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Review of Scientific Instruments

Fiber-integrated acousto-optic-modulator-based phase-controlled Rydberg atomic electrometer

Taisen Gao, Hongmei Yan, Hao Zhang, Mingyong Jing, Linjie Zhang

Published Jul 1, 2026• 0 citations

Abstract

A Mach-Zehnder interferometer (MZI) provides an effective interferometric readout approach for enhancing the performance of Rydberg-atom-based microwave electric-field sensing. The phase tuning based on a piezoelectric transducer (PZT) relies on mechanical path length modulation, which can limit phase precision, modulation frequency, and the level of system integration. Here, we demonstrate a fiber-integrated MZI architecture in which the interferometric phase is controlled electronically by a pair of double-pass acousto-optic modulators (AOMs). The additional propagation phase accumulated by the frequency-shifted light in an optical fiber enables continuous tuning of the relative phase between the two interferometer arms over a fixed optical path, without using moving components. A frequency adjustment Δf = 9.463 MHz produces a full 2π phase shift, confirming the reproducibility and continuous tunability of the method, with an experimentally measured phase stability at the milliradian level. Based on this interferometric readout, we implement a Rydberg-atom-based microwave electric-field measurement scheme in a room-temperature cesium vapor cell. At the optimized absorption-dominated operating point of Δϕ = π, corresponding to an AOM driving frequency of 93.9 MHz, the interferometric readout improves the measured signal-to-noise ratio by about 4 dB compared with the non-interferometric case. The directly measured electric-field sensitivity at the position of the cesium vapor cell is 4.2×10-6V/m/Hz. Compared with PZT-based schemes, this approach improves interferometric stability and tuning precision, and provides better compatibility with compact and integrated implementations.

DOI: 10.1063/5.0328932

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A Mach-Zehnder interferometer (MZI) provides an effective interferometric readout approach for enhancing the performance of Rydberg-atom-based microwave electric-field sensing. The phase tuning based on a piezoelectric transducer (PZT) relies on mechanical path length modulation, which can limit phase precision, modulation frequency, and the level of system integration. Here, we demonstrate a fiber-integrated MZI architecture in which the interferometric phase is controlled electronically by a pair of double-pass acousto-optic modulators (AOMs). The additional propagation phase accumulated by the frequency-shifted light in an optical fiber enables continuous tuning of the relative phase between the two interferometer arms over a fixed optical path, without using moving components. A frequency adjustment Δf = 9.463 MHz produces a full 2π phase shift, confirming the reproducibility and continuous tunability of the method, with an experimentally measured phase stability at the milliradian level. Based on this interferometric readout, we implement a Rydberg-atom-based microwave electric-field measurement scheme in a room-temperature cesium vapor cell. At the optimized absorption-dominated operating point of Δϕ = π, corresponding to an AOM driving frequency of 93.9 MHz, the interferometric readout improves the measured signal-to-noise ratio by about 4 dB compared with the non-interferometric case. The directly measured electric-field sensitivity at the position of the cesium vapor cell is 4.2×10-6V/m/Hz. Compared with PZT-based schemes, this approach improves interferometric stability and tuning precision, and provides better compatibility with compact and integrated implementations.

We present a broadband and robust Mach-Zehnder interferometer (MZI) with meter-scale arm length, aiming to acquire the full information of an atomic system. We utilize a pre-loading phase shifter as servo actuator, broadening the servo bandwidth to 108 kHz without sacrificing the size of the piezoelectric transducer (PZT) and mirror. An auxiliary laser at 780 nm, counter-propagating with the probe laser, is employed to achieve arbitrary phase locking of the MZI, boosting a phase accuracy of 0.45 degrees and an Allan deviation of 0.015 degrees, which breaks the current record. By utilizing our robust MZI, the measurement accuracy of atomic system can be theoretically predicted to improve by 2.3 times compared to the most stable MZI in other literatures. In addition, we also demonstrate the sensitivity improvement in imaginary part and real part of the susceptibility in virtue of the completed interferometer, which exhibits tremendous potential in atom-based measurement system.

High-precision phase measurement of microwave fields underpins a wide range of applications, including wireless communications, distributed radar, plasma diagnostics, and antenna metrology. Existing Rydberg-atom-based approaches, however, often face trade-offs among phase resolution, measurement range, and system complexity. Here we demonstrate a Rydberg-atom-based microwave Mach-Zehnder-type interferometer using a dual-local-oscillator configuration. The two local oscillators establish two coherent interferometric pathways in the Rydberg medium. Their coherent mixing with the signal field produces an interferometric intermediate-frequency output governed by a phase-to-intensity transfer characteristic that enables critical-point enhancement. This scheme supports direct phase retrieval with a resolution exceeding

0.1^\circ

and unambiguous full

360^\circ

phase coverage with the reconfigurable dual-LO architecture. Moreover, near the critical interference point, the system exhibits a sharply enhanced phase-to-amplitude transduction, where weak amplitude variations are converted into pronounced phase responses, yielding a sensitivity enhancement exceeding 25 dB. Besides, the same interferometric transfer mechanism enables microwave propagation-distance and polarization metrology, achieving a propagation-distance precision below 20

μ

m at 5.7 GHz together with a polarization-angle resolution exceeding

0.1^\circ

. This approach eliminates the need for complex optical configurations and lock-in detection, providing a simple, scalable, and reconfigurable Mach-Zehnder-type quantum microwave interferometry framework for multifunctional high-precision microwave metrology.

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.

The electric field measurement sensitivity based on the Rydberg atomic vapor cell has great theoretical advantages over traditional dipole antennas. We combine the Rydberg atomic heterodyne receiver and the Mach-Zehnder interferometer (MZI) with high phase detection sensitivity to evaluate the system reception sensitivity based on the transmitted laser phase shift. Numerical results show that the probing laser frequency detuning can improve the system detection sensitivity. It also shows that the phase-based readout approach of heterodyne Rydberg atomic receiver based on MZI can achieve better sensitivity than the intensity-based readout approach of heterodyne Rydberg atomic receiver.

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.

Atomic heterodyne dressed by a local oscillator resonant with Rydberg transitions allows high sensitivity and robust phase measurement of a microwave electric field, but it is typically limited to detection of discrete frequencies within the narrow bandwidth of Rydberg transitions. Here we demonstrate an atomic heterodyne scheme for continuous-frequency electric field measurement based on multilevel Rydberg atoms in a room-temperature vapor cell. Driven by two off-resonant microwaves acting as a tunable local oscillator field, the heterodyne receiver can retrieve the amplitude, phase, and frequency information of signal microwave in a continuous frequency band. In our experiment, the receiver achieves an electric field sensitivity of up to $1.5\phantom{\rule{0.2em}{0ex}}\ensuremath{\mu}\mathrm{V}\phantom{\rule{0.2em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}\phantom{\rule{0.2em}{0ex}}{\mathrm{Hz}}^{\ensuremath{-}1/2}$, 80-dB linear dynamic range, and over 1 GHz of continuous frequency range. We also demonstrate the reliable reception of continuously tunable phase-modulated carriers in the digital communication. This work will facilitate the application of atomic heterodyne in the areas such as radar technique, radio monitoring, and radio astronomy.