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

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 $\mu$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.