At present, the accuracy of the optical clock has reached the 10⁻¹⁹ level^[1,2]. Internationally, there is discussion about redefining the time unit “second” using optical clocks in the future. However, the ability to transfer time and synchronize it determines the limits of time and frequency for the application of optical clocks. Building high-precision time and frequency transfer systems has always been a hot topic^[3].

Thanks to such factors as low attenuation, high reliability, and great potential for phase noise cancellation of optical fiber transfer, time transfer over fibers (TTOF) technology has emerged and become one of the globally recognized high-precision time transfer technologies. High-precision fiber-optic time transfer technology has a wide range of applications in the areas of fundamental physics research and engineering technology, such as VLBI, optical clock comparison, and deep-space exploration^[4–8]. Therefore, many research teams have implemented both in laboratory fibers and in field telecom fiber links^[9–21].

It has been demonstrated over a 50 km single-fiber and same-wavelength (SFSW) time transfer over branching fiber-optic networks with a synchronous time division multiple access (TDMA)^[22]. The experimental results show that the stabilities of better than 45 ps@1 s and 10 ps@1 d can be achieved. The expanded uncertainty is calculated at 103 ps.

The authors’ research group previously reported on time transfer over a 1085 km telecom fiber link in 2021, achieving a time transfer instability of 9.2 ps@1 s and 5.4 ps@40,000 s^[23]. Subsequently, in 2023, it successfully implemented high-precision time transfer over an 1839 km fiber loop back link, with time transfer stabilities of 6.5 ps@1 s and 4.6 ps@40,000 s by the authors’ group^[24].

In the laboratory, the TTOF demonstration fibers have been extended to cover a 2000 km distance. Remarkably, the stabilities of $<89\mathrm{ps}@1\mathrm{s}$ and $23\mathrm{ps}@{10}^5\mathrm{s}$ have been achieved^[25]. However, the indicators of this research cannot meet the requirements of the onsite foundation “High Precision Ground-based Time Service System” projects of the authors’ group.

The current study builds upon these advancements, leveraging the proliferation of fiber communication networks and the “High Precision Ground-based Time Service System” project, a significant national scientific initiative in China. In this paper, we demonstrate the achieved time transfer performance over such a 2061 km fiber link. The time transfer performance was evaluated. The result showed time stability of 5.5 ps@1 s and 1.1 ps @100,000 s, which outperformed that shown in our previous publication^[24]. The results are, to our knowledge, a record for the real-field test of the time transfer in 2000 km-level fiber links. We have thus validated an optical fiber time transfer system that operates with enhanced accuracy over extended distances, a crucial milestone for the establishment of a national fiber-optic time service network.

The layout of the fiber link, stretching between Shaanxi and Hubei provinces, is depicted in Fig. 1. It originates from the National Time Service Center (NTSC) at the Lintong campus in Xi’an, traverses six relay stations in Shaanxi (Hangtiancheng, Shuniulou, Lantian, ShangLuo, Shanyang, and Manchuanguan) and nine in Hubei (Yunxi, Shiyan, Wudangshan, Gucheng, Xiangyang, Zaoyang, Suizhou, Yunmeng, and Zhangdian). The system returns to Xi’an via a parallel fiber, completing the measurement and comparison. The system comprises 31 devices, with 29 relay/download devices installed across 15 relay stations and one local and one remote device at the Xi’an station. Each relay station between Xi’an and Yunmeng is equipped with two relay/download devices, while the Zhangdian station has a single device.

In this paper, based on single-fiber and two-wavelength time transfer (SFTWTT) over a 2061 km field fiber loop-back link networks, a synchronous wavelength-division and time-division multiplexing access (WD-TDMA) method was implemented. This system utilizes wavelength-division multiplexing to avoid the impact of backscatter. The time-division multiplexing is adopted to enable multiple bidirectional comparisons between the local and remote devices to improve accuracy.

The architecture of the transfer system of the local device and the remote device is delineated in Fig. 2. The local device receives the standard time-frequency signals in the forms of 1 PPS, 10 MHz of the clock (UTC-NTSC). The local device receives 1 PPS and 10 MHz frequency, which outputs from the time reference source (UTC-NTSC). The 10 MHz frequency is multiplied to 125 MHz by a low phase noise frequency multiplier based on a digital phase-locked loop (PLL), which is one of the differences from the device of the authors’ group^[24]. Then, the 1 PPS and 125 MHz frequency are encoded into optical signals for downlink fiber transfer with a laser diode over the wavelength of 1549.32 nm (C35) combining a dense wavelength-division multiplexer. The local device detects the uplink transfer optical signal and decodes the carried 125 MHz frequency signal with a laser diode over the wavelength of 1548.51 nm (C36). At the same time, by calculating the time interval count (TIC), the time delay related to the reference is extracted and fed into the encoder for processing.

The relay/download devices are used to detect and receive optical signals from the uplink (downlink) fiber link. And complete 1 PPS and 10 MHz regeneration of the optical signals occurs before forwarding them to the downlink (uplink) fiber link.

