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arXiv:2602.11563

Nonlinear optical spectra from Rydberg-mediated photon-photon interactions

Xinghan Wang, Yupeng Wang, Aishik Panja, Qiyu Liang

Published Feb 12, 2026• 0 citations
arXivHTMLPDF

Abstract

While Rydberg-Rydberg interactions are essential for quantum nonlinear optics and quantum information processing, their role in microwave and radio-frequency sensing remains poorly understood. Here we experimentally investigate Rydberg interaction-induced nonlinearity in cold-atom Rydberg electromagnetically induced transparency (EIT). In a three-level EIT system, increasing photon-photon interactions produces nonlinear spectral broadening accompanied by resonance shifts, while a microwave-dressed four-level system exhibits pronounced nonlinear broadening without detectable spectral shifts. Our three-level data can be explained by a conditional superatom model, whereas our four-level observations are surprisingly captured by a simple dephasing model. Comparisons with three representative models provide key insights to the role of many-body interactions in Rydberg EIT spectroscopy. Furthermore, our results clarify the conditions under which microwave field characterization can be performed in the nonlinear regime without introducing systematic bias. Our study advances both fundamental understanding of many-body physics and practical development of atomic sensors.

DOI
10.48550/arxiv.2602.11563

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While Rydberg-Rydberg interactions are essential for quantum nonlinear optics and quantum information processing, their role in microwave and radio-frequency sensing remains poorly understood. Here we experimentally investigate Rydberg interaction-induced nonlinearity in cold-atom Rydberg electromagnetically induced transparency (EIT). In a three-level EIT system, increasing photon-photon interactions produces nonlinear spectral broadening accompanied by resonance shifts, while a microwave-dressed four-level system exhibits pronounced nonlinear broadening without detectable spectral shifts. Our three-level data can be explained by a conditional superatom model, whereas our four-level observations are surprisingly captured by a simple dephasing model. Comparisons with three representative models provide key insights to the role of many-body interactions in Rydberg EIT spectroscopy. Furthermore, our results clarify the conditions under which microwave field characterization can be performed in the nonlinear regime without introducing systematic bias. Our study advances both fundamental understanding of many-body physics and practical development of atomic sensors.
We present an improved superatom model for examining nonlinear optical responses of cold Rydberg atoms in the regime of electromagnetically induced transparency (EIT). By going beyond the weak-probe approximation, we find that several higher-order collective states should be included to correctly describe the coherent Rydberg excitation of superatoms. Otherwise, numerical results based on the simple ladder system of superatoms will contribute wrong predictions on light intensity and photon correlation of the transmitted probe field. In particular, a great photon-bunching effect will be improperly expected somewhere out of the EIT window in one dilute atomic sample. The essence of this improved superatom model lies in that it can provide reliable predictions on the nonlinear Rydberg-EIT phenomena even in dense atomic samples and may be extended to realize lossless conditional light interactions in appropriate multilevel systems exhibiting dipole blockade.
We present an electromagnetically induced transparency and Aulter-Townes (EIT-AT) spectrum of a Rydberg three-level atom that is dressed with a microwave field in a room-temperature cesium cell. The EIT is a quantum coherent effect produced by the interaction of atoms with electromagnetic waves, which leads to the decrease of the absorption for a weak resonant probe laser. AT splitting refers to the phenomenon, that the absorption line splits when an electromagnetic field that is in resonance or near resonance acts on the transition of atoms. Rydberg atoms are extremely sensitive to an external electric field due to their large polarizabilities and microwave transition dipole moments, which can be used to measure the external field. In this work, a Rydberg three-level EIT is used to detect Rydberg atom and AT splitting induced by the microwave field. Cesium levels 6S1/2, 6P3/2 and 50S1/2 constitute a Rydberg three-level system, in which a weak probe laser locking to the transition from 6S1/2 to 6P3/2 couples ground-state transition and the strong coupling laser resonates on the Rydberg transition from 6P2/3 to 50S1/2. The two Rydberg levels 50S1/2 and 50P1/2 are coupled with the microwave field at a frequency of 30.852 GHz, leading to the AT splitting of EIT line and forming an EIT-AT spectrum, which is used to measure the electric field amplitude of microwave. In order to further study the EIT-AT splitting characteristics of the Rydberg levels, we carry out a series of measurements by changing the microwave field. The experimental