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arXiv:2208.07325

Modeling Line Broadening and Distortion Due to Spatially Non-Uniform Fields in Rydberg Electrometry

Andrew P. Rotunno, Amy K. Robinson, Samuel Berweger, Nukunjkumar Prajapati, Alexandra B. Artusio‐Glimpse, Matthew T. Simons, Christopher L. Holloway

Published Aug 15, 2022• 3 citations
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Abstract

We present a model for calculating broadened Autler-Townes spectra when probing ac electric field magnitudes by use of Rydberg atom electromagnetically-induced transparency. This model approximates the atom vapor as a multi-layered media and uses Beer's law to combine probe beam absorption through many discrete thin segments, replicating the broadening seen in experimental measurements. The methodology can be easily applied to other non-uniform optical parameters when monitoring total spectral transmission or phase delay. Field non-uniformity is present in standing waves of unmatched waveguides and glass vapor cells, which are generally due to source characteristics and environmental reflections. We present broadening and distortion effects caused by various types of electric-field distributions, and compare this model to results obtained from measured atomic spectra.

DOI
10.48550/arxiv.2208.07325

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We present a model for calculating broadened Autler-Townes spectra when probing ac electric field magnitudes by use of Rydberg atom electromagnetically-induced transparency. This model approximates the atom vapor as a multi-layered media and uses Beer's law to combine probe beam absorption through many discrete thin segments, replicating the broadening seen in experimental measurements. The methodology can be easily applied to other non-uniform optical parameters when monitoring total spectral transmission or phase delay. Field non-uniformity is present in standing waves of unmatched waveguides and glass vapor cells, which are generally due to source characteristics and environmental reflections. We present broadening and distortion effects caused by various types of electric-field distributions, and compare this model to results obtained from measured atomic spectra.
We investigate the effects of spatially non-uniform radio-frequency electric (E) field amplitudes on the spectral line shapes of electromagnetically induced transparency (EIT) signals in Rydberg atomic systems used in electrometry (i.e., the metrology of E-field strengths). Spatially non-uniform fields distort the EIT spectra from that of an ideal case, and understanding this distortion is important in the development of Rydberg atom-based sensors, as these distortions can limit accuracy and sensitivity. To characterize this distortion, we present a model that approximates the atom vapor as multi-layered media and then uses Beer’s law to combine the absorption through its many discrete thin segments. We present a set of expected line distortions caused by various RF electric-field distributions found in practice. This provides an intuitive diagnostic tool for experiments. We compare this model to measured experimental atomic spectra in both two-photon and three-photon excitation schemes in the presence of non-uniform radio-frequency fields. We show that we can accurately model and reproduce the EIT lineshape distortion observed in these experimental data.
Highly excited Rydberg atoms in a room-temperature vapor cell are promising for developing a radio-frequency (RF) electric field (E-field) sensor and relevant measurement standards with high accuracy and sensitivity. The all-optical sensing approach is based on electromagnetically-induced transparency and Autler-Townes splitting induced by the RF E-field. Systematic investigation of measurement uncertainty is of great importance for developing a national measurement standard. The presence of a dielectric vapor cell containing alkali atoms changes the magnitude, polarization, and spatial distribution of the incident RF field. In this paper, the field distortion of rubidium vapor cells is investigated, in terms of both field strength distortion and depolarization. Full-wave numerical simulation and analysis are employed to determine general optimization solutions for minimizing such distortion and validated by measuring the E-field vector distribution inside different vapor cells. This work can improve the accuracy of atom-based RF E-field measurements and contributes to the development of related RF quantum sensors.
The use of Rydberg atoms for radio frequency electric field sensing has emerged as a promising alternative to traditional antenna-based designs that enables all-optical readout. However, the need for atomic vapor cells comprised of dielectric materials can adversely affect the electric field distribution at the probing volume. Here we describe the effects of electric field inhomogeneity on measured optical electromagnetically induced transparency (EIT) spectra. This is accomplished using custom-designed waveguide-embedded atomic vapor cells with stub tuners that allow control of the degree of electric field inhomogeneity within the cell. We describe the resulting broadening of the measured EIT feature and the associated reduction in magnitude, which results in an overall reduced sensitivity of the resulting measurement.
We investigate the effect of band-limited white Gaussian noise (BLWGN) on electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, when performing atom-based continuous-wave (CW) radio-frequency (RF) electric (E) field strength measurements with Rydberg atoms in an atomic vapor. This EIT/AT-based E-field measurement approach is currently being investigated by several groups around the world as a means to develop a new International System of Units traceable RF E-field measurement technique. For this to be a useful technique, it is important to understand the influence of BLWGN. We perform EIT/AT based E-field experiments with BLWGN centered on the RF transition frequency and for the BLWGN blue-shifted and red-shifted relative to the RF transition frequency. The EIT signal can be severely distorted for certain noise conditions (bandwidth, center frequency, and noise power), hence altering the ability to accurately measure a CW RF E-field strength. We present a model to predict the line shifts and broadenings in the EIT signal in the presence of noise. This model includes AC Stark shifts and on resonance transitions associated with the noise source. The results of this model are compared to the experimental data, and we find very good agreement between the two.
Rydberg atoms are neutral atoms excited to high principal quantum number states, which endows them with exaggerated properties such as large electric dipole moments, long lifetimes, and extreme sensitivity to external electromagnetic fields. These characteristics form the foundation of Rydberg atom-based sensors, an emerging class of quantum devices capable of optically detecting electric fields across frequencies from DC to the terahertz regime. Rydberg-based electrometry operates through both Autler–Townes (AT) splitting of resonant Rydberg transitions and Stark-shift measurements for high-frequency or far-detuned fields, enabling broadband field sensing from DC to the THz regime. Using ladder-type electromagnetically induced transparency (EIT) and AT splitting, these sensors enable non-invasive, SI-traceable measurements of field amplitude, frequency, phase, and polarization. Recent developments have demonstrated broadband electric field probes, voltage calibration standards, and compact RF receivers based on thermal vapor cells and integrated photonic architectures. Furthermore, innovations in multi-photon EIT, superheterodyne readout, and multi wave mixing have expanded the dynamic range and bandwidth of Rydberg-based electrometry. Despite challenges related to environmental perturbations, linewidth broadening, and laser stabilization, ongoing advances in atomic control, hybrid photonic integration, and EIT-based readout promise scalable, chip-compatible sensors. This review summarizes the physical principles, experimental progress, and emerging applications of Rydberg atom-based sensing, emphasizing their potential for next generation quantum metrology, wireless communication, and precision field mapping.
Rydberg atom-based electrometry based on electromagnetic induced transparency (EIT) and Autler–Townes splitting (EIT-AT) could achieve ultra-high sensitivity measurements. The amplitude and linewidth of EIT spectra significantly impact the accuracy of electric field measurements. This research utilizes cascade diffraction gratings to generate 2×2 probe laser arrays for the excitation of Rydberg atoms, thereby enhancing spectral resolution under the power broadening. Compared with one laser, the laser array boosts EIT amplitude, narrowing the linewidth from 23.53 MHz to 12.66 MHz, making EIT-AT more distinguishable under identical fields and achieving an enhancement of the sensitivity of 77.96 nV/cm/Hz. These results indicate that laser arrays can optimize the sensitivity of measurement systems based on the Rydberg EIT effect.