Time-division multiplexing access is adopted to enable multiple bidirectional comparisons between the local and remote devices to improve accuracy. The timing signal of the local device is broadcast to all relays or remote devices through the fiber-optic network. Each relay or remote node transfers back to the local device according to the predetermined time slots. All nodes return within 200 ms, and each node achieves five bidirectional time comparisons with the local device node within 1 s. The remote device corrects for fiber transfer delays using a combination of a TDC, a microcontroller unit (MCU), and frequency regeneration modules. Then the remote device detects the optical signals from the downlink fiber transfer and outputs 1 PPS, 10 MHz frequency. Comparing the 10 MHz transferred from the local device with the 10 MHz of a low-phase noise at the remote device, a frequency phase adjustment of $\phi 1$ is obtained. Controlling it through the MCU achieves frequency synchronization; this is called frequency regeneration. The time regeneration is divided into frequency signals based on phase stability and synchronization.

Compare the 1 PPS generated by time regeneration with the 1 PPS transferred by the local device through TDC to obtain $\phi 2$. Then use a phase shifter to obtain synchronized 1 PPS. Similarly, the 10 MHz frequency signal at the remote device is converted to 125 MHz by a low-phase noise frequency multiplier based on a digital PLL. The 1 PPS and 10 MHz frequency signals obtained and output by the remote device have been synchronized.

Meanwhile, to further improve the performance of the whole system, each device was designed with high-precision multipoint measurements and subjected to temperature stabilization. Therefore, a precision temperature control unit is added to each device. Each core board of the device has undergone precise five-point temperature control. We collected the four corners and midpoints of the board to achieve temperature stability control. The precision temperature control module calculates the error by collecting real-time temperature values and comparing them with the set temperature values. The error amount is then calculated through digital PID to determine the heating power correction amount. The specific software workflow is shown in Fig. 3.

Based on the requirements and impact of actual environmental temperature, we have evaluated and selected a temperature of 40.3°C, which can make the overall system stable. During the 136,351 s monitoring period, the measured peak-to-peak temperature fluctuations remained within a range of $40.28°\mathrm{C}\pm 0.15°\mathrm{C}$, as is shown in Fig. 4.

Prior to installation, each device’s additional time delay was precalibrated to the picosecond level. The asymmetric delay caused by dispersion related to wavelength differences between lasers can be automatically calibrated to improve accuracy.

The SFTWTT system’s temperature sensitivity was assessed by subjecting the local and remote devices to a temperature-controlled environment ranging from 15°C to 55°C. When the temperature stabilization function is turned off, it is enlarged to 230 ps. The device before temperature control changed 40°C, with a corresponding phase change of 230 ps. The device before temperature control changed 40°C, as is shown in Fig. 5, with a corresponding phase change of 230 ps. Therefore, the corresponding rate is 5.75 ps/°C. When temperature stabilization is enabled, the measurement time difference experienced remains constant at $\pm 25\mathrm{ps}$. This demonstrates that the new scheme has increased long-term stability compared to the previous scheme.

The performance of the 1 PPS and 10 MHz frequency transfer system over 2061 km was effectively evaluated by measuring the time difference between the local device’s input signals and the remote device’s output signals, synchronized to a common clock. The phase difference of the 10 MHz signals and the time difference of the time signals between the local device and remote device in the Lintong station are measured by a phase noise tester (53100 A) and a time interval counter (SR620), respectively.

The SFTWTT is also designed with the function of timing for a certain period to avoid fiber interruption using a highly stable crystal oscillator. The crystal oscillator used is 8 × 10⁻¹³, with an aging rate of $\le \pm 0.5\mathrm{ppb}/\mathrm{day}$. The experiment in Fig. 6 was disconnected from the 440th point. After 3 min, it drifted to 100 ps. The actual data formula for crystal oscillator aging and drift is consistent with Eq. (1). The system returned to normal after 50 s when connecting the fiber optic at the 900th point. The system has time-holding capability, avoiding phase jitter caused by transient changes in the fiber phase. This formula describes the variation of punctuality accuracy over time, $$\text{Timing}\text{Accuracy}=\text{Initial}\text{Accuracy}\times \mathrm{T}1+0.5\times \text{Aging}\times ({\mathrm{T1}}^2).$$(1)

Initial accuracy is the initial level of accuracy. ${\mathrm{T}}_1$ is the time that has passed. Aging is the aging coefficient that reflects the decay of the system over time.

The time difference measurement was evaluated after connecting the local and remote devices to the 2061 km field fiber link. Data collected over 400,000 s are presented in Fig. 7, revealing an average time difference of 52 ps ($2\sigma$), with a standard deviation fluctuation of 7.7 ps. Although we use common clock measurement, theoretically the average clock bias should be 0. When the SFTWTT system is laid on site, the reference line cannot manually pull down to zero. However, the actual center reference for the time difference measurement of 2061 km is not at 0 ps, as in Fig. 7. There are asymmetric factors such as optic fiber and cables.

