With the continuous progress in science and technology, the performance of time and frequency standards have been constantly improved, which brings about higher requirements for the accuracy of time and frequency transfer technology. Optical fiber has the advantages of low loss, large bandwidth, high stability, and resistance to electromagnetic interference, and optical fiber networks have spread all over the world. Optical fiber time transfer has been recognized as an effective solution to long-distance and high-precision time transfer. When optical fibers reach a certain length, the regeneration and amplification of signals must be installed for boosting the signals' amplitude. Additionally, optical amplifiers will lead to asymmetric bidirectional transmission delays, and complex delay calibration must be carried out to meet the requirements of high-precision time transfer. At the same time, the signal-to-noise ratio (SNR) will gradually deteriorate with the increasing transmission distance, which will reduce the stability of time transfer. Based on the high sensitivity of single photon detectors, this paper proposes a non-relay long-distance optical fiber time transfer scheme based on single photon detection. The scheme not only does not require link calibration, which reduces the complexity of the experiment, but also ensures the symmetry of bidirectional transmission delays to improve the accuracy of time transfer. The dynamically adjustable external trigger control system is designed and implemented to achieve the gating mode of single photon detectors with low dark counts. Consequently, the detectors can continuously detect the time signals without the effect of transmission delay variations of the optical fiber link.

Optical fiber time transfer mainly includes one-way and two-way methods, and this paper adopts the two-way method to design the experimental scheme. The scheme employs the laser pulse sequence controlled by the local (remote) 1 pulse/s time signal as the transmission signal and utilizes single photon detectors with extremely high detection sensitivity to receive the signals arriving at the remote (local) site. It is unnecessary to install optical amplifiers or perform link calibration. The system adopts the bidirectional time-division multiplexing time comparison method over a single fiber with the same wavelength. According to the time-correlated single-photon counting method, the two-way variations at both the sites obtained per second are counted separately. Then the statistical values of the two-way variations with the maximum probability per second are obtained by the Gaussian fitting method. Finally, the time transfer stability (time deviation, TDEV) of the clock difference between both the sites is acquired. The ambiguity of the integer number of the pulse periods of the clock difference can be calibrated by other methods such as GPS or Beidou satellites. In addition, the gating signal is dynamically adjusted to ensure that the optical pulses arriving at the single photon detector always appear in the gating signal.

The Gaussian fitted values of the variations for the two-way transmission delays of the optical link are obtained to verify the effectiveness of the trigger control system of the single photon detector, which proves that the system can work normally (Fig. 5). The changes of these values of the variations for two-way transmission delays during the test time of 47137 s have the same trends over time. Because the sending and receiving delays of signals between the local and remote sites are not exactly the same, there is a difference of about 6.7 ns between the two-way Gaussian fitted values at the same time (Fig. 6). The results of the bidirectional comparison and TDEV of the bidirectional comparison are acquired by the two-way Gaussian fitted values (Fig. 7). The peak-to-peak value of the fluctuation is no more than 30 ps. The TDEV of the bidirectional comparison, which is the TDEV of the clock difference between both the sites, is better than 1.5 ps@1 s (short-term stability) and 0.4 ps@8192 s (long-term stability). Since the symmetry of the bidirectional transmission delays can greatly reduce the effect of the environment on transmission delays of the optical fiber link, the long-term stability of the bidirectional comparison is optimized by three orders of magnitude compared with that of the free-running mode. However, the changes in the delay of the outside of the loop signal can bring about the asymmetry of the bidirectional transmission delays, thus resulting in slight deterioration of the stability after 2048 s.

In this paper, a long-distance optical fiber time transfer system is designed based on single photon detection and bidirectional time-division multiplexing transmission over a single fiber with the same wavelength. Owing to the extremely high detection sensitivity of the single photon detector, it is unnecessary to adopt optical amplifiers in the optical fiber link. While the high symmetry of the bidirectional transmission delays is guaranteed, the effect of the backscattering on the time signals transmitted is effectively suppressed, thus improving the received SNR. Experimental results of the optical fiber link of 350 km show that the TDEV of the bidirectional time comparison is better than 1.5 ps@1 s and 0.4 ps@8192 s, providing an effective solution for long-distance and high-precision optical fiber time transfer. In conclusion, the asymmetry of the bidirectional transmission delays caused by the delay changes of the outside of the loop signal affects the long-term stability. The noises accumulated during sending, transmitting, and receiving the time signals affect the short-term stability. The compensation effect of the dispersion compensation fiber, the width of the single photon Gaussian distribution received, and the time resolution of the single photon detector all influence the overall stability. The dispersion can be adjusted accurately by adjustable dispersion compensation fiber, thereby improving the system stability. The experimental results show that the time transfer distance of the scheme is much longer than that of quantum time transfer, and the stability is better than those of some traditional optical fiber time transfers with a similar or shorter transfer distance.