## 2 Preparation for the \({}^{87}\)Sr Optical Lattice Clock
### The Clock Transition Spectra of \({}^{87}\)Sr  
To obtain the clock transition spectra, the clock laser frequency was changed stepwise by an acousto-optic modulator (AOM) to interrogate the resonant frequency of the clock transition. In order to obtain the resolved sideband spectrum as shown in Figure 2a, the power of the clock laser was about 1 mW and the frequency of the clock laser was scanned around the center frequency of the carrier transition in a range of \(-70\) to \(+70\) kHz with steps of 0.5 kHz. The frequency gap between the carrier and red sideband (the blue sideband) could be approximately viewed as the longitudinal trapping frequency of the lattice. It could be calculated from Figure 2a that the longitudinal trapping frequency was 65 kHz, and the corresponding potential depth was about 87 \(E_{\rm R}\) calculated by longitudinal trapping frequency. Therein, \(E_{\rm R}=(h/\lambda_{\rm L})^{2}/2m\) is the recoil energy, \(h\) is the Planck constant, \(\lambda_{\rm L}\) is the wavelengthof lattice laser, and \(m\) is the atomic mass of \({}^{87}\)Sr. With the method in reference [30], the longitudinal and radical temperatures of trapped atoms were 2.9 \(\upmu\)K and 3.4 \(\upmu\)K respectively.  
Figure 1: Experimental setup for preparing cold atoms and detecting the clock transition of the strontium optical lattice clock. C1: a pair of anti-Helmholtz coils, C2: compensating coils consisting of three pairs of Helmholtz coils, TL: trapping laser, SL: string laser, PL: polarizing laser, LAL: lattice laser, CLL: clock laser, CL: convex lens with a focal length of 300 mm, CM: concave mirror with a radius of 250 mm, GP: Glan-Taylor polarizer of which the polarization axis is along the direction of gravity.  
Figure 2: Clock transition spectra. (**a**) Resolved sideband spectrum of the \({}^{87}\)Sr clock transition. (**b**) Spin-polarized spectrum for the transitions of \(m_{\rm F}=+9/2\)\(\rightarrow\)\(m_{\rm F}=+9/2\) and \(m_{\rm F}=-9/2\)\(\rightarrow\)\(m_{\rm F}=-9/2\).  
In order to pump all atoms to Zeeman sublevels of \(m_{\rm F}\) = +9/2 or \(m_{\rm F}\) = -9/2, a polarizing laser with a linewidth of 300 Hz was employed. Its frequency was resonant with the \({}^{1}S_{0}\) (\(F\) = 9/2)\(\rightarrow^{3}P_{1}\) (\(F\) = 9/2) transition at \(\lambda\) = 689 nm. During the process of pumping atoms to \(m_{\rm F}\) = \(\pm\)9/2, a group of three-dimensional compensating coils were turned on to remove the horizontal magnetic field and simultaneously supply a weak bias magnetic field of about 50 mG in the direction of gravity. Meanwhile, the polarizing laser was turned on along the direction of gravity. A liquid crystal waveplate was applied to control the polarization of the polarizing laser, so that its polarization was \(\sigma^{+}\) as driving atoms to the stretched-state \(m_{\rm F}\) = +9/2 and \(\sigma\)- as driving atoms to \(m_{\rm F}\) = -9/2. The power and pulse duration of the polarizing laser were 200 uW and 15 ms respectively, and about 95% atoms were driven to the stretched-state, completing spin polarization. During the process of detecting spin-polarized spectra, the horizontal magnetic field was maintained at zero and the magnetic field in the direction of gravity was about 400 mG to separate different Zeeman sublevels. The typical spin-polarized spectrum is shown in Figure 2b with a clock laser duration of 150 ms and power of 200 nW, and the full width at half maximum (FWHM) of the two Zeeman sublevels transition were 6.8 Hz (\(m_{\rm F}\) = -9/2) and 6.2 Hz (\(m_{\rm F}\) = +9/2) by Lorentz fitting.