The stability of the transferred 1 PPS signal is analyzed in Fig. 8, demonstrating time stabilities [time deviation (TDEV)] of 5.6 ps@1 s, 2.0 ps@10,000 s, and 3.1 ps@40,000 s. The time transfer stability consistently has been less than 5.6 ps across all averaging time, which is better than the performance of the authors’ group^[24].

At the same time, the transfer stability of the accompanying 10 MHz was evaluated using a phase noise analyzer (53,100 A), with Allan deviation (ADEV) measurements indicating high stability. The result is shown in Fig. 9. The current transfer frequency stability has been improved to 9.81 × 10⁻¹³/s and 9 × 10⁻¹⁶/10,000 s, which is better than the previous field transfer experiments, with 4.5 × 10⁻¹²/s and 1.9 × 10⁻¹⁵/10,000 s, of the author’s group. The reason is that we chose to multiply the frequency to 125 MHz and use a digital PLL to complete the frequency regeneration module. At the same time, thanks to the high stability of the frequency transfer, a high-precision time signal with enhanced time stability and accuracy can be obtained at the remote device. The 10 MHz enhanced the carrier frequency to 125 MHz for electrical signals, which can result in higher symbol transfer rates and improved transmission accuracy. The digital PLL is completed by adding a high-stability, low-phase noise crystal oscillator to filter and suppress the out-of-band noise transferred by the SFTWTT. The indicator of the crystal oscillator of the equipment is less than 7 × 10⁻¹³@1 s, 1 × 10⁻¹²@10 s. The system and PLL combine the short and stable characteristics of crystal oscillators. The loop bandwidth is set at 0.2 Hz, so as to have minimal phase jitter between the outputs 10 MHz and the reference. This performance has been enhanced from the previous version^[24].

In addition to the stability performance, the uncertainty of the time-transfer system is further detailed in Table 1^[26], with the first term representing the uncertainty of the measured time differences on the SFTWTT. The time difference measurements conducted over the 400,000 s, which is shown in Fig. 4, was evaluated as 7.7 ps. In our experiment, the system uncertainty is mostly restricted by the used TDCs in the time transfer whose measurement accuracy is 10 ps. The second term accounts for the uncertainty from the TDCs in the local and remote devices. The uncertainty of each TDC is 7.07 ps^[24].

Thanks to the advantage of a single fiber-optic link, most of the delay caused by changes in received power in the uplink can be offset by the delay in the downlink. Small form-factor pluggable (SFP) modules are the core of transfer systems and one of the most influential factors in introducing uncertainty. As with the previous calculation method, the uncertainty induced by each SFP can be estimated at less than 10 ps. In total, this term contributes an uncertainty of 38 ps as follows: $$u_{\mathrm{SFP},\text{total}}=\frac{\sqrt{{\sum }_{j=1}^{29}{u}_{\mathrm{SFP},j}^2+{\sum }_{k=1}^{29}{u}_{\mathrm{SFP},k}^2}}{2}=\frac{\sqrt{29\times {10}^2+29\times {10}^2}}{2}\approx 38.$$(2)

The fourth and fifth terms pertain to the uncertainty of components in the time regeneration unit and frequency regeneration unit, which encompassed the field programmable gate array (FPGA) and electrical variable delay line (EVDL). Similarly, the uncertainty of FPGA was determined to be 1.2 ps and EVDL was evaluated by an uncertainty of 1.4 ps was acquired, the same as in Ref. [24].

The nonreciprocal time delay variation of chromatic dispersion and wavelength differences was also calculated^[25]. Real-time compensation is achieved for the delay difference caused by dispersion measured by each remote site and local site. The actual nonreciprocal time delay variation changes related to dispersion in each section of the fiber yields, which was determined to be 6 ps.

The uncertainty of the polarization mode dispersion (PMD) obtained is 2.23 ps on a 2061 km field fiber, which was calculated by the typical coefficient $\sim 0.05\mathrm{ps/}\sqrt{\mathrm{km}}$^[10,11].

The Sagnac effect correction’s uncertainty was estimated under the assumption of precise positioning accuracy facilitated by GPS. The uncertainty of the Sagnac effect for any point of the fiber route is better than 1 km^[24]. All in all, the combined uncertainty for the time-transfer system over the 2061 km field fiber was estimated at 41.8 ps.

In conclusion, the first on-site high-precision fiber-optic time-transfer system exceeding 2000 km has been validated. Experimental results show that the stabilities of 5.6 ps @1 s and 3.1 ps@40,000 s can be achieved. The successful implementation of high-precision time transfer over an unprecedented 2061 km fiber-optic link is reported. The time-transfer stability has been consistently less than 5.6 ps across all averaging times, with an overall system uncertainty of 41.8 ps. The measured average time difference over 2061 km is 52 ps. These results of the 2061 km field fiber represent a higher precision and longer distance optical fiber time transfer over a field fiber link spanning thousands of kilometers, which marks a breakthrough in time transfer in terms of stability and distance. This achievement is instrumental in the construction of China’s national fiber-optic time service network.