High-Precision Distribution of Highly Stable Optical Pulse Trains with 8.8 × 10−19 instability

The high-precision distribution of optical pulse trains via fibre links has had a considerable impact in many fields. In most published work, the accuracy is still fundamentally limited by unavoidable noise sources, such as thermal and shot noise from conventional photodiodes and thermal noise from mixers. Here, we demonstrate a new high-precision timing distribution system that uses a highly precise phase detector to obviously reduce the effect of these limitations. Instead of using photodiodes and microwave mixers, we use several fibre Sagnac-loop-based optical-microwave phase detectors (OM-PDs) to achieve optical-electrical conversion and phase measurements, thereby suppressing the sources of noise and achieving ultra-high accuracy. The results of a distribution experiment using a 10-km fibre link indicate that our system exhibits a residual instability of 2.0 × 10−15 at1 s and8.8 × 10−19 at 40,000 s and an integrated timing jitter as low as 3.8 fs in a bandwidth of 1 Hz to 100 kHz. This low instability and timing jitter make it possible for our system to be used in the distribution of optical-clock signals or in applications that require extremely accurate frequency/time synchronisation.

In this paper, we demonstrate a new fibre-based distribution system for optical pulse signals. Instead of using traditional electronic devices, we utilise some easily implemented fibre Sagnac-loop-based optical-microwave phase detectors (OM-PDs) to perform all the aforementioned optics-and microwave-related procedures with timing accuracies of several hundred attoseconds. We test our system on a 10-km outdoor fibre link, and the results indicate that the distribution precision overcame the limitation of conventional RF transfer [14][15][16][17][18][19][20][21][22] by achieving a 3.8-fs integrated timing jitter in a bandwidth of 1 Hz to 100 kHz and a 22-fs root-mean-square (rms) timing drift over 72 hours. The residual instability reached the 8.8 3 10 219 level at 40,000 s averaging times, which is quite sufficient for the longterm transfer of the majority of advanced clock standards, such as optical clocks. Therefore, our frequency-distribution technique may provide a very powerful tool for transferring the timing signals of optical clocks without loss of stability. This technique can also be used in the application of facilities which necessarily require highprecision and long-term synchronisation, such as the next-generation of X-ray free-electron lasers.

Results
High-precision stabilisation of a femtosecond MLL. Figure 1a outlines the principles of the high-precision stabilisation of an MLL achieved by locking the laser to a microwave reference via an OM-PD. Stabilisation of an MLL is achieved by phase locking the laser to a stable microwave reference with ultra-high accuracy. Conventionally, the phase locking is achieved by first detecting the phase of the MLL using a photodiode, comparing the phases of the MLL and the reference microwave using a frequency mixer and finally, using the phase-error signal to adjust the length of an intra-cavity piezoelectric transducer (PZT), thereby controlling the phase of the MLL. This technique, however, suffers from shot and thermal noise generated by the photodiode and thermal noise generated by the frequency mixers; it is also limited by the resolution and response time of the PZT. As a result, the accuracy of the stabilisation is limited to tens of femtoseconds. To overcome these limitations, we remove the photodiode and frequency mixer and use an OM-PD for the phase comparison. Moreover, to control the phase of the MLL much more accurately, we introduce a new technique. Both pump modulation and PZT control are applied to ensure long-term, highaccuracy control of the laser phase 28 . More information concerning this technique can be found in Ref. 28 (also see the Methods section).
Using the new stabilisation technique for the MLL, we can successfully phase lock the MLL to a 6-GHz reference microwave signal. The residual phase noise 29,30 of the phase locking is measured to evaluate the performance. Figure 1b presents the measured data. The phase noise reaches-121 dBc/Hz and -145 dBc/Hz at 1 Hz and 100 kHz offset frequency, respectively. By integrating the phase noise in a bandwidth of 1 Hz to 100 kHz, we find an integrated timing jitter of 1.2 fs. With the combination of pump modulation and PZT control and the use of OM-PD, we can archive both high precision and long-term stabilisation performance. The ultra-low timing jitter proves that the optical pulses have been extremely well stabilised to the microwave reference.
