Phase-noise measurements in long-fiber interferometers for quantum-repeater applications

Many protocols for long distance quantum communication require interferometric phase stability over long distances of optical fibers. In this paper we investigate the phase noise in long optical fibers both in laboratory environment and in installed commercial fibers in an urban environment over short time scales (up to hundreds of $\ensuremath{\mu}\text{s}$). We show that the phase fluctuations during the travel time of optical pulses in long-fiber loops are small enough to obtain high visibility first-order interference fringes in a Sagnac interferometer configuration for fiber lengths up to 75 km. We also measure phase fluctuations in a Mach-Zehnder interferometer in installed fibers with arm length 36.5 km. We verify that the phase noise respects Gaussian distribution and measure the mean phase change as a function of time difference. The typical time needed for a mean phase change of 0.1 rad is of order of $100\text{ }\ensuremath{\mu}\text{s}$, which provides information about the time scale available for active phase stabilization. Our results are relevant for future implementations of quantum repeaters in installed optical fiber networks.