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Laser frequency combs, which are composed of a series of equally-spaced coherent frequency components, have triggered revolutionary progress for precision spectroscopy and optical metrology. Length/distance is of fundamental importance in both science and technology. In this work, we describe a ranging scheme based on chirped pulse interferometry. In contrast to the traditional spectral interferometry, the local oscillator is strongly chirped which is able to meet the measurement pulses at arbitrary distances, and therefore the dead zones can be removed. The distances can be precisely determined via two measurement steps based on time-of-flight method and synthetic wavelength interferometry, respectively. To overcome the speed limitation of the optical spectrum analyzer, the spectrograms are stretched and detected by a fast photodetector and oscilloscope, and consequently mapped into the time domain in real time. The experimental results indicate that the measurement uncertainty can be well within 2 $\upmu$m, compared with the reference distance meter. The Allan deviation can reach 0.4 $\upmu$m at averaging time of 4 ns, 25 nm at 1 $\upmu$s, and can achieve 2 nm at 100 $\upmu$s averaging time. We also measure a spinning disk with grooves of different depths to verify the measurement speed, and the results show that the grooves with about 150 m/s line speed can be clearly captured. Our method provides a unique combination of non-dead zones, ultrafast measurement speed, high precision and accuracy, large ambiguity range, and with only one single comb source. This system could offer a powerful solution for the field measurements in practical applications in future.

We report on the development and performance evaluation of an ultra-stable clock laser for an $\rm ^{27}Al^+$ optical clock. The thermal noise limited ultra-stable laser is developed based on a 30 cm long ultra-stable cavity. Three independent evaluation methods, including the frequency noise summation method, the three-cornered hat (TCH) method, and the optical clock transition detection method, are used to evaluate the clock laser performance. The summation result of various frequency noise terms is compared with the result of the TCH method. In addition, the $\rm ^{27}Al^+$ ion optical clock transition with ultra-narrow linewidth is also used to detect the frequency noise of the laser at lower Fourier frequencies. The results of the three methods show good agreements, showing a frequency instability level of $1.3\times10^{-16}$, and giving us confidence that these evaluation methods may provides guidance for accurate evaluations of high stability laser sources.

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of $1.9\times10^{-16}$. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is further improved by different mixing ratio of the gas-liquid helium. With this technique, vibrations at frequencies higher than tens of hertz are greatly suppressed., Comment: 4 pages, 4 figures

A cesium atomic fountain clock is under development at Huazhong University of Science and Technology (HUST) in China. In this paper, we describe the construction of the entire fountain clock system and report the preliminary results. A frequency stability of $2.5\times 10^{-13} {\tau}^{-1/2}$ has been achieved by inter-comparison with a hydrogen maser, and the factors limiting the frequency stability are also discussed., Comment: 7 pages, 12 figures,26 references

In the weak-magnetic-field approximation, we derived a general expression of hyperfine-induced Land\'{e} $g$-factors. By using this formula and the multi-configuration Dirac-Hartree-Fock theory, the $g$-factors were calculated for the $3s3p~^3\!P^o_0$ clock state in $^{27}$Al$^+$ and $5s5p~^3\!P^o_0$ in $^{87}$Sr. The present results, $\delta g^{(1)}_{\rm hfs}(^3\!P^o_0) = -1.183(6) \times 10^{-3}$ for $^{27}$Al$^+$ and $\delta g^{(1)}_{\rm hfs}(^3\!P^o_0) = 7.78(30) \times 10^{-5}$ for $^{87}$Sr agree with experimental values very well. Our theory is also useful to predict hyperfine-induced Land\'e $g$-factors for other atomic systems.

Large-scale high sensitivity laser gyroscopes have important applications for ground-based and space-based gravitational wave detection. We report on the development of a 3 m$\times$3 m heterolithic passive resonant gyroscope (HUST-1) which is installed on the ground of a cave laboratory. We operate the HUST-1 on different longitudinal cavity modes and the rotation sensitivity reaches $1.6\times10^{-9}$ rad/s/$\rm \sqrt{Hz}$ beyond 1 Hz. The drift of the cavity length is one of the major sensitivity limits for our gyroscope in the low frequency regime. By locking cavity length to an ultra-stable reference laser, we achieve a fractional cavity length stability of $5.6\times10^{-9}$ m$/\rm \sqrt{Hz}$ at 0.1 mHz, a four orders of magnitude improvement over the unconstrained cavity in the low frequency regime. We stabilize the cavity length of a large-scale heterolithic passive resonant gyroscope through active feedback and realize long-term operation. The rotation sensitivity reaches $1.7\times10^{-7}$ rad/s/$\sqrt{\rm{Hz}}$ at 0.1 mHz, a three orders of magnitude improvement, which is no longer limited by the cavity length drift in this frequency range.

In this paper, we demonstrate a simple scheme of 6.835 GHz microwave frequency synthesizer based on the sub-sampling phase lock loop (PLL) technique. The application of the sub-sampling PLL is the key to simplify the architecture of the synthesizer in this scheme. A 100 MHz oven controlled crystal oscillator (OCXO) with ultra-low phase noise is used as the initial signal source. Then a dielectric resonant oscillator (DRO) of 6.8 GHz is directly phase locked to the 100 MHz OCXO utilizing the sub-sampling PLL. Benefiting from the sub-sampling PLL, the processes of microwave frequency multiplication and phase lock which are necessary in the development of microwave synthesizer are greatly simplified. Therefore, the architecture of the synthesizer is very simple. Correspondingly, the power consumption and cost of the synthesizer are low. The absolute phase noises of the 6.835 GHz output signal are measured to be -47 dBc/Hz, -77 dBc/Hz, -104 dBc/Hz and -121 dBc/Hz at 1 Hz, 10 Hz, 100 Hz and 1 kHz offset frequencies, respectively. he synthesizer can be used as the local oscillator of the Rb atomic clocks. For the Rb atomic clocks operated in the continuous or pulsed optically pumped (POP) mode, Tthe short-term frequency stability limited by the absolute phase noises of the synthesizer through the intermodulation or the Dick effect is theoretically calculated to be better than 5.0E10^-14/t^1/2. This low phase noise microwave frequency synthesizer can be used in other experiments of fundamental physics measurement.

