Experimental observation of quantum tunneling in shallow optical lattice
Authors: Li Ting , Wang Tao , Wang Ye-Bing , Lu Ben-Quan , Lu Xiao-Tong , Yin Mo-Juan , Chang Hong ,   Key Laboratory of Time and Frequency Primary Standards, National Time Service Center, CAS, Xi’an 710600, China,   School of Astronomy and Space Science, University of Chinese Academy of Sciences, Beijing 100049, China,   Center of Quantum Materials and Devices, College of Physics, Chongqing University, Chongqing 401331, China,   Chongqing Key Laboratory for Strongly Coupled Physics, Chongqing 401331, China
Published: March 2022

For a one-dimensional optical lattice clock built in the horizontal direction, when the stability and uncertainty of the system reach the order of 10<sup>–18</sup> or more, the clock frequency shift caused by the quantum tunneling effect becomes not negligible. In the shallow optical lattice, the quantum tunneling effect will cause the clock transition spectrum to be significantly broadened. So, in this paper the quantum tunneling phenomenon in the shallow optical lattice is studied, laying a foundation for the evaluation of uncertainty of <sup>87</sup>Sr atomic optical lattice clock system. In this experiment, on the platform of one-dimensional <sup>87</sup>Sr atomic optical lattice clock, the narrow-linewidth <sup>1</sup>S<sub>0</sub>(<inline-formula><tex-math id="M4">\begin{document}$ \left|g \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M4.png"/></alternatives></inline-formula>)→<sup>3</sup>P<sub>0</sub>(<inline-formula><tex-math id="M5">\begin{document}$ \left|e \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M5.png"/></alternatives></inline-formula>) transition (that is, the clock transition) is excited by an ultra-stable and ultra-narrow linewidth 698 nm laser, and the distribution of strontium atoms in a specific quantum state is prepared. In the deep optical lattice, after the cold <sup>87</sup>Sr atoms in preparation reach a <inline-formula><tex-math id="M6">\begin{document}$ \left|e,{n}_{z}=1 \right\rangle $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="7-20212038_M6.png"/></alternatives></inline-formula> state, the lattice depth of the optical lattice is adiabatically reduced. Then, the carrier-sideband resolved clock transition spectral line is detected in the shallow optical lattice. The obvious splitting of the carrier spectral line is observed from the clock transition spectral line, which indicates that the strontium atom has an obvious quantum tunneling phenomenon between the adjacent lattice sites of the optical lattice. In addition, when the lattice potential lattice depth is reduced, owing to the incommensurability of lattice light wavelength (813 nm) and clock laser wavelength (698 nm), the tunneling of atoms between adjacent lattice points will lead to spin-orbit coupling effect. Owing to the exceptionally long lifetime (120(3) s) of <sup>3</sup>P<sub>0</sub> state, it can not only suppress the decoherence, but also reduce the atomic loss rate caused by spontaneous emission. This has a natural advantage for studying the spin-orbit coupling of fermions. Therefore, the understanding of quantum tunneling mechanism in optical lattice is not only conducive to improving the uncertainty of the <sup>87</sup>Sr atomic optical lattice clock, but also lays the foundation for observing the spin-orbit coupling effect of fermions on this platform.