. In this article, we demonstrate that a known rf frequency scale can be used to infer a laser's frequency scan using Autler-Townes (AT) splitting. In other words, we show that frequency-axis calibration can be achieved using the avoided-crossing behavior of near-resonant rf radiation. The relative separation between AT-split features is measured as a function of an applied rf field's power and detuning from atomic resonance. These peak separations are then fit to a simple, two-level model using a weighted nonlinear least-squares regression analysis that utilizes three fitting parameters, one of which is the desired calibration factor. While we do not benchmark this method against an absolute frequency reference, we do show that this method is (1) consistent with calibration via known fine-structure separation to within approximately 1.11% or better, and (2) robust against substantial experimental deviation from the system's known rf power dependence.

DOI
10.48550/arxiv.2610.04175

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Rydberg atom-based electrometry is a pivotal technology that enables radio-frequency (rf) field measurements traceable to the International System of Units. This is typically accomplished by converting the direct rf power measurement of classical probes to a frequency measurement referenced to two well-defined spectral features, a commercial wavemeter, or narrow cavity lines produced via clock disciplined electro-optic modulators, although there exist cases where none of these are available. In this article, we demonstrate that a known rf frequency scale can be used to infer a laser's frequency scan using Autler-Townes (AT) splitting. In other words, we show that frequency-axis calibration can be achieved using the avoided-crossing behavior of near-resonant rf radiation. The relative separation between AT-split features is measured as a function of an applied rf field's power and detuning from atomic resonance. These peak separations are then fit to a simple, two-level model using a weighted nonlinear least-squares regression analysis that utilizes three fitting parameters, one of which is the desired calibration factor. While we do not benchmark this method against an absolute frequency reference, we do show that this method is (1) consistent with calibration via known fine-structure separation to within approximately 1.11% or better, and (2) robust against substantial experimental deviation from the system's known rf power dependence.
Atom-based radio-frequency (rf) electromagnetic field sensing using atomic Rydberg states is a promising technique that has recently attracted significant interest. Its unique advantages, such as extraordinary bandwidth, self-calibration, and all-dielectric sensors, are a tangible improvement over antenna-based methods in applications such as test and measurement and development of broad-bandwidth receivers. Here, we demonstrate how an optical-frequency comb can be used to acquire data in the Autler-Townes regime of Rydberg-atom-based electrometry in a massively parallel fashion, eliminating the need for laser scanning. Two-photon electromagnetically induced transparency readout and preparation of cesium is used for the demonstration. A flat quasicontinuous optical comb is generated with the probe laser at 852 nm using an electro-optic modulator and arbitrary waveform generator. A single-frequency coupling laser at 509 nm is tuned to the Rydberg launch state. An enhanced transmission signal is obtained using self-heterodyne spectroscopy, where the comb signal is beat against a local oscillator derived from the single-frequency probe laser on a fast photodiode. The transmission of each probe-laser comb tooth is observed. We resolve electromagnetically induced transparency peaks with line widths below 5 MHz, with and without laser locking. Radio-frequency electromagnetic fields as low as $66\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{Vcm}}^{\ensuremath{-}1}$ are detected, with sensitivities of $2.3\phantom{\rule{0.2em}{0ex}}\text{\ensuremath{\mu}}{\mathrm{Vcm}}^{\ensuremath{-}1}{\mathrm{Hz}}^{\ensuremath{-}1/2}$. The method offers a significant advantage for reading out electromagnetically induced transparency and Autler-Townes splitting, as neither laser needs to be scanned and slow frequency drifts can be tolerated in some applications. The method enables the detection of the amplitude of a pulsed rf electromagnetic field when the incoming pulse Autler-Townes splits the electromagnetically induced transparency peak.
In this work, we demonstrate an approach for improved sensitivity in weak radio frequency (RF) electric-field strength measurements using Rydberg electromagnetically induced transparency (EIT) in an atomic vapor. This is accomplished by varying the RF frequency around a resonant atomic transition and extrapolating the weak on-resonant field strength from the resulting off-resonant Autler-Townes (AT) splittings. This measurement remains directly traceable to SI compared to previous techniques, precluding any knowledge of experimental parameters such as optical beam powers as is the case when using the curvature of the EIT line shape to measure weak fields. We use this approach to measure weak RF fields at 182 GHz and 208 GHz demonstrating improvement greater than a factor of 2 in the measurement sensitivity compared to on-resonant AT splitting RF electric field measurements.
The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.
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.
We discuss a fundamentally new method for electric (E) field strength (V/m) metrology applicable to the near-field. This new approach is significantly different from currently used field measurement techniques in that it is based on the interaction of radio-frequency (RF) E-fields with Rydberg atoms (alkali atoms placed in a glass vapor cell that are excited optically to Rydberg states). The applied RF E-field alters the state of the atoms. The Rydberg atoms act like an RF-to-optical transducer, converting an RF E-field strength to an optical-frequency response. In this new approach, we employ the phenomena of electromagnetically induced transparency (EIT) and Autler-Townes splitting. The RF transition in the four-level atomic system causes a split of the EIT transmission spectrum of a probe laser into two peaks. This splitting is easily measured and is directly proportional to the applied RF E-field amplitude. The significant dipole response of Rydberg atoms enables this technique to make self-calibrating measurements over a large frequency band including 500 MHz to 500 GHz (and possibly up to 1 THz and down to 10s of megahertz). In this paper, we report on our results in the development of this metrology approach, including the first fiber-coupled vapor-cell for E-field measurements. We also discuss key applications, including self-calibrated measurements, millimeter-wave and sub-THz measurements, field mapping, and sub-wavelength and near-field imaging. We show results for mapping the fields inside vapor cells, for measuring the E-field distribution along the surface of a circuit board, and for measuring the near-field at the aperture in a cavity. We also discuss the uncertainties of this measurement technique.
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.