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Journal of Physics B Atomic Molecular and Optical Physics

Improving the spectral resolution and measurement range of quantum microwave electrometry by cold Rydberg atoms

Fei Zhou, Feng-Dong Jia, Xiubin Liu, Yonghong Yu, Jiong Mei, Jian Zhang, Feng Xie, Zhiping Zhong

Published Dec 23, 2022• 28 citations
Publisher

Abstract

Abstract We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler–Townes splitting (EIT-AT splitting). In cold atoms, a spectral linewidth of ∼500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e. by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity (E MW) that can be measured is 430 µV cm−1, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if E MW is so large that the EIT-AT splitting interval Δ f m exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ω p ). Moreover, EIT-AT splitting can be observed if Δ f m exceeds the natural linewidth Γ eg of the intermediate states while scanning the coupling laser (ω c ) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ω c , the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV cm−1, nearly three times higher than that of 6.8 mV cm−1 while scanning ω p . The results indicate that the linear range of E MW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.

DOI
10.1088/1361-6455/acae4f

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Abstract We theoretically and experimentally studied quantum microwave electrometry in a cold atomic system using Rydberg electromagnetic induction transparency (EIT) and Autler–Townes splitting (EIT-AT splitting). In cold atoms, a spectral linewidth of ∼500 kHz for EIT was achieved owing to a significant reduction in residual Doppler width, i.e. by at least an order of magnitude, compared to that in vapor cells at room temperature. Therefore, the minimum microwave electric field intensity (E MW) that can be measured is 430 µV cm−1, which is one order higher sensitivity in the EIT-AT regime than that in vapor cells at room temperature. Unlike microwave electrometry in atomic vapor cells, EIT-AT splitting cannot be observed if E MW is so large that the EIT-AT splitting interval Δ f m exceeds the absorption peak width of the cold atom while scanning the frequency of the probe laser (ω p ). Moreover, EIT-AT splitting can be observed if Δ f m exceeds the natural linewidth Γ eg of the intermediate states while scanning the coupling laser (ω c ) and maintains a high spectral resolution with a high signal-to-noise ratio. While scanning ω c , the upper microwave electric field intensity is limited by the scanning range of our setup. Using our system, we measure the maximum field to be 21.6 mV cm−1, nearly three times higher than that of 6.8 mV cm−1 while scanning ω p . The results indicate that the linear range of E MW measured using EIT-AT splitting considerably improves in cold Rydberg atoms.
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.
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 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) field. In addition to the two zero-crossing points, the dispersion signal has two positive maxima with an interval defined as the shoulder interval of the dispersion signal ΔfshoΔf_{\text{sho}}Δfsho​. The relationship of MW field strength EMWE_{\text{MW}}EMW​ and ΔfshoΔf_{\text{sho}}Δfsho​ are studied at the MW frequencies of 31.6 GHz, 22.1 GHz, and 9.2 GHz respectively. The results show that ΔfshoΔf_{\text{sho}}Δfsho​ can be used to character the much weaker EMWE_{\text{MW}}EMW​ than the interval of two zero-crossing points ΔfzerosΔf_{\text{zeros}}Δfzeros​ and the traditional EIT-AT splitting interval ΔfmΔf_{\text{m}}Δfm​, the minimum EMWE_{\text{MW}}EMW​ measured by ΔfshoΔf_{\text{sho}}Δfsho​ is about 30 times smaller than that by ΔfmΔf_{\text{m}}Δfm​. As an example, the minimum EMWE_{\text{MW}}EMW​ at 9.2 GHz that can be characterized by ΔfshoΔf_{\text{sho}}Δfsho​ is 0.056 mV/cm, which is the minimum value characterized by frequency interval using vapour cell without adding any auxiliary fields. The proposed method can improve the weak limit and sensitivity of EMWE_{\text{MW}}EMW​ measured by spectral frequency interval, which is important in the direct measurement of weak EMWE_{\text{MW}}EMW​.
Abstract We have systematically investigated the influence of the gas temperature (T), the Rabi frequencies of the probe laser (Ωp), the coupling laser (Ωc) and the radio-frequency (RF) (ΩRF) on the Rydberg electromagnetically induced transparency (EIT) and Autler–Townes (AT) splitting (Δf) by defining a general Doppler mismatch factor D g = ΩRF/Δf in the Rydberg atom-based microwave electrometry. The effect of T on D g is studied in detail from 0 to 1000 K, the results show that D g is insensitive to T when T < 10 μK or T > 10 K, while D g changes significantly with 10 K > T > 10 μ K . Then the effects of Ωp, Ωc and ΩRF on factor D g at T = 300 K (typical room temperature) and T = 10 μK (typical temperature of cold atom by laser cooling) are studied in detail, respectively. The results show that the linewidth of Rydberg EIT (ΓEIT) can be used as a key parameter to characterize the dependence of D g on Ωp and Ωc in both cases. D g is insensitive to T, Ωp and Ωc when ΩRF > 3ΓEIT which means that ΓEIT determines the lower limit of the linear region of the RF electric field strength measured by EIT–AT splitting. More interesting, the range where D g is insensitive to Ωp and Ωc can be greatly expanded by lowering the gas temperature to 10 μK. The ranges of parameters where D g is insensitive to T, Ωp, Ωc and ΩRF are given, and such relationship can be easily scaled to other atomic systems. The results can help the selection of various parameters in the experiments and specific applications to ensure the accuracy of measuring the RF electric field.
Abstract In this study, we investigated Rydberg atom-based microwave (MW) electrometry using polarization spectroscopy in a room-temperature vapor cell. By measuring Autler-Townes splitting in the electromagnetically induced transparency (EIT) spectrum, we determined that the minimum measurable MW electric field is approximately five times lower than conventional EIT techniques. The results are well reproduced by a full optical Bloch equation model, which takes into account all the hyperfine levels involved. Subsequently, the EIT setup was used to characterize a custom MW cylindrical lens, which increases the field at the focus by a factor of three, decreasing the minimum measurable MW electric field by the same amount. Our results indicate that the combination of polarization spectroscopy and a MW lens may enhance MW electrometry, and may allow its use as a secondary standard.
The Rydberg electromagnetically induced transparency (EIT)--Autler Townes (AT) splitting proportional to the target microwave electric field strength is an atom-based primary traceable standard in microwave electrometry. The minimum detected microwave electric field is limited when the EIT-AT splitting is indistinguishable. We design a method for auxiliary microwave-dressed Rydberg atoms that extends the electrometric span. We theoretically and experimentally show that the low bound of the direct SI-traceable microwave electric field is extended by two orders of magnitude, which is from several mV/cm to $\ensuremath{\mu}\mathrm{V}/\mathrm{cm}$ in a room-temperate Rb cell with a modest setup.