Real-Field Hong-Ou-Mandel Interference of Indistinguishable Coherent Photons via Long Optical Injection-Locking over 50 km Fiber

Abstract: Measurement-device-independent quantum key distribution (MDI-QKD) has garnered significant attention for its potential to enable security-loophole-free quantum communication. Successful MDI-QKD protocols rely on performing a two-photon Bell-state measurement at an intermediate node, with a high-visibility Hong-Ou-Mandel (HOM) interference pattern between two independent coherent photons being crucial. In this study, we present a novel approach for developing indistinguishable coherent photon sources over 50 km of optical fiber in a real-world setting. We introduce the long optical injection-locking (long-OIL) technique, which enables frequency locking between two long-distance coherent photons beyond the coherence length of the master laser. Using the long-OIL technique, we achieved time-resolved HOM interference with a visibility of 48(2)%, approaching the theoretical 50% limit for two independent continuous-wave coherent photons. Our results demonstrate that the long-OIL platform is a promising solution for MDI-QKD with repeaterless secret key capacity.