Atom-based quantum technologies enable standards for the electromagnetic fields with an important role in science, technology and everyday life. Comparing to previous detection approaches based on antennas, the atom-based measurements improve sensitivity, stability, resolution and reproducibility performances. Based on invariant atomic properties, such measurements are self-calibrated, as they translate electric field strengths into Rabi frequencies that depend on atomic constants. Compact experimental setups were demonstrated in the microwave and up to the sub-THz domain by exploiting the Autler-Townes effect and the electromagnetic induced transparency in Rydberg spectroscopy of alkali atoms. It is not possible to express exactly the relevant alkali atom parameters in function of the SI fundamental constants. On the experimental side, full measurement of a monochromatic electromagnetic wave requires determination not only of its amplitude or power but also of the polarization, the phase and the angle-of-arrival. Development of multi-parameter quantum measurement techniques are required for future quantum sensing applications. Increase in frequency is also needed, as the THz-waves have applications in precision measurements for fundamental physics, free-space communications, remote sensing and medical diagnosis, but the ‘THz gap’ lacks of competitive calibration capabilities. The hydrogen molecular ions (HMI) are the simplest three-body quantum systems. The frequencies of HMI transitions and their shifts in external fields were calculated accurately by ab-initio quantum molecular theory and precisely measured with Doppler-free spectroscopy of trapped and sympathetically cooled molecular ions. The comparison of precise experimental measurements with accurate ab-initio theory predictions of the frequency shifts induced on HD+ transitions by external fields may be exploited for full electromagnetic field calibration against the values of the fundamental constants and the SI second. Precisely, a THz-wave slightly detuned to the fundamental rotational transition of HD+ may be non-destructively detected using the lighshift induced on the two-photon fundamental vibrational transition. The metrological performances of this approach are subsequently evaluated using the state-of-the-art HMI precision physics. This method enables sensitivity to low THz-wave intensity at the 10^(-8) W/m2 level. A THz-wave with an intensity at the W/m2 level may be calibrated with 10^(-3) fractional uncertainty limited by the accuracy of the ab-initio theory prediction of the lightshift. The static magnetic field in the ion trap may be also calibrated by Zeeman spectroscopy and is exploited further as a directional reference for full characterization of the THz-wave electric field. Six lightshift measurements for suitable magnetic field strengths and orientations in the trap may be converted into the polarization ellipse of the THz electric field, which is described in the ideal laboratory frame with three electric field amplitudes and two phases. Such approach enables determination of the Cartesian components of the electric field of a linearly polarized THz-wave with 1 W/m2 intensity with uncertainties at the mV/m level for the amplitudes and the mrad level for the phases. This contribution proposes an application of precision physics in quantum technologies that ensures full traceability of the THz electric field measurements by accounting uncertainties in frequency measurements with HD+ ions and their ab-initio theory predictions based on fundamental physical constants.
