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arXiv:2608.13222

Critical Microwave Mach-Zehnder-Type Interferometry with Dual-LO Rydberg Atoms

Jun-Rong Chen, Guo-Qing Qin, Peng-Fu Liang, He Hao, Ming-Min Zhao, Ling-Qiang Meng, Gui-Lan Li, Min-Jian Zhao, Bin-Bin Wei, Hao Tian

physics.atom-phquant-phSubmitted Aug 13, 2026• Announced Aug 14, 2026• 0 citations
arXivHTMLPDF

Abstract

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.

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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∘0.1^\circ0.1∘ and unambiguous full 360∘360^\circ360∘ 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 μμμm at 5.7 GHz together with a polarization-angle resolution exceeding 0.1∘0.1^\circ0.1∘. 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.
Although Rydberg atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum-interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full 360∘^\circ∘ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four phase-state signal broadcast on the atoms. Our approach opens up new sensing schemes and provides a clear path towards all-optical Rydberg atom sensing implementations.
Although Rydberg-atom-based electric field sensing provides key advantages over traditional antenna-based detection, it remains limited by the need for a local oscillator (LO) for low-field and phase-resolved detection. In this work, we demonstrate that closed-loop quantum interferometric schemes can be used to generate a system-internal reference that can directly replace an external LO for Rydberg field sensing. We reveal that this quantum interferometrically defined internal reference phase and frequency can be used analogously to a traditional LO for atom-based down-mixing to an intermediate frequency for lock-in phase detection. We demonstrate that this LO-equivalent functionality provides analogous benefits to an LO, including full ${360}^{\ensuremath{\circ}}$ phase resolution as well as improved sensitivity. The general applicability of this approach is confirmed by demodulating a four-phase-state signal broadcast on the atoms. Our approach may open up new sensing schemes and although the present implementation still uses an auxiliary rf field, we provide a clear path toward all-optical Rydberg-atom sensing implementations by discussing several schemes that allow for all-optical rf phase detection without the need for an external rf LO field.
Measurement sensitivity is crucial for the practical application of Rydberg atomic microwave superheterodyne receiver systems in communication, radar, and navigation. Based on laser-atom-microwave interaction mechanisms, the influence of laser powers and local-oscillator (LO) microwave field intensity on measurement sensitivity is systematically studied in this paper. Measurement sensitivity is analyzed through electromagnetically induced transparency (EIT) spectral characteristics, specifically EIT amplitude and full-width-half-maximum (FWHM),larger amplitudes and narrower FWHM indicate improved signal-to-noise ratios. For a 60D-state Rydberg atomic system with fixed probe and coupling laser beam waists (800 µm and 875 µm), optimal parameters are determined: probe laser power of 60 µW(Rabi frequency: 2π×7.02 MHz), coupling laser power of 40 mW (Rabi frequency: 2π×0.66 MHz), and LO microwave Rabi frequency of 2π×8.34 MHz. Experimental results demonstrate a 4.6 dB sensitivity enhancement, advancing from −137.5dBm/Hz to −142.1 dBm/Hz at 3.21 GHz microwave field. This improvement is attributed to precise alignment of laser-atom and microwave-atom interactions, bridging the gap toward quantum sensitivity limits.
A long baseline phase-coherent microwave receiver is demonstrated using a remotely interrogated cesium Rydberg atom sensor over an 8 m free-space optical link. A 3.989 GHz local oscillator (LO) is intensity-modulated onto an 852 nm optical probe and recovered remotely for atomic superheterodyne detection. A 509 nm coupling laser establishes a Rydberg electromagnetically induced transparency (EIT) system addressing the 6S1/2 to 6P3/2 to 56D5/2 ladder, with microwave coupling to 57P3/2. A test signal offset by 5 kHz generates an optically detected intermediate-frequency (IF) response returned to the reference station for centralized coherent acquisition. This eliminates independent remote oscillators, electronic IF acquisition, and distributed clock synchronization. Over 10 min, the differential phase between remote and local reference exhibits a standard deviation of 0.476 deg and a minimum overlapping phase Allan deviation of 0.048 deg at approximately 200 s averaging. Following optical-link interruption, the differential phase recovers without recalibration, with a measured pre- and post-interruption difference of 0.01 deg. These results demonstrate phase coherent remotely interrogated atomic microwave reception with reduced instrumentation, supporting future distributed interferometry, multistatic radar, and coherent sensor arrays.
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.
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.