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arXiv:2610.39921

Simultaneous SI-traceable measurement of the amplitude and the ellipticity of microwave fields with cold Rydberg atoms

Anthony El Bekai, R. Granier, Miguel Angel Cifuentes Marin, Cédric Blanchard, Nassim Zahzam, Yannick Bidel, Alexandre Bresson, Alexis Bonnin, Sylvain Schwartz

Published Oct 29, 2026• 0 citations
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Abstract

We present a method for the simultaneous measurement of the amplitude and the ellipticity of microwave fields using trap-loss spectroscopy based on Rydberg excitation of a cold ensemble of 87Rb atoms. The measurement consists of probing the energy spectrum of the $61S_{1/2}$ to $61P_{1/2}$ transition in the presence of microwave, which depends on the electric field amplitude $|E|$ and the third Stokes parameter $|S_3|$. We use a millimeter-size magneto-optical trap to perform strongly-localized measurements, which mitigates the effect of microwave field inhomogeneities. This allows us to work with large Rabi frequencies and thus resolve small deviations from linear or circular states of polarization. Taking into account the effect of non-resonant couplings to neighboring Rydberg states, we measure $|E|$ and $|S_3|$ with an accuracy on the order of 1 percent in the Autler-Townes regime where the measurements can be traced to the international system of units. By studying the visibility of the spectral features as a function of the polarization of the excitation laser beams, we extract some information on the angle of arrival of the microwave field onto the atoms, with good agreement between theory and experiment.

DOI
10.48550/arxiv.2610.39921

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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 $\ensuremath{\sim}100\phantom{\rule{4pt}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$.
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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.
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.
This paper reports on the results of experiments with cold rubidium Rydberg atoms in a magneto-optical trap. The specific feature of the experiments is the excitation of Rydberg atoms in a small volume within a cloud of cold atoms and the sorting of measured signals and spectra according to the number of detected Rydberg atoms. The effective lifetime of the 37 P Rydberg state and its polarizability in a weak electric field are measured. The results obtained are in good agreement with theoretical calculations. It is demonstrated that the localization of the excitation volume in the vicinity of the zero-magnetic-field point makes it possible to improve the spectral resolution and to obtain narrow microwave resonances in Rydberg atoms without switching off the quadrupole magnetic field of the trap. The dependence of the amplitude of dipole-dipole interaction resonances in Rydberg atoms on the number of atoms is measured. This dependence exhibits a linear behavior and agrees with the theory for a weak dipole-dipole interaction.
We demonstrate a new approach for the metrology of microwave fields based on the trap-loss spectroscopy of cold Rydberg atoms in a magneto-optical trap. Compared to state-of-the-art sensors using room-temperature vapors, cold atoms allow longer interaction times, better isolation from the environment, and a reduced Doppler effect. Our approach is particularly simple, as the detection relies on fluorescence measurements only. Moreover, our signal is well described by a two-level model across a broad measurement range, allowing one, in principle, to reconstruct the amplitude and the frequency of the microwave field simultaneously without the need for an external reference field. We report on a scale-factor linearity at the percent level and no noticeable drifts over two hours, paving the way for new applications of cold Rydberg atoms in metrology, such as calibrating black-body shifts in state-of-the-art optical clocks, monitoring the Earth's cryosphere from space, measuring the cosmic microwave background, or searching for dark matter.