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arXiv:2407.16433 · Physical Review Applied

Arbitrary-phase locking of fiber unbalanced Mach-Zehnder interferometers

Ruiyang Chen, Yi-Han Luo, Jinbao Long, Junqiu Liu

Published Nov 19, 2024• 5 citations

Abstract

Optical interferometers are extensively used in fundamental physics studies, gravitational wave detection, quantum metrology, topological photonics, and quantum information processing. Fiber-based interferometers are compact, mechanically robust, and cheap, and thus are ubiquitously deployed. However, the optical phase in fiber interferometers is sensitive to ambient perturbation, resulting in compromised phase-sensing precision. Therefore, phase control, shifting, and stabilization of fiber interferometers are essential. Methods to create stable interference patterns and to lock a fiber interferometer at arbitrary phase have been shown, which however are sophisticated, bulky, and delicate, preventing wider application in harsh environments outside laboratories or in space. Here we demonstrate an innovative method for arbitrary-phase locking of fiber unbalanced Mach-Zehnder interferometers. Compared with existing methods, our method is much simpler. We showcase the preparation and characterization of a narrow-band, energy-time-entangled photon state generated in integrated nonlinear microresonators, where two-photon interference visibility reaches 0.993(6). Our method constitutes a critical building block for photonic quantum networks, and is useful to emerging single-photon interference in curved space-time that facilitates exploration of the interface of quantum mechanics and general relativity.

DOI: 10.1103/physrevapplied.22.054051

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Optical interferometers are extensively used in fundamental physics studies, gravitational wave detection, quantum metrology, topological photonics, and quantum information processing. Fiber-based interferometers are compact, mechanically robust, and cheap, and thus are ubiquitously deployed. However, the optical phase in fiber interferometers is sensitive to ambient perturbation, resulting in compromised phase-sensing precision. Therefore, phase control, shifting, and stabilization of fiber interferometers are essential. Methods to create stable interference patterns and to lock a fiber interferometer at arbitrary phase have been shown, which however are sophisticated, bulky, and delicate, preventing wider application in harsh environments outside laboratories or in space. Here we demonstrate an innovative method for arbitrary-phase locking of fiber unbalanced Mach-Zehnder interferometers. Compared with existing methods, our method is much simpler. We showcase the preparation and characterization of a narrow-band, energy-time-entangled photon state generated in integrated nonlinear microresonators, where two-photon interference visibility reaches 0.993(6). Our method constitutes a critical building block for photonic quantum networks, and is useful to emerging single-photon interference in curved space-time that facilitates exploration of the interface of quantum mechanics and general relativity.

We experimentally demonstrate stable and user-adjustable single-photon interference in a 1 km long fiber-optic Mach-Zehnder interferometer, using an active phase control system with the feedback provided by a classical laser. We are able to continuously tune the single-photon phase difference between the interferometer arms using a phase modulator, which is synchronized with the gate window of the single-photon detectors. The phase control system employs a piezoelectric fiber stretcher to stabilize the phase drift in the interferometer. A single-photon net visibility of 0.97 is obtained, yielding future possibilities for experimental realizations of quantum repeaters in optical fibers and violation of Bell's inequalities using genuine energy-time entanglement.

We report a single-photon Mach-Zehnder interferometer stabilized to a phase precision of 0.05 degrees over 15 hours. To lock the phase, we employ an auxiliary reference light at a different wavelength than the quantum signal. The developed phase locking operates continuously, with negligible crosstalk, and for an arbitrary phase of the quantum signal. Moreover, its performance is independent of intensity fluctuations of the reference. Since the presented method can be used in a vast majority of quantum interferometric networks it can significantly improve phase-sensitive applications in quantum communication and quantum metrology.

Recent advances in quantum photonics have enabled increasingly robust protocols in optical phase estimation, achieving precisions beyond the standard quantum limit and approaching the Heisenberg limit. While intrinsic losses hinder the realization of unconditional super-sensitivity, reaching quantum advantage, defined as sensitivity surpassing that of any classical counterpart with identical resources, remains achievable. Here we experimentally demonstrate such an advantage using a fully fibered Mach-Zehnder-type interferometer operating at telecom wavelengths, free of post-selection. The scheme relies on the conversion of polarization-entangled photon pairs, a degree of freedom commonly favored for experimental convenience, into energy-time entanglement, which is particularly well suited for scalable fiber-based sensors. All system imperfections, including asymmetric losses and detector inefficiencies, are accounted for in the Fisher information analysis, yielding a measured quantum advantage of 10%. This result highlights the practicality of compact, alignment-free quantum interferometers for real-world sensing applications.

By using photons to carry quantum information, optical quantum information technology plays an essential role in quantum communication, quantum metrology, and linear optical quantum computing. In recent years, the unbalanced fiber interferometer has been widely applied in preparing, manipulating, and measuring photon qubits. However, the unbalanced fiber interferometer based on fiber devices is sensitive to the environment's thermal, mechanical, and acoustic noise. Thus, phase stabilization based on feedback control is essential in utilizing an unbalanced fiber interferometer. The existing phase stabilization methods typically employ a reference laser combined with optoelectronic detection, thus introducing additional noise to photon qubits. In this paper, we propose and demonstrate a feedback control method to stabilize a phase in an unbalanced fiber interferometer by combining weak coherent reference light and single photon counting. Using theoretical analysis, we realized the phase stabilization of an unbalanced fiber Michelson interferometer with an arm-length difference of about 1 m. The results showed that the jitter of the stabilized phase is less than 0.042 rad, while the visibility of single-photon interference fringes is higher than 99%.

Quantum mechanics and general relativity are the foundational pillars of modern physics, yet experimental tests that combine the two frameworks remain rare. Measuring optical phase shifts of massless photons in a gravitational potential provides a unique quantum platform to probe gravity beyond Newtonian descriptions, but laboratory-based interferometers have not yet reached the sensitivity needed to access this regime. Here, we report the realization of a 50-km table-top Mach-Zehnder fiber interferometer operating at the single-photon level, achieving a phase sensitivity of

4.42\times10^{-6}

rad root-mean-square (RMS) within the frequency range of 0.01 Hz to 5 Hz. We demonstrate that this sensitivity is sufficient to resolve a phase-shift signal of

(6.18 \pm 0.44)\times10^{-5}

rad RMS at 0.1 Hz, associated with a modulated gravity-induced signal. Our results establish a milestone for quantum sensing with large-scale optical interferometry, demonstrating the capability to detect gravitational redshifts in a local laboratory, thereby paving the way for testing quantum phenomena within general relativistic frameworks.

Fiber-optic sensors enable high-sensitivity measurements of various physical parameters. Here, we demonstrate a quantum-enhanced interrogation of an all-fiber-optic Fabry-Perot resonator, employing entangled two-photon interference to probe directly strain-induced optical phase shifts. The resonator is interrogated by a narrow-linewidth laser that is frequency-locked to its resonance mode, thereby exploiting the cavity's inherent sensitivity to variations in the fiber length. To access the phase fluctuations transferred to the interrogation field due to external perturbations on the sensor, we implement an in-fiber Mach-Zehnder interferometer readout. This configuration allows the sensor to operate both with classical coherent light and with entangled photon pairs generated via spontaneous parametric down-conversion. Harnessing two-photon entangled states corresponding to an N = 2 NOON state, we experimentally demonstrate a reduction of the measurement noise below the standard quantum limit. These results provide clear evidence of the quantum advantage in enhancing fiber-optic sensors under practical constraints on optical power.