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Optics Express

Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency and Autler-Townes spectra in 87 Rb vapor cell

Xinheng Li, Yue Cui, Jianhai Hao, Fei Zhou, Yuxiang Wang, Feng-Dong Jia, Jian Zhang, Feng Xie, Zhiping Zhong

Published Oct 17, 2023• 24 citations
Publisher

Abstract

We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87 Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each m F state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute m F states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme m F states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.

DOI
10.1364/oe.505488

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Acta Physica Sinica•Dec 9, 2022•5 citations
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87 Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each m F state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the theoretical calculations agree qualitatively with experimental results. The Rydberg atom microwave electric field sensor performance was enhanced by making use of the splitting interval between the two maximum absolute m F states separated by the static magnetic field, which was attributed to the stronger Clebsch-Gordon coefficients between the extreme m F states and the frequency detuning of the microwave electric field under the static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.
Magnetic-field-induced splitting of Rydberg Electromagnetically Induced Transparency (EIT) and Autler-Townes (AT) spectra in 87^{87}87Rb vapor cell
We theoretically and experimentally investigate the Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting of 87^{87}87Rb vapor under the combined influence of a magnetic field and a microwave field. In the presence of static magnetic field, the effect of the microwave field leads to the dressing and splitting of each mFm_FmF​ state, resulting in multiple spectral peaks in the EIT-AT spectrum. A simplified analytical formula was developed to explain the EIT-AT spectrum in a static magnetic field, and the calculations are in excellent agreement with experimental results.We further studied the enhancement of the Rydberg atom microwave electric field sensor performance by making use of the splitting interval between the two maximum absolute mFm_FmF​ states under static magnetic field. The traceable measurement limit of weak electric field by EIT-AT splitting method was extended by an order of magnitude, which is promising for precise microwave electric field measurement.
We provide the simultaneous traceable measurements of microwave electric fields at two different frequencies by the electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting. A static magnetic field working together with a linearly polarized probe and coupling light prepares Rydberg atoms in Zeeman sublevels with maximal |mJ| in an atomic vapor cell. Using the EIT-AT splitting of these two maximal |mJ| states, the microwave electric fields at two different frequencies are simultaneously measured, in which their frequency difference can be adjustable within the linear range of magnetic field-induced level shifts. The proposed method provides a promising prospect for calibrating multiple microwave frequencies simultaneously in the future.
We have theoretically and experimentally studied the dispersive signal of the Rydberg atomic electromagnetically-induced transparency (EIT) Autler–Townes (AT) splitting spectra obtained using amplitude modulation of the microwave (MW) electric field. In addition to the two zero-crossing points interval Δf zeros, the dispersion signal has two positive maxima with an interval defined as the shoulder interval Δf sho, which is theoretically expected to be used to measure a much weaker MW electric field. The relationship of the MW field strength E MW and Δf sho is experimentally studied at the MW frequencies of 31.6 GHz and 9.2 GHz respectively. The results show that Δf sho can be used to characterize the much weaker E MW than that of Δf zeros and the traditional EIT–AT splitting interval Δf m; the minimum E MW measured by Δf sho is about 30 times smaller than that by Δf m. As an example, the minimum E MW at 9.2 GHz that can be characterized by Δf sho is 0.056 mV/cm, which is the minimum value characterized by the frequency interval using a vapor cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of E MW measured by the spectral frequency interval, which is important in the direct measurement of weak E MW.
We report the Rydberg electromagnetically induced transparency (EIT) spectra of the 87 Rb 5 S 1/2 → 5 P 3/2 → 5 D 5/2 → 38 F 7/2 transition in a vapor cell with a DC magnetic field and demonstrate its use for tunable, resonant L-band microwave electric field detection via the Autler-Townes (AT) splitting. Compared to conventional two-photon Rydberg excitation, three-photon EIT exhibits a markedly richer and more intricate spectral structure resulting from extra transition pathways under a DC magnetic field. Under copropagating linearly-polarized optical fields and a static magnetic field, we resolve as many as eight distinct EIT peaks and extract their linear Zeeman-shift coefficients. The measured Zeeman-shifts are all in agreement with the predictions of a simple analytical equation. More interestingly, we demonstrate a single-Zeeman-sublevel Rydberg excitation using three-photon EIT with circular light fields and a quantization axis. We subsequently exploit single-Zeeman-sublevel Rydberg-EIT at the low principal quantum number n = 38 to perform a tunable, resonant EIT–AT measurement of 1.5 GHz (L-band) microwave electric fields. The observed characteristics confirm that L-band microwave measurement via three-photon excited low- n F Rydberg states is advantageous by avoiding the autoionization and high laser power demands of two-photon excited high- n Rydberg states.
An electromagnetically induced transparency (EIT) of a cascade-three-level atom involving Rydberg level in a room-temperature cell, formed with a cesium 6S 1 / 2-6P 3 / 2-66 S 1 / 2 scheme, is employed to detect the Autler-Townes (AT) splitting resulted with a 15.21-GHz microwave field coupling the 66 S 1 / 2 → 65 P 1 / 2 transition. Microwave field induced AT splitting, f A T, is characterized by the distance of peak-to-peak of an EIT-AT spectrum. The f A T dependence on the microwave Rabi frequency, Ω M W , demonstrates two regions, the strong-coupling linear region, f A T ≈ Ω M W and the weak-coupling nonlinear region, f A T ≲ Ω M W. The f A T dependencies on the probe and coupling Rabi frequency are also investigated. Using small probe- and coupling-laser, the Rabi frequency is found to enlarge the linear regime and decrease the uncertainty of the microwave field measurements. The measurements agree with the calculations based on a four-level atomic model.
Microwave electric fields are measured by using cold Rydberg atoms. We obtain spindle-shaped cold atomic clouds in a magneto-optical trap and then pump the cold atoms to quantum state 5S1/2, F = 2, mF = 2 by using an optical-pump laser. We obtain the Rydberg electromagnetic induction transparency (EIT) spectrum peak with narrow linewidth by the low temperature and small residual Doppler broadening. The results show that the typical EIT linewidth with 16 μK cold atoms is about 460 kHz which is 15 times narrower than that of 7 MHz obtained in the thermal vapor cell. The microwave electric field amplitude is measured by Autler-Townes splitting (EIT-AT splitting) in the cold atoms at frequencies of 9.2, 14.2 and 22.1 GHz, receptively. The results show that there is a good linear relationship between the EIT-AT splitting interval and the microwave electric field amplitude. The lower limit of the microwave electric field amplitude that can be measured in the linear region can reach as low as 222 μV/cm, which is about 22 times larger than the lower limit in the traditional thermal vapor cell about of 5 mV/cm. The improvement of the lower limit by EIT-AT splitting method is roughly proportional to the narrowing EIT line width by cold atom samples. This demonstrates that benefiting from the smaller residual Doppler effect and the narrower EIT linewidth in cold atoms, the cold atom system is more advantageous in the experimental measuring of the weak microwave electric field amplitude by using the EIT-AT splitting method. This is of great benefit to the absolute calibration of very weak microwave electric fields. Furthermore, the lower limit of the microwave electric field amplitude that can be measured is smaller than 1 μV/cm by using the change of transmittance of the prober laser at the EIT resonance, and the corresponding sensitivity can reach 1 μV·cm–1·Hz–1/2. These results demonstrate the advantages of cold atomic sample in microwave electric field measurement and its absolute calibration.