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Optica

Enabling phase stabilization of quantum networks via displacement-enhanced photon counting

M. V. Jabir, Daehyun Ahn, N. Fajar R. Annafianto, Ivan A. Burenkov, A. Battou, Sergey Vladimirovich Polyakov

Published Mar 21, 2025• 8 citations

Abstract

Optical phase stabilization, tracking, and locking in long fiber links are pivotal for the functionality of many communication protocols and distributed sensors. However, conventional phase stabilization methods use strong optical probe signals that may contaminate and destroy fragile quantum signals propagating in the same fiber link. Here, we experimentally demonstrate phase locking of fiber spools up to 100 km and over 120 km deployed optical communication link using faint coherent states with an average of just photons per second detected at the receiving detector as a probe signal. The power spectral density of phase noise, integrated from 1 Hz to 50 kHz, yields an excess rms phase noise of 110 mrad (corresponding to timing jitter below 0.09 fs) for a 100 km fiber spool and 140 mrad (corresponding to rms timing jitter below 0.12 fs) for deployed fiber. The displacement-enhanced measurement protocol that we employ for phase stabilization yields Fisher information that is greater than that of homodyne and heterodyne measurement protocols for fiber links longer than 100 m and, therefore, exceeds the canonical shot noise limit of accuracy. By implementing this stabilization strategy with a 50% duty cycle, we enable time-division multiplexed faint light and quantum payloads to coexist within the same communication channel.

DOI: 10.1364/optica.540759

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Establishing phase-stable links over long-distance fiber infrastructure is crucial for phase-sensitive networking protocols. Faint-light and quantum networking present an additional challenge of keeping the payload channel dark. In this work, we present a scalable solution for phase stabilization of dark metropolitan-scale fiber links using wavelength-division-multiplexing (WDM). We implement a combined feed-back and feed-forward phase stabilization for a target channel by combining error signals from two separate reference channels over a 120 km deployed aerial fiber link. Residual phase noise in the dark target channel is reduced by two orders of magnitude compared to a WDM feedback-only strategy and reaches subfemtosecond root-mean-square (RMS) values. Observed cross-talk photon noise is ≈500 photons per second. Potentially, several dark target channels can be phase-stabilized without injecting additional reference channels. This solution is a major step toward scalable metropolitan-distance quantum networking applications, including single-rail entanglement distribution, quantum key distribution, coherent clock transfer, and coherent optical communication.

We demonstrate the distribution of single-photon-level pulses from a mode-locked laser source over a phase-stable fiber link, achieving an optical timing jitter of less than 100 as over 10 minutes of data accumulation. This stability enables a fidelity greater than 0.998 between two stabilized 2.1 km long deployed fiber links. Building on time and frequency metrology techniques traditionally used for high-stability optical atomic clock signal distribution, we use time and frequency multiplexing to achieve an isolation of quantum and classical channels of 8×10 10 . Our results mark a necessary step towards scalable, high-rate quantum networks with a provable quantum advantage.

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it, which is a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.

To study channel-to-channel phase drift in broadband links, we implement a dense wavelength-division multiplexing (DWDM)-based phase stabilization testbed. We systematically study phase stabilization in adjacent DWDM channels of metropolitan-scale fiber links. A 25GHz frequency comb with a sub-Hz laser generated two DWDM-separable frequency components at 1550.12 nm and 1549.32 nm as signal and reference channels. One of these components is stabilized using a phase-locked-loop circuit, while the phase noise in the other channel is monitored. We demonstrate a significantly reduced phase noise in the monitored channel over a 100 km link. This approach mitigates phase noise in wavelength-detuned long-distance network links while wavelength-separating the classical probing signal and reducing its impact on the quantum channel through Raman scattering in a long fiber.

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multistep quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of ∼1 MHz and a duty cycle ≤6.5%, the system maintains interferometric visibility >97% over fiber links of 10 km and 100 km. This phase control yields long-lived ion-ion entanglement with parity contrast exceeding 85%, enabling device-independent quantum key distribution with finite-size security analysis over 10 km and a positive asymptotic key-rate over 100 km. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it-a fundamental requirement for quantum repeaters. This Letter establishes a robust and scalable foundation for practical long-distance quantum networks.