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Laser Physics Letters

Theoretical simulation of double resonance phenomenon in ladder-type Rydberg electromagnetically induced transparency

Chao Li, Xinhua Lu, Jing Fan, Guo Ma, Bao Wang

Published Aug 1, 2026• 0 citations
Publisher

Abstract

Abstract The double resonance phenomenon of electromagnetically induced transparency (EIT) in a ladder-type Rydberg atomic system is theoretically investigated. Based on the cesium 6 S 1 / 2 → 6 P 3 / 2 → n D 5 / 2 transition, we establish a density-matrix model incorporating the Doppler effect and simulate the absorption spectra under counter-propagating laser configurations. The numerical approach is adopted: a two-velocity-group approximation (Lorentzian line-shape superposition). The results show that when the probe detuning Δ p is fixed and nonzero, scanning the coupling laser frequency yields two symmetric transparency peaks separated by δ = 2 ( λ p / λ c ) | Δ p | , in excellent agreement with recent experimental observations. The two-velocity-group approximation is computationally efficient and physically transparent, while the high-precision integration confirms its validity. We also reveal that conventional uniform velocity averaging fails to resolve the narrow EIT peaks due to insufficient sampling, and propose effective numerical strategies. This work provides a reliable theoretical tool for simulating Rydberg EIT spectra and offers insights into Doppler-induced double resonance, which may find applications in laser frequency stabilization and self-calibration of Rydberg atom-based sensors.