We report precision measurement of aluminum atoms ${^{2}P_{1/2}}-{^{2}S_{1/2}}$ transition at 394 nm and ${^{2}P_{3/2}}-{^{2}S_{1/2}}$ transition at 396 nm in a hollow-cathode lamp (HCL). Both absorption spectroscopy and saturated absorption spectroscopy (SAS) are performed. From the absorption spectroscopy the Doppler linewidth is estimated to be 2.6 GHz. The SAS spectroscopy is analyzed based on the velocity-changing-effect model. With a frequency comb calibrated wavemeter, the frequencies of ${^{2}P_{1/2}},{F=3}-{^{2}S_{1/2}},{F=2}$ transition and ${^{2}P_{3/2}},{F=4}-{^{2}S_{1/2}},{F=3}$ transition are measured to be 759.905401(10) THz and 756.547403(10) THz, respectively. The hyperfine structure constants of aluminum atoms are determined and compared with previously reported measurement results and theoretical calculation. Reasonable agreement is found for the magnetic dipole constant (A constant), while the electric quadrupole constant (B constant) has a large deviation., Comment: 11 pages, 5 figures

We report on the development and phase noise performance of a 9.1926 GHz microwave frequency synthesizer to be used as the local oscillator for a Cs fountain clock. It is based on frequency multiplication and synthesis from an ultralow phase noise 5 MHz Oven Controlled Crystal Oscillator (OCXO) and 100 MHz Voltage Controlled Crystal Oscillator (VCXO).The key component of the frequency multiplication is a non-linear transmission-line (NLTL) used as a frequency comb generator. The phase noise of the synthesizer is improved by carefully optimizing the input power, the input and output impedances of the NLTL. The absolute phase noises of the 9.1926 GHz output signal are measured to be -64 dBc/Hz, -83 dBc/Hz, -92 dBc/Hz, -117 dBc/Hz and -119 dBc/Hz at 1 Hz, 10Hz, 100Hz, 1 kHz and 10 kHz offset frequencies, respectively. The residual phase noise of the synthesizer is measured to be -82 dBc/Hz at 1 Hz offset frequency. The measurement result shows that the absolute phase noise at the frequency range of 1 - 100 Hz is mainly limited by the phase noise of the OCXO. The contribution of the absolute phase noise to the fountain clock short-term frequency stability is calculated to be 7.0x10^(-14). The residual frequency stability of the synthesizer is measured to be1.5x10^(-14), which is consistent with the calculated frequency stability due to the residual phase noise of the synthesizer. Meanwhile we designed and realized an interferometric microwave switch in the synthesizer to eliminate the frequency shifts induced by the microwave leakage. The extinction ratio of the switch is measured to be more than 50 dB. In the scheme, we use only commercially available components to build the microwave frequency synthesizer with excellent phase noise performance for high-performance Cs fountain clocks.

Residual amplitude modulation (RAM) effect in a Pound-Drever-Hall (PDH) technique locked cavity system is analysed in this paper. Frequency shift caused by RAM in PDH is found to be both related to the amplitude of the RAM and to the cavity's mode matching and impedance matching. The cavity reflection contrast depends on the mode matching of the incident laser light and impedance matching of the cavity. The suppression of the amplitude of the RAM has been investigated by many groups, while the effect of the cavity response has not received full attention. According to our analysis, RAM effect can be fully suppressed by proper impedance matching and magic mode coupling. We have measured the RAM to frequency conversion coefficients at different coupling efficiencies. The result agrees well with the calculation, demonstrating the potential of full suppression of the RAM effect through proper design of cavities., Comment: (120.3940) Metrology; (120.4800) Optical standards and testing; (140.2020) Diode lasers; (140.3425) Laser stabilization; (140.3580) Lasers, solid-state

We calculated the magnetic dipole and the electric quadrupole hyperfine interaction constants of 3s3p $^{3,1}P^o_1$ states and the isotope shift, including mass and field shift, factors for transitions from these two states to the ground state 3s$^2~^1S_0$ in Al$^+$ ions using the multiconfiguration Dirac-Hartree-Fock method. The effects of the electron correlations and the Breit interaction on these physical quantities were investigated in detail based on the active space approach. It is found that the CC and the higher-order correlations are considerable for evaluating the uncertainties of the atomic parameters concerned. The uncertainties of the hyperfine interaction constants in this work are less than 1.5\%. Although the isotope shift factors are highly sensitive to the electron correlations, reasonable uncertainties were obtained by exploring the effects of the electron correlations. Moreover, we found that the relativistic nuclear recoil corrections to the mass shift factors are very small and insensitive to the electron correlations for Al$^{+}$. These atomic parameters present in this work are valuable for extracting the nuclear electric quadrupole moments and the mean-square charge radii of Al isotopes., Comment: accepted by Phys. Rev. A