Experimental setup for an ultra-stable optical-pulse-train distribution system with fibre stabilisation. The experimental setup for our distribution system with fibre stabilisation is illustrated in Figure 2. A classical round-trip fibre-stabilisation method is used here to compensate for the phase fluctuation induced by acoustic and thermal noise. A 6-GHz microwave signal generated by a commercial RF signal generator (Agilent, E8257D) is used as the reference microwave. Using an RF signal amplifier and a 1-to-3 power splitter, we obtain three identical microwave reference signals with powers of ,25 mW at the local site. One of the microwave signals is used for the stabilisation of the MLL via the OM-PD. The second signal is used to measure the phase fluctuation of the fibre link. The third is used for the out-of-loop measurement. The laser beam generated by the MLL is split into two beams. One beam, with a power of ,10 mW, is phase detected using a reference microwave in an OM-PD to generate an error signal for the phase locking of the MLL. The other beam, with a power of ,30 mW, is fed into a fibre link. The fibre link consists of a motorised optical delay line (ODL), a fast PZT-based optical delay line, a 1.1-km dispersioncompensated fibre (DCF) and an 8.9-km commercial single-mode fibre (SMF).The fibre link is installed in spools and directly exposed to an outdoor environment. The total attenuation of the fibre link is ,7 dB. The optical pulses received at the remote site have durations of less than 100 ps. A 90510 fibre coupler and a back reflector are used to cause 90% of the received optical beam to be reflected back, whereas the remaining10% of the beam is used for RF signal extraction and measurements. The portion of this beam with lower power first passes through an Er-doped fibre amplifier (EDFA) to compensate for the optical loss from the 90510 fibre coupler. The optical pulses then pass through a 50550 fibre coupler. One portion of the beam, with a power of ,27 mW, is used for an out-of-loop performance test that determines the phase difference between the optical pulses and the microwave reference in an out-of-loop OM-PD, whereas the remainder is available to the user for high-accuracy RF signal extraction or optical-optical synchronisation [31][32][33][34][35] .
The 90% of the optical pulse trains that are reflected are received by an optical circulator at the local site. A second EDFA is also used at this location to obtain high-power pulses. The backward pulses are amplified to ,25 mW and fed into an OM-PD to detect the phase fluctuation for a single round trip. The phase-error signal is filtered by a proportional-integral-derivative (PID) module to remove longterm drift and fast noise. Then, the PID-regulated error signal is used to drive the PZT-based optical delay line at a high rate (,1000 times/ s), whereas the motorised ODL is adjusted at a rate of ,1 time/s to ensure that the fibre length drift is within the locking bandwidth of the PZT-based optical delay.
Frequency instability and phase noise of the optical-pulse-train distribution. Figure 3 presents the phase-noise performance of the optical-pulse-train distribution measured at the out-of-loop. As in most studies, the residual phase noise of the distributed pulse timing signal is measured to determine the short-term distribution performance. Figure 3 shows that the phase noise with link compensation reaches -104 dBc/Hz and -140 dBc/Hz at 1 Hz and 100 kHz offset frequency, respectively. By integrating the phase noise in a bandwidth of 1 Hz to 100 kHz, we find a short-term integrated timing jitter of 3.8 fs. The timing jitter reaches sub-10-fs scale. We also test the long-term performance of our system by recording the residual timing drift. Figure 4a presents the timing drift in freerunning loop and fibre link temperature change over a 72-hour period of operation. Figure 4b presents the timing drift in compensated loop. The drift is measured and calculated using a separate OM-PD and a high-accuracy voltmeter (3-Hz measurement bandwidth, 2 samples/s). A 22-fs rms timing drift is observed, while the drift range could achieve as high as 160-ps (peak to peak) (40-ps rms) when the compensation system is turned off. Furthermore, the Allan deviation calculated from the recorded timing-drift data represents the residual instability of the distributed pulse timing signal (filled triangles in Figure 4c). Figure 4c shows that the instability reaches 2.0 3 10 215 and 8.8 3 10 219 for averaging times of 1 s and 40,000 s, respectively (3-Hz measurement bandwidth). This residual instability is even lower than that of the H maser clock 36 or an optical clock 37 . The demonstrated technique in our study can be potentially applicable to more and more stable Sr optical clock.
