System stability and uncertainty are the two most important indicators of a clock, which represent the fluctuation of the clock output frequency in the time domain and the possible deviation between the clock output frequency and the absolute frequency, respectively. Stability improvement can reduce the measurement error of system frequency shifts and thus decrease systematic uncertainty. At present, the factors that limit the stability of an optical lattice clock mainly include quantum projection noise and Dick noise. By extending the optical probing time (τ_p), the effective operating rate of the clock can be improved, and the quantum projection noise and Dick noise can be reduced at the same time. However, compared with those of a case having smaller τ_p (such as 100 ms), the collisional frequency shifts are in the same order of magnitude as the Rabi frequency, and the loss of particles in the excited state due to inelastic scattering is enhanced when both τ_p and the number of atoms are large (e.g., τ_p=500 ms, N=6000). At the same time, the difference in Rabi frequency between the atoms in different external states and different lattice sites also rises (inhomogeneous excitation induced by atomic temperature, atomic interactions, clock laser frequency noise, and the detuning angle between the clock laser and the lattice light). All these factors make the excitation fraction of the clock transition spectrum line decrease and the linewidth widen when τ_p is large and eventually lead to the stability of the clock below the corresponding Dick limit.

In this paper, based on the prototype of the ⁸⁷Sr one-dimensional space optical lattice clock, we experimentally observe the influence of atomic interactions on spectral linewidth and excitation fraction and even the corresponding influence on system stability. In the experiment, we measure the Rabi spectrum of clock transition at 6000 and 2000 atoms. In the measurements, the atomic temperature is kept at 3 μK (for T is constant, the number of atoms is proportional to the atomic density). The detuning angle between the clock laser and the lattice light is 13 mrad, and the optical probing time is set as 500 ms. Additionally, the stability of the optical lattice clock at two different atomic densities (for 6000 and 2000 atoms, respectively) is measured by the interleaved self-comparison method.

The research results of the dramatic effect of atomic interactions on the Rabi spectrum (Fig. 4) are shown. The Rabi spectrum of clock transition at the high atomic density (6000 atoms) is achieved experimentally, which has a maximum excitation fraction of 0.49 and a full width at half maximum (FWHM) of 4 Hz [Fig. 4(a)]. On the contrary, the maximum excitation fraction is 0.68, and the FWHM is 1.9 Hz under the condition of the low atomic density (2000 atoms) [Fig. 4(c)]. The results clearly demonstrate that the suppression of the excitation fraction and the broadening of the spectrum are caused by atomic interactions [Fig. 4(a) and (c)], which is coincident with the theoretical expectation. Moreover, when the clock laser resonates with the clock transition, the atoms trapped in the lattice are decreased distinctly [Fig. 4(b)]. This indicates that inelastic collisions between excited particles make a part of atoms escape from the trapping of the lattice. When the total number of atoms is reduced, the atomic loss caused by inelastic collisions is nearly not observed [Fig. 4(d)] in the experimental setup. This result also conforms to the two-body interaction theory. We also present the experimental results of the self-comparison stability at high and low atomic densities (Fig. 5). The self-comparison stability under the high-density condition is 2.6×10^-15 (τ/s)^-0.5, while it is 1×10^-15 (τ/s)^-0.5 under the low-density condition. The stability of the system is improved to 2.6 times by reducing the number of atoms.

In summary, the suppression of the excitation fraction and the broadening of the clock transition spectrum induced by atomic interactions are observed experimentally on the prototype of the ⁸⁷Sr one-dimensional space optical lattice clock, and the atomic loss due to inelastic collisions is also found. The Rabi spectra are measured experimentally in the conditions of 6000 and 2000 atoms in lattice. The excitation fraction and linewidth for the large number of atoms are 0.49 and 4 Hz, and those for the small number of atoms are 0.68 and 1.9 Hz, respectively. At the same time, the atomic loss caused by inelastic collisions is also observed when the number of atoms is large. In the experiment, by measuring self-comparison stability at different atomic densities, we confirm that reducing the number of atoms to 1/3 can improve the system stability by 1.6 times. Finally, a spectrum with a linewidth of 1.9 Hz is achieved, and the self-comparison stability of the prototype of the space optical lattice clock is improved to 1×10^-15 (τ/s)^-0.5. The experimental results in this paper are significant for the study of the influence of many-body interactions in optical lattices on the clock transition spectrum. The measurement results of stability show that the best stability can be obtained by optimizing the atomic density of the optical lattice atomic clock.