Two-way optical frequency comparisons at $5\times {10}^{-21}$ relative stability over 100-km telecommunication network fibers

By using two-way frequency transfer, we implement a real-time frequency comparison over a uni-directional telecommunication network of 100 km using a pair of parallel fibers with simultaneous digital data transfer. The relative frequency stability is ${10}^{-15}$ at 1-s integration time and reaches $2\times {10}^{-17}$ at 40 000 s, three orders of magnitude below the one-way fiber instability. We also demonstrate ultrahigh-resolution comparison of optical frequencies with a bidirectional scheme using a single fiber. We show that the relative stability at 1-s integration time is $7\times {10}^{-18}$ and scales down to $5\times {10}^{-21}$. The same level of performance is reached when an optical link is implemented with an active compensation of the fiber noise. The fractional uncertainty of the frequency comparisons was evaluated for the best case to $2\times {10}^{-20}$. These results open the way to accurate and high-resolution frequency comparison of optical clocks over intercontinental fiber networks.

Figure 1

Experimental setups for frequency comparison: (a) two-way unidirectional, (b) two-way bidirectional, and (c) active noise compensated link. AOM, acousto-optic modulator; PC, polarization controller; FM, Faraday mirror; OC, optical coupler; PD, photodiode; PLL, phase lock loop.

Figure 2

Fractional frequency instability derived from data recorded with $\Lambda$ counter and expressed as the modified Allan deviation for (a) one-way fiber noise, (b) two-way unidirectional as reconstructed from data recorded at the two ends, (c) local two-way unidirectional, (d) active noise compensated link, (e) two-way bidirectional, and (f) two-way bidirectional noise floor. The other noise floors are similar and are not shown for the sake of clarity.

Figure 3

Phase noise PSD for the three setups of Fig. 1. 1 s: (a) one-way, (b) free-running fiber noise for the ANC setup, (c) two-way unidirectional, where real-time and postprocessed overlapped themselves, (d) active noise compensation $\left(÷4\right)$, (e) expected ANC $\left(÷4\right)$, and (f) two-way bidirectional.