www.nature.com/scientificreports Discussion In this study, we demonstrate a high-precision fibre-based opticalpulse-train distribution system. In the system, we remove traditional devices, such as photodiodes and microwave mixers, because photodiodes can introduce shot noise, thermal noise and AM-to-PM noise. Instead, we apply several OM-PDs to perform the tasks of MLL stabilisation and fibre-link stabilisation. The OM-PD is constructed based on the principle of the Sagnac loop and is very robust and reliable. Different with the research presented in Ref. 33, we use a different ultra-stability MLL and a new stabilization method to make sure ultra-low noise RF can be received at remote end. Compared with Ref. 21 and 22, we archive a better performance of phase noise and long-term transfer instability. Especially for phase noise and short-term stability, the instabilities are improved by over one order of magnitude.The timing-stabilised pulse trains at the end-station have many applications; for example, they can be used to synchronise with a VCO for RF extraction or an MLL for ultra-low-noise opticaloptical synchronisation. Many alternative electro-optic techniques have been demonstrated for RF extraction 31,32,34,35 and optical-optical synchronisation 2,33 . All these techniques have reached the sub-fs level, which is sufficient for signal synchronisation.
The results of the experiment prove that our study provide a ultralow-noise system for the distribution of optical pulse signals which can achieve accuracy at sub-10-fs scale for short-term performance (1 s) and at 30-fs scale for long-term performance (72 hours) for long-distance (longer than 10 km) transfer via a low-cost SMF link, while the sub-5-fs integrated timing jitter could also be achieved. Compared with other high-accuracy fibre-stabilisation techniques, e.g., the use of periodically poled KTiOPO 4 (PPKTP) single-crystal cross-correlators 2,33 , the OM-PD method is much more easily imple-mented and more robust, with a larger timing-delay detection range and a lower cost.
The demonstrated residual instability of our distribution system is superior to that of optical clocks. This makes it possible to synchronise the timing signal of an optical clock to a remote facility when the optical pulses are stabilised to the optical clock. Especially, with further improvement, the proposed frequency-distribution technique may provide a very powerful tool for transferring the timing signals of most stable Sr optical clocks without loss of stability. Compared with Ref. 40, we did longer distance and lower noise optical-pulse-train distribution, which is more suitable for that of optical clocks. Meanwhile, the system is potentially suitable for use in timing synchronisation for the next generation of XFELs and particle accelerators, various parts of which may need to be distantly located to achieve sufficient accelerating distance while working in tightly synchronised conditions. These facilities are being built throughout the world, although the technologies to satisfy their requirements of extremely high timing-synchronisation accuracy are still under development. The demonstrated technique which can provide sub-10-fs accuracy in short term and 10 219 level in long term is a potential tool for most facilities, while the 10-km distribution distance is also long enough for them. Furthermore, the different harmonics of the pulse trains' repetition rate can be simultaneously extracted into multiple RF signals with different frequencies. This is a valuable feature for microwave extraction at various frequencies. Similar with the system in Ref. 40, the performance of our system is also limited by polarization mode dispersion. In future studies, the techniques proposed in this work could be applied to the distribution of time and frequency signals over free space to reduce the effect.

