Evaluation of systematic uncertainty for transportable <sup>87</sup>Sr optical lattice clock

Abstract

Transportable optical clocks have broad applications in scientific research and engineering. Accurate evaluation of systematic uncertainty for the transportable <sup>87</sup>Sr optical lattice clock is a prerequisite for the practical realization of the optical clock. Four main frequency shifts of the <sup>87</sup>Sr optical lattice clock are measured, i.e. blackbody-radiation (BBR) shift, collision shift, lattice alternating current (AC) Stark shift, and second-order Zeeman shift. Firstly, by measuring the temperature distribution on the surface of the magneto-optical trap cavity and analyzing the influence of different heat sources on atomic cloud, the BBR shift correction is measured to be 50.4 × 10<sup>–16</sup> Hz with an uncertainty of 5.1 × 10<sup>–17</sup>. Secondly, the time-interleaved self-comparison method is used under high and low atom density condition to evaluate the collision shift of the system. The correction of collision shift is 4.7 × 10<sup>–16</sup> with an uncertainty of 5.6 × 10<sup>–17</sup>. Thirdly, the lattice AC Stark shift is evaluated by the time-interleaved self-comparison method. By measuring the dependence of the lattice AC Stark shift on the wavelength of the lattice light, the magic wavelength is measured to be 368554393(78) MHz. As a result, the lattice AC Stark shift correction is 3.0 × 10<sup>–16</sup> with an uncertainty of 2.2 × 10<sup>–16</sup>. Finally, using the time-interleaved self-comparison technology, the second-order Zeeman frequency shift is evaluated by measuring the fluctuation of the difference in center frequency between the <inline-formula><tex-math id="M300">\begin{document}${m_{\text{F}}} = + {9 / 2} \to {m_{\text{F}}} = + {9 / 2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M300.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M300.png"/></alternatives></inline-formula> polarization spectrum and <inline-formula><tex-math id="M301">\begin{document}${m_{\text{F}}} = - {9 / 2} \to {m_{\text{F}}} = - {9 / 2}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M301.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20201204_M301.png"/></alternatives></inline-formula> polarization spectrum. The correction of second-order Zeeman shift is calculated to be 0.7 × 10<sup>–16</sup>, and corresponding uncertainty is 0.2 × 10<sup>–17</sup>. Experimental results indicate that the frequency shift correction due to the blackbody radiation is the largest, while the uncertainty caused by the lattice AC Stark effect is the largest in the evaluated shifts. The systematic shift is 58.8 × 10<sup>–16</sup>, the total uncertainty is 2.3 × 10<sup>–16</sup>. In the next work, the magneto-optical trap cavity will be placed in a blackbody-radiation cavity to reduce the blackbody-radiation shift. The uncertainty of the collision shift will be reduced by increasing the beam waist of the lattice and reducing the potential well depth of the lattice, which will reduce the density of atoms. What is more, the light source for the optical lattice after spectral filtering will be measured by an optical frequency comb locked to the hydrogen clock signal to reduce the uncertainty of the lattice AC Stark frequency shift. The systematic uncertainty is expected to be on the order of 10<sup>–17</sup>. The evaluation of the systematic uncertainty for the transportable <sup>87</sup>Sr optical lattice clock lays the foundation for the practical application.