Fig. 1. Clock laser system. (a) Schematic diagram of the experimental setup for laser frequency stabilization. The solid lines represent laser beam paths, and the dashed lines represent electrical paths. The numbered selection switch corresponds to different experimental scenarios: ① comparison between two ultra-stable systems; ② optical clock operation. ECDL, external cavity diode laser; AOM, acoustic-optic modulator; G-T prism, Glan-Thompson prism; EOM, electro-optic modulator; ISO, optical isolator; QWP, quarter wave plate; PD, photodetector; LIA, lock-in amplifier; RF, radio frequency source; PID, proportional-integral-differential servo; FNC, fiber noise cancellation. (b) Summary of all noise contributions of FPC2. The sum of all noise contributions (red line) approaches the thermal noise limit (black line).

Fig. 2. Experimental setup and timing of synchronous comparison. (a) Schematic diagram for stability measurement. PMT, photo-multiplier tube; pol., polarization of the laser; B⇀, magnetic field quantization axis; g, gravity direction. (b) Time sequence for completing a clock transition detection. MOT, magneto-optical trap; SBC, sideband cooling; OL, optical lattice. (c) Time sequence for synchronous comparison.

Fig. 3. Rabi spectrum of the ¹⁷¹Yb optical clock. (a) 200 ms Rabi spectroscopy with 20 times single-sweeps overlapped; (b) 400 ms Rabi spectroscopy with 10 times single-sweeps overlapped; (c) 200 ms single-sweep Rabi spectroscopy; (d) 400 ms single-sweep Rabi spectroscopy. The black scatter points are the spectrum data, and the red line is the sinc fitting. The line widths of the observed spectral lines are Fourier-limited.

Fig. 4. Stability measurement and decoupling of systematic effects. (a) Frequency difference of Yb1 and Yb2. (b) Total Allan deviation characterizes the stability of a single clock. (c) Number of atoms during the comparison process, black for Yb1 and red for Yb2. (d) Dependence of collision shift and the number of atoms. (e) Contribution to the instability of the optical clock expressed by Allan deviation. The black dashed line represents the estimated quantum projection noise. The red dot indicates the measured stability. Green rhombus: collision shift. Purple square: BBR shift. Blue inverted triangle: lattice shift. Brown triangle: Zeeman shift.

Fig. 5. Improved stability of the optical clock with a 400 ms clock-laser pulse. (a) Frequency difference of Yb1 and Yb2. (b) Number of atoms during the comparison process, black for Yb1 and red for Yb2. (c) Measured stability of the clock and the decoupled systematic effect contribution to the instability.