Methods
The Er-doped fibre MLL. We use a passively nonlinear polarisation rotation (NPR) mode-locked Er-doped fibre as the optical source. The MLL operates in the stretchedpulse regime and has a fundamental repetition rate of 173 MHz. Its 35 th harmonic of repetition rate, 6 GHz, is used for RF signal extraction and phase measurements to provide a high sensitivity. A 40-cm highly doped Er gain fibre with a cumulative anomalous group-velocity dispersion is used, and the remainder of the fibre cavity is constructed using common SMF. To reduce the intra-cavity negative dispersion, we use a space isolator instead of a fibre isolator. By optimising the ratio of the positive dispersion fibre to the negative dispersion fibre, we set the intra-cavity dispersion to the close-to-zero dispersion condition to minimise the timing jitter. The MLL is pumped through a 980-nm/1550-nm wavelength-division multiplexing (WDM) fibre coupler by a 650-mW, 980-nm diode. A polarisation beam splitter, a half-wave   39 . The OM-PD consists of a circulator, a unidirectional high-speed LiNbO 3 phase modulator and a specially designed polarisation-maintaining (PM) fibre Sagnac loop of a short length. When a microwave signal with a frequency that is an integer multiple of that of the laser is applied to the unidirectional phase modulator, the copropagating pulses experience a phase modulation, whereas the counterpropagating pulses do not. The phase of the copropagating pulses is modulated according to the temporal position between the optical pulses and the driving microwave signals. The power difference between the two outputs of the Sagnac loop is proportional to the phase error between the optical pulse trains and the driving microwave signal. A balanced photodetector is used for precise optical-microwave phase detection. The most important feature of the OM-PD is that the implementation of phase detection is completed optically prior to photodetection. Stabilisation of an MLL via both pump modulation and PZT control. The stabilisation of our MLL is based on both pump modulation and PZT control. The principle behind the use of pump modulation to adjust the phase of the MLL is that a change in the intra-cavity optical intensity will lead to linear changes in the refraction indices of both the Er-doped fibre and the SMF. The underlying basis of this principle is that the intra-cavity optics will interact with the Er atoms and the silicon in the cavity based on nonlinear effects, and these effects occur in such a manner that when the optical intensity changes linearly over a very short range, the refraction indices of the two materials will also change linearly 28 . The repetition rate f r of the MLL is determined by the MLL cavity length L and the average refractive index of the cavity n as follows: where c is the speed of light. It can be observed that changing n will also change f r , thereby changing the phase of the laser. Although the range of adjustment is short, the advantage of the pump-modulation method is that the modulation speed and accuracy are greatly improved compared with the use of a PZT alone 28 . Therefore, to achieve long-term and high-accuracy stabilisation, we combine pump modulation and PZT control. Whereas pump modulation is used to achieve fast, high-accuracy stabilisation, long-term stabilisation is ensured by means of adjusting the PZT length. A commercial current supply (Thorlabs, ITC110) is used for the pump modulation, and the PZT (PI, P-840.20) is driven by a 100-V voltage supply and has an adjustment range of 30 mm.
Fibre-link stabilisation using both fast and slow feedbacks. We use both motorised and PZT-based optical delay lines to stabilise the fibre link. The advantage of this method is that the accuracy is very high, and the compensation range is also very large. The PZT-based optical delay line (XMT, 40VS12) is driven by a 150-V voltage supply and has a resolution of 2 fs/V and a compensation range of 200 fs. The motorised optical delay line (General Photonics, MDL-002) has an adjustment accuracy of 1 fs and a large compensation range of 500 ps. It is driven slowly to ensure that the fast drift remains within the compensation range of the PZT-based optical delay line. The stabilisation link and the long fibre link operate in a reciprocal manner, so by simply locking the phase error between the local microwave reference and the backward optical pulse trains to nearly zero, the entire link can be stabilised, ensuring that optical pulses with stable phases are received at the remote site. Furthermore, phase fluctuations induced by optical-intensity noise can be significantly reduced by detecting the near-zero phase differences, as in this way the detections are operated when the in-Sagnac-loop signals are almost orthogonal.