We theoretically and experimentally investigate double-electromagnetically-induced transparency (double-EIT) cooling of two-dimensional ion crystals confined in a Paul trap. The double-EIT ground-state cooling is observed for ${{}^{171}\mathrm{Yb}}^{+}$ ions with a clock state, for which EIT cooling has not been realized like many other ions with a simple $\mathrm{\Lambda }$ scheme. A cooling rate of $\dot{\overline{n}}=34(\pm 1.8){\mathrm{ms}}^{-1}$ and a cooling limit of $\overline{n}=0.06(\pm 0.059)$ are observed for a single ion. The measured cooling rate and limit are consistent with theoretical predictions. We apply double-EIT cooling to the transverse modes of two-dimensional (2D) crystals with up to 12 ions. In our 2D crystals, the micromotion and the transverse mode directions are perpendicular, which makes them decoupled. Therefore, the cooling on transverse modes is not disturbed by micromotion, which is confirmed in our experiment. For the center of mass mode of a 12-ion crystal, we observe a cooling rate and a cooling limit that are consistent with those of a single ion, including heating rates proportional to the number of ions. This method can be extended to other hyperfine qubits, and near ground-state cooling of stationary 2D crystals with large numbers of ions may advance the field of quantum information sciences.

中文翻译：

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固定二维离子晶体的双电磁感应透明基态冷却

我们在理论上和实验上研究了限制在Paul阱中的二维离子晶体的双电磁感应透明（double-EIT）冷却。观察到双EIT基态冷却${{}^{171}b}^{+}$ 带有时钟状态的离子，没有像其他许多离子一样简单地实现EIT冷却 $\mathrm{\Lambda }$方案。冷却速度为$\dot{\overline{ñ}}=34（\pm 1.8）{\mathrm{多发性硬化症}}^{-\mathrm{1个}}$ 冷却极限为 $\overline{ñ}=0.06（\pm 0.059）$观察单个离子。测得的冷却速率和极限与理论预测一致。我们将双EIT冷却应用于具有12个离子的二维（2D）晶体的横向模。在我们的2D晶体中，微运动和横向模式方向是垂直的，这使它们解耦。因此，横向运动的冷却不会受到微运动的干扰，这在我们的实验中得到了证实。对于12离子晶体的质心模式，我们观察到的冷却速率和冷却极限与单个离子的一致，包括与离子数量成比例的加热速率。该方法可以扩展到其他超精细量子位，并且具有大量离子的固定2D晶体的近基态冷却可以推动量子信息科学领域的发展。