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arXiv:2307.15617 · Science Advances

Approaching the standard quantum limit of a Rydberg-atom microwave electrometer

Hai-Tao Tu, Kai-Yu Liao, Hong-Lei Wang, Yi-Fei Zhu, Si-Yuan Qiu, Hao Jiang, Wei Huang, Bian Wu, Hui Yan, Shi-Liang Zhu

Published Dec 20, 2024• 58 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1126/sciadv.ads0683

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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.
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The Rydberg atom-based microwave electric field sensor has high sensitivity for weak RF-field detection. Selection of Rydberg states with larger electric dipole moment is beneficial to enhance the sensitivity, and we choose Rydberg states with its principal quantum number up to n ∼ 80. We study the probe laser transmission response to a microwave field for these chosen high Rydberg states at room temperature. It agrees well with theoretical simulation based on an optical Bloch equation with considered microwave-atom interaction and Doppler broadening effect. In our experiment, the microwave sensing sensitivity based on 85 Rb transition | 78 S 1 / 2 ⟩ → | 78 P 3 / 2 ⟩ arrives at 5.102(49) nV cm − 1 Hz − 1 / 2 at 1 kHz.
There is no fundamental limit to the precision of a classical measurement. The position of a meter's needle can be determined with an arbitrarily small uncertainty. In the quantum realm, however, fundamental quantum fluctuations due to the Heisenberg principle limit the measurement precision. The simplest measurement procedures, involving semi-classical states of the meter, lead to a fluctuation-limited imprecision at the standard quantum limit. By engineering the quantum state of the meter system, the measurement imprecision can be reduced down to the fundamental Heisenberg Limit (HL). Quantum-enabled metrology techniques are thus in high demand and the focus of an intense activity. We report here a quantum-enabled measurement of an electric field based on this approach. We cast Rydberg atoms in Schrödinger cat states, superpositions of atomic levels with radically different polarizabilites. We use a quantum interference process to perform a measurement close to the HL, reaching a single-shot sensitivity of 1.2 mV/cm for a 100 ns interaction time, corresponding to 30 μμμV/cm/Hz^(1/2) at our 3 kHz repetition rate. This highly sensitive, non-invasive space- and time-resolved field measurement extends the realm of electrometric techniques and could have important practical applications. Detection of individual electrons in mesoscopic devices at a ~100 μμμm distance, with a MegaHertz bandwith is within reach.
Highly sensitive detection of microwave (MW) fields throughout ultra-wideband spectrum is always an important subject in metrology, electromagnetism and cosmology. Rydberg atomic electrometers, which implement electric field measurements by detecting the disturbance of atomic energy levels, have the potentials to breakthrough the sensitivity and size limits of conventional sensors. However, due to the discrete structure of the energy levels, current measurements can only exhibit high sensitivity at the discontinuous frequencies which correspond to certain transitions. In this work, by implementing energy level modulation of Rydberg atom through Zeeman effect, we achieve continuous highly sensitive MW fields detection within 1-40 GHz ultra-wideband spectrum where the detection sensitivity is roundly below 65 nV cm-1 Hz-1/2, which is 2-3 orders of magnitude lower than that of the state-of-the-art continuous measurement architectures. The proposed method is expected to expand the working bandwidth from MHz to THz and therefore greatly accelerate the practical applications in the areas of radar and electronic reconnaissance. Detecting microwave fields across an ultra-wideband spectrum is crucial for advancements in metrology, electromagnetism, and cosmology. Here, the authors utilize Zeeman effect modulation of Rydberg atoms to achieve continuous, highly sensitive detection from 1-40 GHz, significantly enhancing sensitivity and potentially transforming radar and electronic reconnaissance applications.
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.
Rydberg atom-based microwave electric field sensing has attracted growing interest owing to its inherent advantages, such as absolute calibration, wideband operability, and compatibility with room-temperature devices. A critical bottleneck that limits sensitivity is the inefficient coupling between the Rydberg atoms and the incident microwave field, particularly when detecting weak signals propagating in free space. Here we propose and experimentally validate a scheme that integrates a horn antenna with a resonant microwave cavity to significantly improve this coupling for free-space signal reception in the S-band. Using a two-photon excitation scheme in a cesium vapor cell, we systematically characterize the sensing performance under three configurations: a bare cell, direct cavity injection, and a cavity coupled to a horn antenna that captures free-space microwave signals over a 1 m distance. In the antenna-coupled cavity configuration, we achieve an optimal sensitivity of 2.33 nV/cm/Hz\sqrt{\text{Hz}}Hz​ at the receiving antenna, which corresponds to an enhancement of approximately 17.9 dB compared to the optimized bare vapor cell configuration. Our findings offer a practical and effective route to boost the sensitivity of Rydberg atomic sensors, facilitating their adoption in real-world microwave metrology and wireless communication applications where weak free-space electric fields must be reliably measured.