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AIP Advances

Simultaneously measuring microwave electric fields at different frequencies by Rydberg-atom-based electrometry with Zeeman-resolved Autler–Townes splitting

Yuxiang Wang, Yuqing Liu, Qianyi Zhang, Pengwei Gong, Wen Xie, Zinan Wu, Feng-Dong Jia, Zhi-Ping Zhong

Published Oct 1, 2024• 4 citations
Publisher

Abstract

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.

DOI
10.1063/5.0233994

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The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.

arXiv:2002.00855•Physical Review A•May 21, 2020•115 citations
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.
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 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.
Significant progress has been made in atom-based measurements of length, time, gravity and electromagnetic fields in recently years. Rydberg atom-based microwave electric field measurement, using electromagnetically induced transparency (EIT) in room temperature alkali-metal vapors, has been extensively investigated and aroused the broad interest. This approach may establish a new standard for the measurements of microwave (MW) and radio frequency (RF) electric fields.In this review, we describe the work on a new method of measuring electric fields based on quantum interference by using either cesium or rubidium atoms contained in a dielectric vapor cell. Rydberg atoms with principal quantum number n >>1 have large direct current (DC) polarizabilities and microwave transition dipole moments, thereby making them extremely sensitive to external electric fields. Using the Rydberg three-level EIT to detect the level splitting and shift that is induced by the external field, we can realize a rapid and robust self-calibration method of measuring the electric field in a frequency range from 0.01 GHz to 1000 GHz. For the MW electric field (frequency range > 1 GHz), the MW field causes the Rydberg states to split, known as an Autler-Townes splitting (A-T) effect when the applied microwave can resonate with adjacent Rydberg states. The MW coupled A-T splitting is proportional to the applied electric field strength, from which the field strength is measured. Using the EIT window, a high sensitivity of 3 μV·cm-1·Hz-1/2 and small electric field of 1 μV/cm are expected to be achieved with a modest setup, and the limitations of the sensitivity are also addressed in the review. For the RF field at frequency mj EIT lines, and avoided crossings formed with the fine-structure levels of equal mj and different J's, which is used to calibrate and measure the RF field amplitude. On the other hand, the dependence of the EIT-line strength on the RF field polarization provides a fast and robust polarization measurement of RF fields based on matching experimental data with a theoretical simulation. The measurements of minimum strengths and sensitivity of RF fields based on Rydberg atoms are one order magnitude below the values obtained by traditional antenna methods. The atom-based field measurement paves the way for determining fields through calibration-free, invariable atomic properties and miniaturization. We also propose its various potential applications in the future.
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.
Rydberg electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting in an atomic vapor cell can be used as novel methods for electric-magnetic field detection. Here we make use of 3 infrared lasers to realize a Rydberg EIT system in a thermal rubidium vapor cell. With the AT splitting induced by the THz radiation, we observe a linear trend between THz field amplitude and the frequency splitting of the absorption dips and EIT transmission peaks. Due to the well-known atomic transition dipole moment of the Rydberg state, the THz electric field can be calibrated from the frequency splitting, making this Rydberg atomic measurement system a practical tool for THz field detection.
The atom-based traceable standard for microwave electrometry shows promising advantages by enabling stable and uniform measurement. Here we theoretically propose and then experimentally realize an alternative direct International System of Units (SI)--traceable and self-calibrated method for measuring a microwave-electric-field strength based on electromagnetically induced absorption (EIA) in cold Rydberg atoms. Comparing with the method of electromagnetically induced transparency, we show that the equivalence relation between the microwave Rabi frequency and Autler-Townes splitting is more valid and is even more robust against the experimental parameters in the EIA's linear region. Furthermore, a narrower linewidth of cold Rydberg EIA enables us to realize a direct SI-traceable microwave-electric-field measurement as small as $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.