results show a broadened EIT-AT signal for the weak field range and the four-peak spectrum for the strong field, which is attributed to the inhomogeneity of the microwave field. The microwave in cesium cell, emitted by a function generator, shows inhomogeneous behavior such that the atoms interacting with the laser field experience the different fields, leading to the line broadened and multi-peak EIT-AT spectra. For the microwave transition of nS1/2-nP1/2 in this paper, a pair of EIT-AT lines should be obtained for an electric field value. The broadening of the EIT-AT spectrum and the multi-peak structure here are due to the inhomogeneity of the microwave field measurement. We propose a method to increase the spatial resolution by reducing the length of cesium cell. The result in this work provides a method of measuring the field amplitude and monitoring the distribution of microwave electric field, meanwhile the spatial resolution of the measurements can be improved by reducing the size of the cell.
We investigate the optical Kerr nonlinearities of an ensemble of cold Rydberg atoms under the condition of electromagnetically induced transparency (EIT). By using an approach beyond mean-field theory, we show that the system possesses not only enhanced third-order nonlinear optical susceptibility, but also giant fifth-order nonlinear optical susceptibility, which has a cubic dependence on atomic density. Our results demonstrate that both the third-order and the fifth-order nonlinear optical susceptibilities consist of two parts, contributed respectively by photon-atom interaction and Rydberg-Rydberg interaction. The Kerr nonlinearity induced by the Rydberg-Rydberg interaction plays a leading role at high atomic density. We find that the fifth-order nonlinear optical susceptibility in the Rydberg-EIT system may be five orders of magnitude larger than that obtained in traditional EIT systems. The results obtained may have promising applications in light and quantum information processing and transmission at weak-light level.
Light propagation through an ensemble of ultracold Rydberg atoms in an electromagnetically-induced-transparency (EIT) configuration is studied. In strongly interacting Rydberg EIT media, nonlinear optical effects lead to a nontrivial dependence of the degree of probe-beam attenuation on the medium density and on its initial intensity. We develop a Monte Carlo rate equation model that self-consistently includes the effect of the probe-beam attenuation to investigate the steady state of the Rydberg medium driven by two laser fields. We compare our results to recent experimental data and to results of other state-of-the-art models for light propagation in Rydberg EIT media. We find that for low probe field intensities, our results match the experimental data best if a density-dependent dephasing rate is included in the model. At higher probe intensities, our model deviates from other theoretical approaches, because it predicts a spectral asymmetry together with line broadening. These are likely due to off-resonant excitation channels, which, however, have not been observed in recent experiments. Atomic motion and coupling to additional Rydberg levels are discussed as possible origins for these deviations.
Abstract We present the electromagnetically induced transparency (EIT) spectra of cold Rydberg four-level cascade atoms consisting of the 6S1/2 → 6P3/2 → 7S1/2 → 60P3/2 scheme. A coupling laser drives the Rydberg transition, a dressing laser couples two intermediate levels and a weak probe laser probes the EIT signal. We numerically solve the Bloch equations and investigate the dependence of the probe transmission rate signal on the coupling and dressing lasers. We find that the probe transmission rate can display an EIT or electromagnetically induced absorption (EIA) profile, depending on the Rabi frequencies of the coupling and dressing lasers. When we increase the Rabi frequency of the coupling laser and keep the Rabi frequency of the probe and dressing laser fixed, flipping of the EIA to EIT spectrum occurs at the critical coupling Rabi frequency. When we apply a microwave field coupling the transition 60P3/2 → 61S1/2, the EIT spectrum shows Autler–Townes splitting, which is employed to measure the microwave field. The theoretical measurement sensitivity can be 1.52 × 10−2 nV⋅cm−1⋅Hz−1/2 at the EIA–EIT flipping point.
We perform spectroscopic measurements of electromagnetically induced transparency (EIT) in a strongly interacting Rydberg gas. We observe a significant spectral shift and attenuation of the transparency resonance due to the presence of interactions between Rydberg atoms. We characterize the attenuation as the result of an effective dephasing and show that the shift and the dephasing rate increase versus atomic density, probe Rabi frequency, and principal quantum number of Rydberg states. Moreover, we find that the spectral shift is reduced if the size of a Gaussian atomic cloud is increased and that the dephasing rate increases with the EIT pulse duration at large-parameter regimes. We simulate our experiment with a semianalytical model, which yields results in good agreement with our experimental data.