The ${}^{1}S_0$-${}^{3}P_0$ clock transition frequency ${\nu }_{\mathrm{Sr}}$ in neutral ${}^{87}\mathrm{Sr}$ has been measured relative to the Cs standard by three independent laboratories in Boulder, Paris, and Tokyo over the last three years. The agreement on the $1\times {10}^{-15}$ level makes ${\nu }_{\mathrm{Sr}}$ the best agreed-upon optical atomic frequency. We combine periodic variations in the ${}^{87}\mathrm{Sr}$ clock frequency with ${}^{199}\mathrm{Hg}^{+}$ and H-maser data to test local position invariance by obtaining the strongest limits to date on gravitational-coupling coefficients for the fine-structure constant $\alpha$, electron-proton mass ratio $\mu$, and light quark mass. Furthermore, after ${}^{199}\mathrm{Hg}^{+}$, ${}^{171}\mathrm{Yb}^{+}$, and H, we add ${}^{87}\mathrm{Sr}$ as the fourth optical atomic clock species to enhance constraints on yearly drifts of $\alpha$ and $\mu$.

We have developed a fiber-based frequency comb system consisting of a simple mode-locked fiber laser and a backward pumping amplifier combined with a highly nonlinear fiber with a short zero-dispersion wavelength. As a result, the signal to noise ratio of the obtained carrier-envelope-offset frequency beat is larger than 45 dB at a bandwidth of 100 kHz. Furthermore, we have succeeded in measuring the optical frequencies of a 1542-nm acetylene-stabilized laser and a 532-nm iodine-stabilized Nd:YAG laser continuously for more than one week using the fiber-based comb system. The long-term measurement revealed that the frequency stability of the iodine-stabilized laser was 5.7×10^-15 with 100 000 s averaging.

We demonstrate that fiber-based frequency combs with multi-branch configurations can transfer both linewidth and frequency stability to another wavelength at the millihertz level. An intra-cavity electro-optic modulator is employed to obtain a broad servo bandwidth for repetition rate control. We investigate the relative linewidths between two combs using a stable continuous-wave laser as a common reference to stabilize the repetition rate frequencies in both combs. The achieved energy concentration to the carrier of the out-of-loop beat between the two combs was 99% and 30% at a bandwidth of 1 kHz and 7.6 mHz, respectively. The frequency instability of the comb was 3.7×10⁻¹⁶ for a 1 s averaging time, improving to 5-8×10⁻¹⁹ for 10000 s. We show that the frequency noise in the out-of-loop beat originates mainly from phase noise in branched optical fibers.