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arXiv:2607.15221

Measuring Interaction-Induced Energy Shifts of Rydberg Atoms in Hot Vapor

Tomasz Prokop, Bartosz Kasza, Wojciech Wasilewski, Michal P. Parniak

Published Jul 16, 2026• 0 citations
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Abstract

We demonstrate a method to measure energy shifts of the top level in a four-level ladder setup induced by atom interactions in thermal vapors. It utilizes the observation of two transmission minima corresponding to a split electromagnetically induced absorption (EIA) effect. We apply this method to measure mean Rydberg atom interactions in a hot vapor. We believe this approach could provide a valuable tool for accurately modeling mean-field Rydberg atom interactions, as well as sensing the occurrence of strong interactions.

DOI
10.48550/arxiv.2607.15221

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We demonstrate a method to measure energy shifts of the top level in a four-level ladder setup induced by atom interactions in thermal vapors. It utilizes the observation of two transmission minima corresponding to a split electromagnetically induced absorption (EIA) effect. We apply this method to measure mean Rydberg atom interactions in a hot vapor. We believe this approach could provide a valuable tool for accurately modeling mean-field Rydberg atom interactions, as well as sensing the occurrence of strong interactions.
Abstract Electromagnetically induced transparency (EIT) and absorption (EIA) are quantum coherence phenomena which result from the interference of excitation pathways. Combining these with Rydberg atoms have opened up many possibilities for various applications. We introduce a theoretical model to study Rydberg-EIT and Rydberg-EIA effects in cold Cs and Rb atomic ensembles in a four-level ladder type scheme taking into account van der Waals type interactions between the atoms. The proposed many-body method for analysis of such systems involves a self-consistent mean field approach and it produces results which display a very good agreement with recent experiments. Our calculations also successfully demonstrate experimentally observed EIT-EIA cross-over in the Rb case. Being able to simulate the interaction effects in such systems has significant importance, especially for controlling the optical response of these.
We study the electromagnetically induced transparency (EIT) effect with two individually addressed four-level Rydberg atoms subjected to the interatomic van der Waals interaction. We derive an effectively atomic Raman transition model where two ladders of the usual Rydberg EIT setting terminating at the same upper Rydberg level of long radiative lifetime are turned into a Rydberg EIT $\ensuremath{\lambda}$ setup via two-photon transitions, leaving the middle levels of each ladder largely detuned from the coupling and probe laser beams. It can hence overcome the limits of applications for EIT with atoms of the ladder-type level configuration involving a strongly decaying intermediate state by inducing coherence between two ground states. By probing one of the atoms, we observe four doublets of absorption induced by the Autler-Townes splitting and the van der Waals interaction. In particular, we find that the location of the EIT center remains unchanged compared to the interatomic-interaction-free case, which demonstrates that the interference among the multiple transition channels is basically destructive. The EIT with controlled Rydberg-Rydberg interaction among a few atoms provides a versatile tool for engineering the propagation dynamics of light.
This study addresses the restrictions imposed by nonlocal van der Waals (vdW) and dipole-dipole (DD) interactions on the microwave electrometry in cold Rydberg atoms driven into the four-level cascade configuration with relatively high excitation densities. Utilizing the mean-field superatom model, we examine, in particular, the effects of vdW and DD interactions on microwave-controlled transmission spectra of a probe field in the regime of electromagnetically induced transparency (EIT). In response to spectral shifts depending on such Rydberg interactions, we propose a modified formula for correctly describing the nonlinear relationship between the microwave electric field and the splitting of two EIT peaks, which could enhance the measurement accuracy. This formula also extends the lower limit set by a certain measurement accuracy into the nonlinear response region by approximately five times, effectively mitigating the restrictions imposed by vdW and DD interactions. Our findings suggest that an accurate measurement of weak microwave electric fields could be achieved under both high and low-density conditions through data correction, yet without altering the experimental method. This research provides an alternative solution for microwave electrometry in weakly interacting atomic gases and highlights its potential applications in integrated quantum devices.
Rydberg-assisted atomic electrometry with thermal vapors offers a promising approach for detecting external electric fields. However, this technique presents significant challenges for measuring low frequencies due to the effects of metal-alkali atoms adsorbed on the interior surface of the vacuum chamber. In this work, we apply high-contrast Rydberg electromagnetically induced transparency (EIT) spectroscopy to systematically investigate these effects, including the influence of laser power and electric field strength. We demonstrate the ability to measure electric field frequencies ranging from 10 Hz to 1 MHz. Additionally, this study identifies a fundamental limit for data capacity in such measurements. Furthermore, we propose a method for precise Stark shift measurements by locking the coupling laser to Zeeman-split Rydberg EIT peaks. Using the Zeeman shift in a reference cell as a stable frequency reference, we are able to track Stark-induced shifts in a science cell and confirm excellent agreement with theoretical predictions. These results provide valuable insights for future precision measurement techniques and field sensing applications based on Rydberg atom systems.
Abstract For multi-level systems in hot atomic vapors the interplay between the Doppler shift due to atomic motion and the wavenumber mismatch between driving laser fields strongly influences transmission and absorption properties of the atomic medium. In a three-level atomic ladder-system, Doppler broadening limits the visibility of electromagnetically-induced transparency (EIT) when the probe and control fields are co-propagating, while EIT is recovered under the opposite condition of counter-propagating geometry and k p < k c , with k p and k c being the wavenumbers of the probe and control fields, respectively. This effect has been studied and experimentally demonstrated as an efficient mechanism to realize non-reciprocal probe light transmission, which may enable applications as magnetic-field free optical isolators. Here, we describe the basics of this effect and discuss a simple picture for the underlying mechanism. We illustrate how the non-reciprocity scales with wavelength mismatch and show how to experimentally demonstrate the effect in a simple Rydberg-EIT system using thermal Rubidium atoms.
Quantum sensing using Rydberg atoms is an emerging technology for precise measurement of electric fields. However, most existing computational methods are all based on a single-particle model and neglect Rydberg-Rydberg interaction between atoms. In this study, we introduce the interaction term into the conventional four-level optical Bloch equations. By incorporating fast iterations and solving for the steady-state solution efficiently, we avoid the computation of a massive 4 N × 4 N dimensional matrix. Additionally, we apply the Doppler frequency shift to each atom used in the calculation, eliminating the requirement for an additional Doppler iteration. These schemes allow for the calculation of the interaction between 7000 atoms around one minute. Based on the many-body model, we investigate the Rydberg-Rydberg interaction of Rydberg atoms under different atomic densities. Furthermore, we compare our results with the literature data of a three-level system and the experimental results of our own four-level system. The results demonstrate the validity of our model, with an effective error of 4.59% compared to the experimental data. Finally, we discover that the many-body model better predicts the linear range for measuring electric fields than the single-particle model, making it highly applicable in precise electric field measurements.