## 3 Experimental Results
### The Collisional Shift Evaluation  
With Rabi spectrum, we further measure the collisional shift using the DISC method in our \({}^{87}\)Gr clock. The clock transition benefits from the detection of thousands of trapped cold-atoms simultaneous optical transitions, resulting in optical lattice clocks with ultra-low quantum projection noise limit. On the other hand, for a one-dimensional optical lattice clock, large number of atoms in the same lattice site will cause the collisional shift. Even for Fermions, the collisional shift can be more than 1 \(\times\) 10\({}^{-16}\)[32,33], indicating that the collisional shift should be carefully evaluated. As the trap potential and atomic temperature keep unchanged, the collisional shift depends on the atomic density and the excitation fraction (\(P_{\rm e}\)). The way of measuring this shift is shown in Figure 1b, where we set \(Para.1\) as high density (\(I_{1}\)) and \(Para.2\) as low density (\(I_{2}\)) and the atomic density is changed by varying the current of the Zeeman slower, which changes the loaded atoms of the first-stage cooling and eventually changes the total atomic number of the lattice. \(I_{1}\) and \(I_{2}\)  
Figure 2: **(a)** Comparison of the traditional self-comparison and the drift-insensitive self-comparison methods. Red circles are measured using the drift-insensitive self-comparison method, the blue squares are obtained using the traditional self-comparison method, and the black dashed line indicate zero frequency difference. Each experimental data point is the average value over 200 s measurement time, and the inset shows the clock laser frequency corrections over the self-comparison process (the blue and red lines correspond the traditional self-comparison and the drift-insensitive self-comparison methods, respectively). **(b)** Comparison of self-comparison instabilities. The blue squares indicate the instability of the traditional self-comparison method and the red circles represent the instability of the drift-insensitive self-comparison method. The error bars correspond to 1\(\sigma\) standard deviation and the solid lines are the linear fitting with a fixed slope of \(-\)0.5. The instability falls again above 10\({}^{3}\) s due to the approximately linear drift in the whole process. which are in direct proportion to the atomic density, represent the fluorescence intensity collected by the photomultiplier (PMT). In order to avoid the influence of the variation of the total atomic number, for the \(i\)th clock feedback cycle, the comparison result is divided by \(\Delta I_{\rm i}=I_{\rm 1i}-I_{\rm 2i}\), to obtain the collisional shift of unit fluorescence intensity (marked by \(\Delta_{\rm uI}\)) [20,24], where the \(I_{\rm 1i}\) and \(I_{\rm 2i}\) correspond to the fluorescence intensity under the conditions of _Para._1 and _Para._2, respectively. Additionally, in terms of the regular operation of the clock, the collisional shift is calculated by multiplying the \(\Delta_{\rm uI}\) by the intensity \(I_{\rm nor}\) that corresponds to the fluorescence intensity as the clock regularly operates. The gain of the PMT and the detection laser intensity remain constant during the whole measurement process. With Rabi spectrum, the collisional shifts under different excitation fraction are measured as shown in Figure 3a. Typically, the atoms are prepared in \({}^{1}S_{0}\) state (the ground state), but those points that the excitation fractions are larger than 0.4 are realized by preparing the atoms in \({}^{3}P_{0}\) state (the excited state). By linear fitting [34,35], the relationship of \(\Delta_{\rm uI}\) and \(P_{\rm e}\) is determined as \(\Delta_{\rm uI}=18.5(18)P_{\rm e}-11.6(7)\). Thus, for the regular clock operation of which the expected collisional shift is about \(45\Delta_{\rm uI}\), \(1\%\) change in the excitation fraction will lead to a change in fractional collisional shift of \(2\times 10^{-17}\).