The behaviour of electromagnetically induced transparency (EIT) resonances in highly excited Rydberg states is significantly affected by external electric fields, a phenomenon recently investigated by Rob Behary, William Torg, Mykhailo Vorobiov, et al. from William & Mary.

Their research details how the orientation of a static direct‑current (dc) electric field relative to laser polarisation alters these EIT resonances, revealing characteristic changes in amplitude dependent on the field’s geometry. Through a combination of experimental demonstration and a simplified analytical model, the team successfully explained these observed variations and used them to map the spatially inhomogeneous electric field produced by a biased wire. This work demonstrates the potential for utilising simultaneous analysis of frequency shifts and amplitudes within Rydberg EIT resonances to achieve vector electrometry of electrostatic fields, a capability with implications for diverse applications.

---

Rydberg EIT for Vector Electrostatic Field Sensing

Analysing both the frequency shifts and amplitudes of Rydberg electromagnetically induced transparency (EIT) resonances could facilitate vector electrometry of electrostatic fields, a capability crucial for numerous quantum‑sensing applications. Complete characterization of any vector field necessitates information regarding both its magnitude and direction. Alkali‑metal atoms in highly excited Rydberg states possess a large polarizability, making them suitable for scalar electric‑field sensing, and research groups have, over the past two decades, demonstrated radio‑frequency and terahertz field sensors utilising room‑temperature rubidium or caesium vapour cells. Most of these sensors employ coherent two‑ or three‑photon EIT to detect alterations in Rydberg‑state energies when exposed to external dc or ac electric fields.

The quadratic relationship between Stark shifts and electric‑field magnitude provides information only about field strength. Directional information can be obtained by interfering the test field with a local oscillator of known polarisation, though this method proves impractical for measuring low‑frequency or dc fields with free charges. Any additional electric field would modify the original charge distribution, disrupting the electric environment under measurement. This research attempts to reconstruct a dc electric‑field vector by recording both the frequencies and areas of EIT two‑photon resonances for differing sub‑levels of a Rydberg state, leveraging the polarisation dependence of transition probabilities between various Zeeman sub‑levels—a concept previously explored for determining the direction of magnetic and radio‑frequency fields.

Experiments demonstrate the ability to determine the orientation of an electric field within a vacuum chamber containing rubidium atoms by rotating laser polarisation and monitoring changes in the amplitudes and areas of Stark‑split EIT peaks. Detection of EIT‑induced fluorescence dips provides spatial information regarding the inhomogeneous electric field, enabling reconstruction of changes in both its magnitude and orientation. The experimental setup utilises a simplified energy‑level configuration of rubidium, employing a 780 nm probe laser resonant with the 5S₁/₂ → 5P₃/₂ transition and a 480 nm coupling laser scanned across the 5P₃/₂ → nD₅/₂ transition with a frequency detuning denoted as Δc. Stark splitting of the Rydberg nD₅/₂ level into |m_J| = 1/2, 3/2, and 5/2 sublevels occurs as static electric‑field strength increases. Allowed transitions for optical fields polarised parallel or perpendicular to the dc electric field are considered, based on a simplified fine‑structure picture of the atomic levels involved.

---

Rydberg EIT Reveals Electric Field Direction

Scientists achieved a breakthrough in vector electrometry by demonstrating how to reconstruct a dc electric field through analysis of EIT resonances involving highly excited Rydberg states in rubidium atoms. The team meticulously measured variations in the amplitude of Stark‑split EIT resonances, linking these changes to the relative orientation between laser polarisation and an external electric field. Experiments revealed that the amplitude of these resonances directly correlates with selection rules governing transitions between Zeeman sub‑levels, providing a pathway to determine both the magnitude and direction of the electric field. The study focused on a ladder‑type EIT scheme using 780 nm and 480 nm lasers to excite rubidium atoms to 46D Rydberg levels.

Researchers observed that the application of an electric field splits the fine‑structure levels of the Rydberg state, with the magnitude of the shift described by

[

h,\Delta f_{|m_J|}(E) = -\tfrac12 \alpha_{|m_J|} E,

]

where α_{|m_J|} is the polarizability of each sublevel and E is the electric‑field strength. Tests proved that while the frequency positions of EIT resonances remain unaffected by the relative orientation of the electric field, the coupling strength to individual Zeeman sub‑levels is demonstrably polarisation‑sensitive. Data show that when laser polarisation is parallel to the electric field, only Δm = 0 transitions are permitted, effectively suppressing transitions to certain Rydberg sublevels. Conversely, perpendicular polarisation maximises Δm = ±1 transitions.

Scientists recorded distinct EIT spectra under these conditions, confirming the predicted behaviour and enabling reconstruction of the electric‑field orientation by rotating laser polarisation and tracking changes in resonance amplitudes. Detection of EIT‑induced fluorescence dips provided spatial information about the inhomogeneous electric field, allowing reconstruction of both magnitude and orientation changes. Furthermore, the team developed a simplified semi‑analytical atomic model that closely reproduces the experimental observations, supporting the findings and providing a theoretical framework for understanding the observed polarisation dependence of EIT resonances. This breakthrough delivers a novel approach to vector electrometry, potentially enabling applications in quantum sensing where precise measurement of electrostatic fields is crucial.

---

EIT Resonance Tracks Electric Field Orientation

This research demonstrates a clear dependence of Stark‑split resonances within EIT on the polarisation of optical fields, offering a novel approach to vector electric‑field measurements. Through experimental observation and a corresponding semi‑analytical model, the team successfully linked variations in EIT resonance amplitude to the relative orientation between laser polarisation and an applied electric field. These findings establish a method for characterising spatially inhomogeneous electric fields, validated by comparing EIT fluorescence measurements with expected angular dependencies. The significance of this work lies in its potential for applications requiring accurate reconstruction of electric‑charge distributions, such as electron‑beam characterisation and plasma diagnostics.

While the current model accurately describes resonances for specific Rydberg states, the authors acknowledge limitations in fully capturing the complete EIT spectrum. Future studies will focus on refining the model to incorporate the interplay of Stark and Zeeman effects, and ideally, directly varying the electric‑field orientation for independent experimental verification. The presented research represents a substantial step towards practical vector electrometry using Rydberg EIT.

---

Reference

Static dc electric field orientation effects on two‑photon Rydberg EIT – arXiv: 2601.09676 (https://arxiv.org/abs/2601.09676)