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.
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.
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.
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.
The waveguide Fabry-Perot interferometer (FPI) (see, e.g., in Phys. Rev. Lett.113, 243601 (2015)10.1103/PhysRevLett.115.243601 and Nature569, 692 (2019)10.1038/s41586-019-1196-1), instead of the free space's one, have been demonstrated for the sensitive quantum parameter estimations. Here, we propose a waveguide Mach-Zehnder interferometer (MZI) to further enhance the sensitivity of the relevant parameter estimations. The configuration is formed by two one-dimensional waveguides coupled sequentially to two atomic mirrors, which are served as the beam splitters of the waveguide photons to control the probabilities of the photons being transferred from one waveguide to another. Due to the quantum interference of the waveguide photons, the acquired phase of the photons when they pass through a phase shifter can be sensitively estimated by measuring either the transmitted or reflected probabilities of the transporting photons. Interestingly, we show that, with the proposed waveguide MZI the sensitivity of the quantum parameter estimation could be further optimized, compared with the waveguide FPI, in the same condition. The feasibility of the proposal, with the current atom-waveguide integrated technique, is also discussed.
For the precision-based measurements, Mach-Zehnder interferometry is a widely used technique. There are various ways to enhance the precision of Mach-Zehnder interferometer (MZI), e.g., having a non-classical input state is one of the ways to enhance the precision of the phase estimation performed by MZI. The phase estimation performed by MZI is investigated here by considering that the input states of MZI are different combinations of photon added and subtracted squeezed coherent states (PASCS and PSSCS). Using quantum Fisher information, it is shown that the use of PASCS in both the input modes of MZI, provides the most precise estimate of the unknown phase. This system is also analyzed in two different measurement scenarios -- single intensity detection (SID) and intensity difference detection (IDD). Systematic analysis has established that the intensity measurement might not be an optimal measurement scheme for phase estimation in MZI as phase and intensity correspond to non-commuting observables. The impact of the photon loss on the MZI-based phase estimation setup is also studied and it is found that PASCS is robust against photon loss, when the loss in MZI is low.
Improving interferometric phase sensitivity is crucial for high-precision measurements in rapidly developing quantum technologies. The Mach–Zehnder interferometer (MZI) is a versatile tool for analyzing this phenomenon. By splitting and recombining a light beam using beam splitters, the MZI allows for precise phase sensitivity analysis using tools like the quantum Cramér–Rao bound (QCRB) and the quantum Fisher information (QFI). This paper analyzes the phase sensitivity of an MZI in various scenarios using different detection schemes and input states. We compare the single- and two-parameter quantum estimation and their associated QCRB for three phase-shift situations: in both arms; only in the upper arm (asymmetric); and in both arms symmetrically. We then investigate the phase sensitivity under three detection schemes: intensity difference; single-mode intensity; and balanced homodyne. Additionally, we explore the use of Perelomov and Barut–Girardello coherent states, two types of SU(1,1) coherent states, in all scenarios. Notably, we demonstrate that, under optimal conditions, all detection schemes can achieve the QCRB by utilizing SU(1,1) coherent states as input states.
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∘ and unambiguous full 360∘ 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 μm at 5.7 GHz together with a polarization-angle resolution exceeding 0.1∘. 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.