Atom-based quantum technologies enable standards for the electromagnetic fields with an important role in science, technology and everyday life. Comparing to previous detection approaches based on antennas, the atom-based measurements improve sensitivity, stability, resolution and reproducibility performances. Based on invariant atomic properties, such measurements are self-calibrated, as they translate electric field strengths into Rabi frequencies that depend on atomic constants. Compact experimental setups were demonstrated in the microwave and up to the sub-THz domain by exploiting the Autler-Townes effect and the electromagnetic induced transparency in Rydberg spectroscopy of alkali atoms. It is not possible to express exactly the relevant alkali atom parameters in function of the SI fundamental constants. On the experimental side, full measurement of a monochromatic electromagnetic wave requires determination not only of its amplitude or power but also of the polarization, the phase and the angle-of-arrival. Development of multi-parameter quantum measurement techniques are required for future quantum sensing applications. Increase in frequency is also needed, as the THz-waves have applications in precision measurements for fundamental physics, free-space communications, remote sensing and medical diagnosis, but the ‘THz gap’ lacks of competitive calibration capabilities. The hydrogen molecular ions (HMI) are the simplest three-body quantum systems. The frequencies of HMI transitions and their shifts in external fields were calculated accurately by ab-initio quantum molecular theory and precisely measured with Doppler-free spectroscopy of trapped and sympathetically cooled molecular ions. The comparison of precise experimental measurements with accurate ab-initio theory predictions of the frequency shifts induced on HD+ transitions by external fields may be exploited for full electromagnetic field calibration against the values of the fundamental constants and the SI second. Precisely, a THz-wave slightly detuned to the fundamental rotational transition of HD+ may be non-destructively detected using the lighshift induced on the two-photon fundamental vibrational transition. The metrological performances of this approach are subsequently evaluated using the state-of-the-art HMI precision physics. This method enables sensitivity to low THz-wave intensity at the 10^(-8) W/m2 level. A THz-wave with an intensity at the W/m2 level may be calibrated with 10^(-3) fractional uncertainty limited by the accuracy of the ab-initio theory prediction of the lightshift. The static magnetic field in the ion trap may be also calibrated by Zeeman spectroscopy and is exploited further as a directional reference for full characterization of the THz-wave electric field. Six lightshift measurements for suitable magnetic field strengths and orientations in the trap may be converted into the polarization ellipse of the THz electric field, which is described in the ideal laboratory frame with three electric field amplitudes and two phases. Such approach enables determination of the Cartesian components of the electric field of a linearly polarized THz-wave with 1 W/m2 intensity with uncertainties at the mV/m level for the amplitudes and the mrad level for the phases. This contribution proposes an application of precision physics in quantum technologies that ensures full traceability of the THz electric field measurements by accounting uncertainties in frequency measurements with HD+ ions and their ab-initio theory predictions based on fundamental physical constants.
Rydberg atoms are neutral atoms excited to high principal quantum number states, which endows them with exaggerated properties such as large electric dipole moments, long lifetimes, and extreme sensitivity to external electromagnetic fields. These characteristics form the foundation of Rydberg atom-based sensors, an emerging class of quantum devices capable of optically detecting electric fields across frequencies from DC to the terahertz regime. Rydberg-based electrometry operates through both Autler–Townes (AT) splitting of resonant Rydberg transitions and Stark-shift measurements for high-frequency or far-detuned fields, enabling broadband field sensing from DC to the THz regime. Using ladder-type electromagnetically induced transparency (EIT) and AT splitting, these sensors enable non-invasive, SI-traceable measurements of field amplitude, frequency, phase, and polarization. Recent developments have demonstrated broadband electric field probes, voltage calibration standards, and compact RF receivers based on thermal vapor cells and integrated photonic architectures. Furthermore, innovations in multi-photon EIT, superheterodyne readout, and multi wave mixing have expanded the dynamic range and bandwidth of Rydberg-based electrometry. Despite challenges related to environmental perturbations, linewidth broadening, and laser stabilization, ongoing advances in atomic control, hybrid photonic integration, and EIT-based readout promise scalable, chip-compatible sensors. This review summarizes the physical principles, experimental progress, and emerging applications of Rydberg atom-based sensing, emphasizing their potential for next generation quantum metrology, wireless communication, and precision field mapping.
Accurate calibration of electromagnetic field strength in the terahertz (THz) frequency regime remains challenging due to the limited availability of SI-traceable field sensors. Here we demonstrate SI-traceable calibration and performance benchmarking of a commercial photomixer-based THz transmitter-receiver system operating near 204 GHz using Rydberg electric-field sensing in a thermal atomic vapor. The THz electric field is extracted from the Autler-Townes (AT) effect of the cesium 17D5/2→18P3/2 Rydberg transition. We measure the strength of AT-split lines as a function of THz detuning from resonance to find the on-resonant Rabi frequency, which, together with atomic transition dipole moments and fundamental constants, yields the THz electric field. The atomically measured field calibrates the photomixer transmitter field and power, while simultaneous measurements with a commercial InGaAs photomixer receiver calibrate the receiver's current-to-field responsivity and convert its current-noise floor into an absolute noise-equivalent THz electric-field sensitivity. Our study demonstrates that Rydberg atomic sensors provide a practical method for SI-traceable calibration and benchmarking of THz transmitter and receiver systems, and for the establishment of a quantitative link between state-of-the-art and absolute atom-based THz sensors.
