We present the frequency control of a 759 nm laser as a lattice laser for an ytterbium (Yb) optical clock. The frequency stability and accuracy are transferred from the Yb optical clock via an optical frequency comb. Although the comb is frequency-stabilized on a rubidium microwave clock, the frequency instability of the 759 nm laser is evaluated at the 10-15 level at 1 s averaging time. The frequency of the 759 nm laser is controlled with an uncertainty within 1 Hz by referencing to the Yb clock transition. Such a frequency-controlled 759 nm laser is suitable for Yb optical clocks as the lattice laser. The technique of laser frequency control can be applied to other lasers in optical clocks.

We report two ultra-stable laser systems automatically frequency-stabilized to two high-finesse optical cavities. By employing analog-digital hybrid proportional integral derivative (PID) controllers, we keep the merits of wide servo bandwidth and servo accuracy by using analog circuits for the PID controller, and, at the same time, we realize automatic laser frequency locking by introducing digital logic into the PID controller. The lasers can be automatically frequency-stabilized to their reference cavities, and it can be relocked in 0.3 s when interruption happens, i.e., blocking and unblocking the laser light. These automatic frequency-stabilized lasers are measured to have a frequency instability of 6×10-16 at 1 s averaging time and a most probable linewidth of 0.3 Hz. The laser systems were tested for continuous operation over 11 days. Such ultra-stable laser systems in long-term robust operation will be beneficial to the applications of optical atomic clocks and precision measurement based on frequency-stabilized lasers.

We report a long-term frequency-stabilized optical frequency comb at 530–1100 nm based on a turnkey Ti:sapphire mode-locked laser. With the help of a digital controller, turnkey operation is realized for the Ti:sapphire mode-locked laser. Under optimized design of the laser cavity, the laser can be mode-locked over a month, limited by the observation time. The combination of a fast piezo and a slow one inside the Ti:sapphire mode-locked laser allows us to adjust the cavity length with moderate bandwidth and tuning range, enabling robust locking of the repetition rate (f_r) to a hydrogen maser. By combining a fast analog feedback to pump current and a slow digital feedback to an intracavity wedge and the pump power of the Ti:sapphire mode-locked laser, the carrier envelope offset frequency (f_ceo) of the comb is stabilized. We extend the continuous frequency-stabilized time of the Ti:sapphire optical frequency comb to five days. The residual jitters of f_r and f_ceo are 0.08 mHz and 2.5 mHz at 1 s averaging time, respectively, satisfying many applications demanding accuracy and short operation time for optical frequency combs.

A cavity-stabilized 578 nm laser is used to probe the clock transition of ytterbium atoms trapped in optical lattice sites. We obtain a Fourier-limited 4.2-Hz-linewidth Rabi spectrum and a Ramsey spectrum with fringe linewidth of 3.3 Hz. Based on one of the spectra, the 578 nm laser light is frequency-stabilized to the center of the transition to achieve a closed-loop operation of an optical clock. Based on interleaved measurement, the frequency instability of a single optical clock is demonstrated to be 5.4 × 10^?16/√τ.

We demonstrate two ultra-stable laser systems at 1064 nm by independently stabilizing two 10-cm-long Fabry–Pérot cavities. The reference cavities are on a cubic spacer, which is rigidly mounted for both low sensitivity to environmental vibration and ability for transportation. By comparing against an independent ultra-stable laser at 578 nm via an optical frequency comb, the 1064 nm lasers are measured to have frequency instabilities of 6 × 10^?16 at 1 s averaging time.

We study a Zeeman slower using the magnetic field generated by a pair of coils for a magneto-optical trap. The efficiency of the Zeeman slower is shown to be dependent on the intensity and frequency detuning of the laser light for slowing the atoms. With the help of numerical analysis, optimal experimental parameters are explored. Experimentally, the optimal frequency detuning and intensity of the slowing beam are explored, and 4 × 10⁷ ytterbium atoms are trapped in the magneto-optical trap.

The length stability of optical cavities is vital in ultra-stable, cavity-stabilized laser systems. Using finite element analysis, we study the length deviation of optical cavities due to thermal expansion and thermo-refractive effects when the incident light power is changed. The simulated fractional length sensitivity of a 7.75-cm-long football cavity to the power fluctuation of incident light is 5×10 14/μW, which is in agreement with the experimental results found by measuring the frequency change of a cavity-stabilized laser when the incident light power is changed. Based on the simulation, the cavity sensitivity to light power fluctuation is found to depend on the cavity size and material.