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arXiv:2503.12007 · Physical Review Applied

Fisher-based sensitivity framework for Rydberg-atom microwave electrometry

Chen-Rong Liu, Runxia Tao, Xiang Lv, Ying Dong, Chuang Li, Bo Wei, Mingti Zhou

Published Feb 6, 2026• 0 citations
arXivHTMLPDF

Abstract

Fisher information provides a rigorous theoretical benchmark for evaluating quantum sensor sensitivity; however, a comprehensive framework for quantifying the fundamental limits of Rydberg-atom microwave electrometers remains lacking. In this work, we establish such a framework by deriving the Fisher information for slope detection and establishing its connection to sensitivity through signal-to-noise ratio, leading to an analytical expression jointly determined by photon shot noise and atomic response. Numerical implementation with real parameters in cesium vapor systems reveals a Fisher-optimized sensitivity below $\mathrm{nV\,cm^{-1}\,Hz^{-1/2}}$, highlighting a substantial potential for sensitivity enhancement in practical experiments through the suppression of technical noise. Importantly, the theory predicts that sub-nanovolt sensitivity is robust against moderate variations in system parameters, thereby delineating both the ultimate sensitivity and optimal operational regime of Rydberg-atom microwave electrometers.

DOI
10.1103/qsmd-yh44

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Fisher information provides a rigorous theoretical benchmark for evaluating quantum sensor sensitivity; however, a comprehensive framework for quantifying the fundamental limits of Rydberg-atom microwave electrometers remains lacking. In this work, we establish such a framework by deriving the Fisher information for slope detection and establishing its connection to sensitivity through signal-to-noise ratio, leading to an analytical expression jointly determined by photon shot noise and atomic response. Numerical implementation with real parameters in cesium vapor systems reveals a Fisher-optimized sensitivity below nV cm−1 Hz−1/2\mathrm{nV\,cm^{-1}\,Hz^{-1/2}}nVcm−1Hz−1/2, highlighting a substantial potential for sensitivity enhancement in practical experiments through the suppression of technical noise. Importantly, the theory predicts that sub-nanovolt sensitivity is robust against moderate variations in system parameters, thereby delineating both the ultimate sensitivity and optimal operational regime of Rydberg-atom microwave electrometers.
The development of a microwave electrometer with inherent uncertainty approaching its ultimate limit carries both fundamental and technological significance. However, because of the thermal motion of atoms, the state-of-art Rydberg electrometer falls considerably short of the standard quantum limit by about three orders of magnitude. Here, we use an optically thin medium with approximately 5.2 × 10 5 laser-cooled atoms to implement the microwave heterodyne detection. By mitigating various noises and strategically optimizing the electrometer parameters, our study reduces the equivalent noise temperature by a factor of 20 and achieves an electric field sensitivity of 10.0 nV cm −1 Hz −1/2 , lastly reaching a factor of 2.6 above the standard quantum limit. Our work also provides valuable insights into the inherent capabilities and limitations of Rydberg electrometers, offering superior sensitivity in detecting weak microwave signals for numerous applications.
Rydberg-atom electrometry is a core technique in the development of highly sensitive quantum electric-field sensors. Its sensitivity based on atom-photon interaction is typically limited by photon shot-noise (PSN) and spectral broadenings. Here, we experimentally demonstrate a near PSN-limited Rydberg electrometry from a 85Rb atomic vapor cell. By engineering atomic coherence through control of residual magnetic fields and laser frequency noise, we achieve the Rydberg electromagnetically induced transparency (EIT) with the narrow linewidth of 1.6 MHz, yielding an enhanced spectral slope for high-sensitivity Rydberg-EIT electrometry. Under optimized superheterodyne detection conditions, we obtain an electric-field sensitivity of 12.5(8) nV cm^-1 Hz^-1/2 at 37 GHz, in close agreement with the calculated PSN limit. These results provide direct experimental evidence of the high-sensitive quantum electrometry and establish a practical route toward quantum-noise-limited Rydberg electrometry.
