Two-way optical phase comparison at 10−21 level

This works demonstrates an improved local two-way optical phase comparison method without the requirement of synchronization. Based on this scheme, we implement a real-time frequency comparison over a bi-directional 50-km fiber spool. The achieved relative frequency stability is 1.2E-16 at 1 s integration time and reaches 1.3E-21 at 40,000 s.