Extended Data Fig. 5: Stabilizing the relative path length between two remote quantum network nodes.

a, Simplified optical setup and pulse sequence. The stabilization laser, L2, at 987.9 nm measures the relative optical path phase. This is achieved using AOM 2, 3 and 4 to generate 10 μs long pulses with a 2π × 5 MHz frequency difference that travel along the two separate device paths with distances L₁ and L₂. AOM 9 routes the pulses to an avalanche photodetector (APD) which detects the resulting beat-note phase, thereby measuring the optical path phase difference, ΔΦ. After a delay of 30 μs, the optical phase is probed using L1 at 984.5 nm using pulses generated by AOM 1, 3 and 4 with a 2π × 26 MHz frequency difference. However, this time, the driving phase of AOM 3 is adjusted to correct the optical phase difference by an angle Θ (defined in Methods), thereby counteracting phase drift and rendering the optical phase constant between consecutive probe periods. The optical phase during each probe period is measured using the APD. b, With the phase correction turned off (Θ = 0), we measure the optical phase stability by plotting the RMS difference between values of ΔΦ in probe periods of varying separation, yielding a 1/e phase correlation timescale of ≈ 282 μs. c, The resulting Fourier transform of the optical phase noise with the correction, Θ, turned off and on are shown in the top and bottom panels, respectively. d, With the phase stabilization turned on, a normalized histogram of the optical phases during the probe periods yields a Gaussian distribution with standard deviation 0.037 × 2π rad, corresponding to an entangled state fidelity limitation of \({\mathcal{F}} < 0.987\). e, The probe pulses are attenuated to the single-photon level and detected using a superconducting nanowire single photon detector (SNSPD), the resulting contrast of 0.944 verifies that SNSPD timing jitter does not contribute significantly to these measurements.