Successful operations of quantum-logic-based $$^{27}\hbox {Al}^+$$ ion optical clocks have been reported by several groups. But there are still several lingering issues. The first is the proper choice of logic ions, and the second is the proper quantum state identification methods. In this paper, the advantage of using $$^{25}\hbox {Mg}^+$$ as the logic ion to ensure smaller time-dilation shift is discussed. We also compare several statistical methods to identify the $$^{27}\hbox {Al}^+$$ ion clock state. Finally, we report the observation of the $$^{27}\hbox {Al}^+$$ ion $${^1S_0} \rightarrow ^{3}{P_0}$$ clock transition based on $$^{25}\hbox {Mg}^+$$ – $$^{27}\hbox {Al}^+$$ ion pair. As a precondition for quantum logic spectroscopy (QLS), both the stretch (STR) mode and the center of mass (COM) mode of the $$^{27}\hbox {Al}^+$$ and $$^{25}\hbox {Mg}^+$$ ion pair are cooled to the vibrational ground state by Raman sideband cooling. The mean phonon number is measured to be 0.10(1) for the STR mode and 0.01(1) for the COM mode, respectively. The heating rate is evaluated to be 0.23(5) phonons/s for the STR mode and 3.0(7) phonons/s for the COM mode, respectively. The clock transition is observed with a full-width-half-maximum (FWHM) of 38(4) Hz at 22 ms interrogation time.

中文翻译：

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基于量子逻辑的$$^{27}\hbox {Al}^+$$离子光钟成功运行的实验问题研究

几个小组已经报告了基于量子逻辑的 $$^{27}\hbox {Al}^+$$ 离子光学时钟的成功操作。但仍有几个挥之不去的问题。第一个是逻辑离子的正确选择，第二个是正确的量子态识别方法。在本文中，讨论了使用 $$^{25}\hbox {Mg}^+$$ 作为逻辑离子以确保较小的时间膨胀偏移的优势。我们还比较了几种统计方法来识别 $$^{27}\hbox {Al}^+$$ 离子钟状态。最后，我们报告了对 $$^{27}\hbox {Al}^+$$ 离子 $${^1S_0} \rightarrow ^{3}{P_0}$$ 基于 $$^{25 的时钟转变的观察}\hbox {Mg}^+$$ – $$^{27}\hbox {Al}^+$$ 离子对。作为量子逻辑光谱 (QLS) 的先决条件，$$^{27}\hbox {Al}^+$$ 和 $$^{25}\hbox {Mg}^+$$ 离子的拉伸 (STR) 模式和质心 (COM) 模式对通过拉曼边带冷却冷却到振动基态。STR 模式的平均声子数测量为 0.10(1)，COM 模式的平均声子数分别为 0.01(1)。STR 模式的加热速率估计为 0.23(5) 个声子/s，COM 模式的加热速率分别为 3.0(7) 个声子/s。在 22 ms 询问时间以 38(4) Hz 的全宽半高 (FWHM) 观察到时钟转换。分别。在 22 ms 询问时间以 38(4) Hz 的全宽半高 (FWHM) 观察到时钟转换。分别。在 22 ms 询问时间以 38(4) Hz 的全宽半高 (FWHM) 观察到时钟转换。