Machine Learning-Powered Optical Phase Comparison

Fiber link-based optical phase comparison (OPC) is crucial for advancing next-generation optical clock networks. However, it faces significant challenges from phase noise induced by the fiber links due to temperature fluctuations and vibrations, which can obscure the desired phase data. At the same time, cycle slips also occur in such systems when the optical signal has a relatively low signal-to-noise ratio (SNR), which can break the phase continuity during the measurement and ultimately deteriorate the fractional frequency instability and accuracy of the OPC system. To mitigate these issues, we introduce machine learning approaches utilizing long short-term memory (LSTM) and radial basis function (RBF) networks to enhance the short-term and mid-term instabilities, respectively. We setup a 200 km two-way OPC system to verify our approaches, and the results indicate that the LSTM network significantly reduces the white phase noise, with short-term instability nearing the intrinsic phase difference of the two ultra-stable lasers. Additionally, the RBF network effectively compensates for the undesired cycle slips, outperforming other existing methods in improving the mid-term instability. The synergistic application of the LSTM and RBF networks enhances both the short-term and mid-term instabilities, offering a novel solution for restoring the intrinsic phase difference of optical clocks in large-scale fiber networks with large phase noise.