DOI
10.1088/1612-202x/ae95ea

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Acta Physica Sinica•Jan 1, 2016•2 citations
Abstract The double resonance phenomenon of electromagnetically induced transparency (EIT) in a ladder-type Rydberg atomic system is theoretically investigated. Based on the cesium 6 S 1 / 2 → 6 P 3 / 2 → n D 5 / 2 transition, we establish a density-matrix model incorporating the Doppler effect and simulate the absorption spectra under counter-propagating laser configurations. The numerical approach is adopted: a two-velocity-group approximation (Lorentzian line-shape superposition). The results show that when the probe detuning Δ p is fixed and nonzero, scanning the coupling laser frequency yields two symmetric transparency peaks separated by δ = 2 ( λ p / λ c ) | Δ p | , in excellent agreement with recent experimental observations. The two-velocity-group approximation is computationally efficient and physically transparent, while the high-precision integration confirms its validity. We also reveal that conventional uniform velocity averaging fails to resolve the narrow EIT peaks due to insufficient sampling, and propose effective numerical strategies. This work provides a reliable theoretical tool for simulating Rydberg EIT spectra and offers insights into Doppler-induced double resonance, which may find applications in laser frequency stabilization and self-calibration of Rydberg atom-based sensors.
The double resonance phenomenon of EIT is studied through the ladder three-level Rydberg system. A probe laser with the wavelength λp=852.35 nm is used to coupling the ground state 6S1/2 to the middle state 6P3/2, and a coupling laser with the wavelength λc=509.08 nm is implemented to couple the state 6P3/2 to the Rydberg state 62D5/2. A special optical scheme is designed, in which the co-propagating and counter-propagating configurations are both used. As a result, the double resonance of electromagnetically induced transparency (EIT) with the Rydberg atom is observed. By comparing the distance between the double peaks, it is found that the double resonance phenomenon comes from the Doppler effect, and the distance between the two resonance peaks in the absorption spectrum is related to the detuning of the resonant lasers.
We present an investigation of electromagnetically induced transparency (EIT) without Doppler background due to a locked probe laser. The EIT is theoretically studied based on a multilevel ladder-type cesium atomic system 6S1/2{S}_{1/2}S1/2​--6P3/2{P}_{3/2}P3/2​--8S1/2{S}_{1/2}S1/2​ in a room-temperature vapor cell. The experimental results agree with the theoretical calculations. Compared with the traditional EIT spectra with a Doppler profile limiting the spectral resolution for keeping the coupling laser locked and scanning the probe laser, these EIT spectra with the probe laser locked and the coupling laser scanned have a flat background, which seem be of great benefit for applications such as the measurement of hyperfine intervals between excited states, the study of highly excited Rydberg states, laser-frequency stabilization, etc.
Based on the cesium 6S1/26{S}_{1/2}6S1/2​-6P3/26{P}_{3/2}6P3/2​-8S1/28{S}_{1/2}8S1/2​ ladder-type atomic system, double-resonance optical pumping (DROP) spectra including electromagnetically induced transparency (EIT) effects have been investigated with a room-temperature cesium vapor cell. For both cases of the probe and the coupling laser beams passing through the cesium vapor cell with the counter-propagation (CTP) and co-propagation (CP) configurations, the DROP spectra measured in the experiment display explicitly different linewidths. Thanks to the EIT effect, the linewidth of the DROP spectrum is explicitly narrower for the CTP configuration than for the CP configuration. Experimental results agree with the theoretical analysis considering Doppler averaging. Furthermore, when the coupling laser has moderate power, the DROP spectrum for the CTP configuration clearly shows two components: the narrow part due to the EIT effect and the broad part caused by optical pumping (but these two different components are never seen in the CP configuration). Also, the effect of the intensity of the coupling and probe lasers on the DROP spectra is investigated.
A high sensitivity spectroscopy of Rydberg atoms is presented by using electromagnetically induced transparency (EIT) in the 6S(1/2)-6P(3/2)-n D ladder-type system of cesium vapor cell at room temperature. The EIT spectra of 40 D Rydberg state are measured and the dependences of the EIT magnitude and linewidth on the coupling laser power are investigated in detail. The Rydberg EIT linewidth is measured to be about 5.6 MHz when the powers of probe and coupling lasers are 50 microW and 5.2 mW, respectively, and which is close to the natural linewidth of cesium atoms. The effect of double resonance optical pumping on EIT is also investigated. The fine structures of nD (n = 39-55) are measured and the experimental result is in agreement with quantum defect theory.
In a Doppler-broadened ladder-type cesium atomic system (6S 1/2 -6P 3/2 -8S 1/2 ), this paper characterizes electromagnetically induced transparency (EIT) in two different experimental arrangements, and investigates the influence of the double-resonance optical-pumping (DROP) effect on EIT in both arrangements. When the probe laser is weak, DROP is explicitly suppressed. When the probe laser is moderate, population of the intermediate level (6P 3/2 F ' = 5) is remarkable, therefore DROP is mixed with EIT. An interesting bimodal spectrum with the broad component due to DROP and the narrow part due to EIT has been clearly observed in cesium 6S 1/2 F = 4−6P 3/2 F ' = 5−8S 1/2 F '' = 4 transitions.
Rydberg atoms, with large principal quantum number n, have been widely investigated in recent years due to their peculiar properties, such as big sizes, long lifetimes and strong interactions with fields and other Rydberg atoms. Rydberg atoms are very sensitive to external fields due to their large polarizabilities scaling as n7.These make Rydberg atoms an ideal candidate for the quantum information, the many-body interaction, etc.In this work, we investigate the Rydberg atoms using electromagneticlly induced transparency (EIT) in a ladder three-level system. The EIT is a quantum interference effect between two excitation path-ways driven by two laser fields. The main idea is performed in a room temperature cesium vapor cell, where the probe laser frequency is modulated. The ground state (6P1/2), excited state (6P3/2), and Rydberg state (nS1/2) constitute a Rydberg three-level system, in which the probe laser is fixed to the 6S1/2 (F = 4)6P3/2 (F = 5) transition by saturated absorption spectrum technique, whereas the coupling laser is scanned across the 6P3/249S1/2 transition. We detect the demodulated EIT signal with the lock-in amplifier (SR830). The modulated EIT signal shows a two-peak structure. The measured spacing between two peaks increases with the frequency detuning, caused by the modulation amplitude, and half the spacing between the peak-to-peak is nearly 1.67 times the modulation amplitude of the probe laser; the measured result shows that the splitting is independent of the modulation frequency. The experimental results are in agreement with the theoretical calculations. The results in our work can be used for real-time monitoring of the laser-line profiles and the fluctuation of laser frequency.