Rydberg atoms, which possess exceptionally large electric dipole moments, offer a promising route for electric field sensing as well as metrology traceable to the International System of Units (SI); however, current research predominantly focuses on the microwave (MW) regime, leaving the quasi-direct current (quasi-DC) and low-frequency bands, ubiquitous in power systems, largely unexplored. In this paper, we present a theoretical investigation into low-frequency electric field detection. To this end, we establish a comprehensive modeling framework incorporating Fisher information (FI) and the Cramér-Rao lower bound (CRLB) to quantify the fundamental precision limits of electromagnetically induced transparency (EIT) readouts. Building upon this framework, we propose a linearized sensing strategy utilizing a DC-biased two-point differential measurement. Numerical validations demonstrate that this approach effectively mitigates the weak-field insensitivity for both DC and AC fields, achieving a CRLB-limited sensitivity bound of approximately 1×10−41\times 10^{-4}1×10−4 V/m/Hz\sqrt{\text{Hz}}Hz​. Furthermore, to surpass the single-pass sensitivity limit, we introduce a Fabry-Pérot (FP) cavity-enhanced configuration. This architecture leverages intracavity phase modulation to significantly steepen the transmission slope, boosting the FI by over two orders of magnitude compared to standard free-space configurations. This work provides a rigorous theoretical basis and design guidance for the high-precision quantum monitoring of electromagnetic environments in smart grids.
Laser frequency or phase noise is a main factor that limits the sensitivity of Rydberg microwave (MW) electrometry. In this study, we proposed a theoretical approach to estimate the effect of laser frequency noise on the atomic coherence of Rydberg sensors based on an atomic superheterodyne receiver. The noisy lasers were characterized using a phase-diffusion model. In particular, explicit formulas were derived to evaluate the noise-limited sensitivity for a given laser linewidth. Furthermore, the effect of Doppler broadening on the sensitivity of the Rydberg sensor at different atomic temperatures was estimated. Our theoretical results provide guidance for the development of Rydberg MW sensors and the method discussed herein can be applied to many other quantum systems.
Rydberg atoms have demonstrated exceptional capabilities in the precise sensing microwave (MW) fields. Previous studies on Rydberg atom-based electrometers (RAEs) have predominantly focused on absorption measurements. Recently, phase-sensitive RAEs employing Mach-Zehnder interferometer (MZI) have been demonstrated, though their performance remains constrained by the standard quantum limit (SQL). In this study, we combine RAEs with advanced quantum interferometrics to enhance MW field sensing. Within the framework of electromagnetically induced transparency (EIT) and Autler-Townes (AT) splitting, the noise of our enhanced electrometer is suppressed below the photon shot noise (PSN) in measuring light dispersion through microwave-dressed atoms, when utilizing phase squeezed states. In our theory, the optimal sensitivity of the MW field can reach 1.36 × 10 −11 V/m/Hz 1/2 with a dressed MW field strength of 2.4 × 10 −4 V/m within a balanced SU(1,1) interferometer.
We have shown that Rydberg states can be used for high-sensitivity, absolute sensing of microwave (MW) electric fields. We achieved a sensitivity of 3 μVcm-1Hz-1/2 for two read-out strategies. Depending on the spectral resolution of the read-out, either the MW induced transmission line frequency splitting, the Autler-Townes regime, or a change in the on-resonant absorption, the amplitude regime, can be used to determine the MW electric field. Results using a Mach-Zehnder interferometer and frequency modulated spectroscopy both achieve similar photon shot noise limited sensitivity. In addition, we have also explored amplitude modulation and the displacement of a probe laser beam due to index of refraction changes in a prism shaped vapor cell. These latter methods were not able to achieve photon shot noise limited performance. Fundamental limits to the sensitivity of the Rydberg atom-based MW electric field sensing have been addressed, but it is important to clarify the differences between noise in different parts or subsystems of the sensor. Shot noise in the probe laser usually dominates the projection noise of the atoms participating in the measurement of the MW electric field because of the desire to operate at low effective Rydberg atom densities in order to avoid collisional dephasing and ionization.