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 $\mu \text{s}$). 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 $100\mu \text{s}$, 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.

Figure 1

Creation of entanglement by single photon detection. (a) The two quantum memories (QMs) are placed in the arms of a balanced Mach-Zehnder interferometer and excited with a common laser. The emitted fields are combined at a beam splitter, which erases information about the origin of the emitted photon. The detection of a single photon with detector after the beam-splitter projects the remote QM into an entangled state. In order to generate entanglement, interferometric stability must be preserved for the duration of the experiment. (b) Sagnac configuration. The excitation pulses for each QM are first reflected at the other QM, using, e.g., optical switches. In this way, the excitation lasers for the two systems and the emitted photons travel the same path in a counterpropagating way. Straight lines indicate excitation lasers and wavy lines indicate emitted fields [6].

Figure 2

Sagnac interferometer: experimental setup. A rectangular laser pulse created by amplitude modulator AM is split at the coupler and phase is applied to one of the pulses by the phase modulator PM. The resulting interference signal is detected by detector D and oscilloscope OSC. ${\text{PC}}_{\text{i}}$ denotes polarization controllers.

Figure 3

(Color online) Example of interference fringe for a Sagnac interferometer of 36.5 km in the telecom network. The solid curve is a sinusoidal fit which gives the visibility 99.2%. The time to scan a fringe is about 10 min, which shows that fast phase fluctuations do not degrade the visibility significantly in this case.

Figure 4

(Color online) Visibility as a function of fiber length for the Sagnac setup. The decrease of visibility with increasing fiber length is obvious as well as the qualitative agreement between laboratory and telecom measurements. High visibilities confirm the robustness of the Sagnac interferometer setup. For the length 71.5 km, the difference between the day (more phase noise) and night (less phase noise) values of visibilities in the telecom network is worth noting (the night measurements have been performed between 11 p.m. and 1 a.m.). Each point in the graph is the average of a set of interference fringes and the errors are the standard deviations.

Figure 5

(Color online) Mach-Zehnder interferometer: experimental setup. Dashed lines denote the telecom fibers. The length difference between the two branches of interferometer was a few cm, i.e., much less than the coherence length of the laser. We used the polarization controller $\text{PC}$ in order to optimize the signal at the output. The resulting interference signal is detected by detector D and oscilloscope OSC.

Figure 6

(Color online) An example of raw measurement of intensity variation as a function of time for the 36.5 km Mach-Zehnder interferometer in the telecom network.

Figure 7

(Color online) Dependence of the mean phase change $\Delta \phi$, resulting from the Gaussian distribution (see Fig. 8), on time difference $\tau$ as described in Eq. (6). An example for 36.5 km Mach-Zehnder interferometer in the telecom network is shown. Here the time corresponding to the phase change $\Delta \phi =0.1\text{rad}$ is ${\tau }_{0.1}=122\mu \text{s}$.

Figure 8

(Color online) The distribution of the phase noise in the 36.5 km Mach-Zehnder interferometer in the telecom network. The distribution is shown for the time of propagation, i.e., $\tau =182\mu \text{s}$. One can see that the fit [Gaussian distribution Eq. (2)] corresponds well to the observed results. The average phase change $\Delta \phi$, plotted in Fig. 7, is proportional to FWHM of the phase-noise distribution.

Figure 9

(Color online) Time intervals needed for phase change 0.1 rad in the 36.5 km Mach-Zehnder interferometer in the telecom network. The first set of measurements consists of points which were measured in the span of 12 days. The second set was obtained during a single day. All measurements are compatible and show the signal with less phase noise during the night (around 3 a.m.) than during the day.

Figure 10

(Color online) Diffusion coefficients in the laboratory and telecom network. The diffusion coefficients measured in the laboratory yield all the same value (within the error) as expected from theory. For the 71.5 km interferometer in the telecom network, there is, however, a significant difference between the measurements during the day (more phase noise, i.e., larger coefficients) and night.