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.
We discuss a fundamentally new method for electric (E) field strength (V/m) metrology applicable to the near-field. This new approach is significantly different from currently used field measurement techniques in that it is based on the interaction of radio-frequency (RF) E-fields with Rydberg atoms (alkali atoms placed in a glass vapor cell that are excited optically to Rydberg states). The applied RF E-field alters the state of the atoms. The Rydberg atoms act like an RF-to-optical transducer, converting an RF E-field strength to an optical-frequency response. In this new approach, we employ the phenomena of electromagnetically induced transparency (EIT) and Autler-Townes splitting. The RF transition in the four-level atomic system causes a split of the EIT transmission spectrum of a probe laser into two peaks. This splitting is easily measured and is directly proportional to the applied RF E-field amplitude. The significant dipole response of Rydberg atoms enables this technique to make self-calibrating measurements over a large frequency band including 500 MHz to 500 GHz (and possibly up to 1 THz and down to 10s of megahertz). In this paper, we report on our results in the development of this metrology approach, including the first fiber-coupled vapor-cell for E-field measurements. We also discuss key applications, including self-calibrated measurements, millimeter-wave and sub-THz measurements, field mapping, and sub-wavelength and near-field imaging. We show results for mapping the fields inside vapor cells, for measuring the E-field distribution along the surface of a circuit board, and for measuring the near-field at the aperture in a cavity. We also discuss the uncertainties of this measurement technique.
A Rydberg atom detector provides a promising approach for characterizing terahertz (THz) electric fields. Electric field polarization detection is crucial for accurately characterizing THz wave propagation, identifying signal sources and interference, and so on. This paper demonstrates a method for accurate measurement of THz polarization using a four-level cesium Rydberg-atom system. By analyzing the evolution of electromagnetically induced transparency and Autler-Townes spectra under different polarization configurations, the THz polarization angle is quantitatively determined from the relative intensities and asymmetry of the spectral peaks. The results show that the spectral response exhibits a clear dependence on the polarization angle with symmetry about 90°, enabling unambiguous angle determination, and a polarization resolution of 1.28° is achieved. Furthermore, compared with a Schottky diode detector, the proposed method exhibits comparable sensitivity while providing improved fitting consistency and robustness. This approach simplifies both theoretical analysis and experimental implementation for THz polarization measurement, and is promising for applications in THz sensing and spectroscopy.
Atoms form the basis of precise measurement for many quantities (time, acceleration, rotation, magnetic field, etc.). Measurements of microwave frequency electric fields by traditional methods (i.e. engineered antennas) have limited sensitivity and can be difficult to calibrate properly. Highly-excited (Rydberg) neutral atoms have very large electric-dipole moments and many dipole allowed transitions in the range of 1 - 500 GHz. It is possible to sensitively probe the electric field in this range using the combination of two quantum interference phenomena: electromagnetically induced transparency and the Autler-Townes effect. This technique allows for very sensitive field amplitude, polarization, and sub-wavelength imaging measurements. These quantities can be extracted by measuring properties of a probe laser beam as it passes through a warm rubidium vapor cell. Thus far, Rydberg microwave electrometry has relied upon the absorption of the probe laser. We report on our use of polarization rotation, which corresponds to the real part of the susceptibility, for measuring the properties of microwave frequency electric fields. Our simulations show that when a magnetic field is present and directed along the optical propagation direction a polarization rotation signal exists and can be used for microwave electrometry. One central advantage in using the polarization rotation signal rather than the absorption signal is that common mode laser noise is naturally eliminated leading to a potentially dramatic increase in signal-to-noise ratio.