## 4 Experimental Results  
The multiple-access time and frequency transfer experiment was conducted in the Innovation Center of our campus, and the experiment lasted about 10,000 s. Figure 4a shows the result of time and frequency transfer between sites A and B. Curve i is the phase  
Figure 3: Experimental setup of the multiple-access time and frequency transfer over a fiber and free-space link. OC: optical coupler, EOM: electro-optical modulator, PD: photodetector, CM: collimator, PS: power splitter, BPF: band-pass filter, AMP: amplifier, DPD: digital phase discriminator.  
difference \(\varphi_{\rm AB}\) between the reference signal of site A and the time-frequency signal sent from site B to A. Curve ii is the phase difference \(\varphi_{\rm BA}\) between the reference signal of site B and the time-frequency signal sent from site A to B. Curve iii is the relative phase difference between site A and B calculated by the \(\varphi_{\rm AB}\) and \(\varphi_{\rm BA}\), based on the two-way time and frequency comparison, without calculation of the fixed phase delay. Here, it can be treated as the estimated time and frequency transfer result between A and B, and the RMS timing fluctuation is 119 ps. Figure 4b shows the result of time and frequency transfer between sites A and C. Curve i is the phase difference \(\varphi_{\rm AC}\) between the reference signal of site A and the time-frequency signal sent from site C to A. Curve ii is the phase difference \(\varphi_{\rm CA}\) between the reference signal of site B and the time-frequency signal sent from site A to C. Curve iii is the relative phase difference between site A and C calculated by the \(\varphi_{\rm AC}\) and \(\varphi_{\rm CA}\), based on the two-way time and frequency comparison, without calculation of the fixed phase delay either. Here, it can also be treated as the estimated time and frequency transfer result between A and C, and the RMS timing fluctuation is 59.5 ps.  
The stability of the time and frequency transfer can be calculated from the phase difference measurement results, generally using the Allan Deviation, whose physical mechanism refers to the RMS value of the timing signal difference measured by the bandpass filter within a given integration time interval [1]. Curves i and ii in Figure 5 represent the frequency transfer stability which is calculated as overlapping Allan Deviation, between sites A and B, and between sites A and C, respectively. As we can see from Figure 5, the stability of the time and frequency transfer between A and B is 3.3 \(\times\) 10\({}^{-11}\) at 1 s and 2.8 \(\times\) 10\({}^{-14}\) at 2000 s. The stability of the time-frequency transfer between A and C is 3.0 \(\times\) 10\({}^{-11}\) at 1 s and 2.6 \(\times\) 10\({}^{-14}\) at 2000 s. The two-way time-frequency comparison method in this scheme can effectively reduce the impact of temperature and other factors on the long-term stability of the optical fiber and free-space transmission link, thereby improving the long-term stability of time-frequency transfer.  
Figure 4: Time fluctuation results of the multiple-access time and frequency transfer. (**a**) Transfer between site A and B; (**b**) transfer between site A and C.  
This experimental setup realizes the simultaneous time and frequency transfer between one master site and two slave sites. The scheme can also be extended to more slave site scenarios. The reference source of the slave site only needs to select the harmonic frequency of the master OFC. The key advantage of this scheme is that the light source of the master site only uses one femtosecond OFC, and there is only one photodetector for receiving the optical signal of the slave sites. This single light source and single receiving photodetector can greatly improve the efficiency of multiple-channel time and frequency phase difference measurements in this system, reduce the complexity, and reduce the cost, which provides important support for building a large-scale multiple-access time and frequency transfer system.