[en] We report on the 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. Both absorption and saturated absorption spectra are measured. From the absorption spectra, the Doppler linewidth is estimated to be 2.65 GHz. The saturated absorption spectra are analyzed based on a velocity-changing collisions model. With a frequency comb calibrated wavemeter, the frequencies of ${}^2{P}_{1/2}(F^{\mathrm{\prime <!--\; ???\; -->}}=3)-<!--\; ???\; -->{}^2{S}_{1/2}(F=2)$ transition and ${}^2{P}_{3/2}(F^{\mathrm{\prime <!--\; ???\; -->}}=4)-<!--\; ???\; -->{}^2{S}_{1/2}(F=3)$ transition are measured to be 759.905 204(1) THz and 756.547 133(3) THz, respectively. The hyperfine coupling constants of aluminum atoms are determined, and are compared with previously reported measurement results and theoretical calculation results. Reasonable agreement is found for the magnetic dipole constant (A constant), while the electric quadrupole constant (B constant) has a large deviation. (paper)

[en] Residual amplitude modulation (RAM) effects in Pound–Drever–Hall (PDH) locking are analyzed in this paper. The suppression of the RAM effect in PDH locking has been investigated by many groups, but the effect of cavity response has not been fully considered. Frequency shifts caused by RAM in PDH locking are found to be both related to the amplitude of the RAM and to the cavity’s mode matching and impedance matching. We measure the RAM-to-frequency conversion coefficients at different coupling efficiencies. The result agrees well with our theoretical model. According to our analysis, the RAM effect in principle can be fully suppressed by choosing proper impedance-matching parameters and mode coupling efficiency, and we give several examples to demonstrate the potential of full suppression of the RAM effect through proper design of cavities.

[en] We report construction of an iodine-stabilized laser frequency standard at 532 nm based on modulation transfer spectroscopy (MTS) technology with good reproducibility. A frequency stability of 2.5 × 10⁻¹⁴ at 1 s averaging time is achieved, and the frequency reproducibility has a relative uncertainty of 3.5 × 10⁻¹³, demonstrating the great stability of our setup. The systematic uncertainty of the iodine-stabilized laser frequency standard is evaluated, especially the contribution of the residual amplitude modulation (RAM). The contribution of the RAM in MTS cannot be evaluated directly. To solve this problem, we theoretically deduce the MTS signal with RAM under large modulation depth, and prove that the non-symmetric shape of the MTS signal is directly related to the MTS effect. The non-symmetric shape factor r can be calibrated with a frequency comb, and in real experiments, this r value can be obtained by least-squares fitting of the MTS signal, from which we can infer the RAMinduced frequency shift. The full frequency uncertainty is evaluated to be 5.3 kHz (corresponding to a relative frequency uncertainty of 9.4 × 10⁻¹²). The corrected transition frequency has a difference from the BIPM-recommended value of 2 kHz, which is within 1 σ uncertainty, proving the validity of our evaluation. (paper)

[en] Laguerre–Gaussian (LG) laser beams carrying orbital angular momentum are attractive vortex sources for a variety of photonic applications. In this work, we investigate the probing method based on a tilted biconvex lens for LG beams and pairs. We theoretically derive the formulation of the general astigmatic transformation of an LG vortex beam with non-zero radial index p and topological charge l after passing through a tilted biconvex lens. It is found that at a certain position after the focus of the lens, the field intensity of the LG beam is converted into a ( p+1) by ( p+|l|+1) slanted matrix of bright spots. The indices of p and l are obtained by examin-ing the converted intensity patterns. Theoretical calculations are in good agreement with experiments using LG beams with p up to 2 and l up to 34 emitted from a nonplanar ring vortex oscillator. Furthermore, we also found the method can also be used to estimate the mode comp-onents, the ratio of beam intensity and phase relationships of any two superposed LG beams. (paper)

[en] 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 × 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 × 10⁻⁹ rad s⁻¹ Hz^−1/2 above 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 cavity length stability of 5.6 × 10⁻⁹ m Hz^−1/2 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 × 10⁻⁷ rad s⁻¹ Hz^−1/2 at 0.1 mHz, a three orders of magnitude improvement over the unconstrained cavity, which is no longer limited by the cavity length drift in this frequency range. (paper)

[en] Highlights: • In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in ${}^{27}$Al${}^{+}$ and ${}^{87}$Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=-1.183\left(6\right)\times {10}^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=7.78\left(30\right)\times {10}^{-5}$ for ${}^{87}$Sr, agree with experimental values very well. • We also estimated the contributions from perturbing states to the $g$-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. • The computational uncertainties were systematically analyzed. In the weak-magnetic-field approximation, we calculated the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in ${}^{27}$Al${}^{+}$ and ${}^{87}$Sr by using the multi-configuration Dirac–Hartree–Fock method. The present results, $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=-1.183\left(6\right)\times {10}^{-3}$ for ${}^{27}$Al${}^{+}$ and $\delta g_{\text{hfs}}^{\left(1\right)}\left({}^3{P}_0^o\right)=7.78\left(30\right)\times {10}^{-5}$ for ${}^{87}$Sr, agree with experimental values very well. The influence of relativistic effects and electron correlations on the involving hyperfine interaction and Zeeman matrix elements, and energy separations were investigated in detail. We also estimated the contributions from perturbing states to the $g$-factors concerned so as to truncate the summation over the perturbing states without loss of accuracy. Based on these, the computational uncertainties were systematically analyzed for the hyperfine-induced Landé $g$-factors of the ${}^3{P}_0^o$ clock states in these two atomic systems.