The majority of ions and other charged particles of spectroscopic interest lack the fast, cycling transitions that are necessary for direct laser cooling. In most cases, they can still be cooled sympathetically through their Coulomb interaction with a second, coolable ion species confined in the same potential. If the charge-to-mass ratios of the two ion types are too mismatched, the cooling of certain motional degrees of freedom becomes difficult. This limits both the achievable fidelity of quantum gates and the spectroscopic accuracy. Here, we introduce a novel algorithmic cooling protocol for transferring phonons from poorly to efficiently cooled modes. We demonstrate it experimentally by simultaneously bringing two motional modes of a ${\mathrm{Be}}^{+}\text{−}{\mathrm{Ar}}^{13+}$ mixed Coulomb crystal close to their zero-point energies, despite the weak coupling between the ions. We reach the lowest temperature reported for a highly charged ion, with a residual temperature of only $T\lesssim 200\mu \mathrm{K}$ in each of the two modes, corresponding to a residual mean motional phonon number of $⟨n⟩\lesssim 0.4$. Combined with the lowest observed electric-field noise in a radio-frequency ion trap, these values enable an optical clock based on a highly charged ion with fractional systematic uncertainty below the ${10}^{-18}$ level. Our scheme is also applicable to (anti)protons, molecular ions, macroscopic charged particles, and other highly charged ion species, enabling reliable preparation of their motional quantum ground states in traps.

中文翻译：

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使用量子逻辑的弱耦合振荡器的算法基态冷却

大多数离子和其他对光谱感兴趣的带电粒子缺乏直接激光冷却所需的快速循环跃迁。在大多数情况下，它们仍然可以通过它们与限制在相同电位中的第二个可冷却离子物质的库仑相互作用而被和谐地冷却。如果两种离子类型的荷质比太不匹配，某些运动自由度的冷却就会变得困难。这限制了量子门可实现的保真度和光谱精度。在这里，我们介绍了一种新颖的算法冷却协议，用于将声子从冷却不佳的模式转移到有效冷却的模式。我们通过同时引入两个运动模式来实验证明它${是}^{+}\text{-}{\mathrm{氩气}}^{13+}$尽管离子之间的耦合很弱，但混合库仑晶体接近零点能量。我们达到了高电荷离子报告的最低温度，剩余温度仅为$吨\lesssim 200\mu \mathrm{钾}$ 在两种模式中的每一种中，对应于剩余的平均运动声子数 $⟨n⟩\lesssim 0.4$. 结合射频离子阱中观察到的最低电场噪声，这些值使基于高度带电离子的光学时钟成为可能，其部分系统不确定性低于${10}^{-18}$等级。我们的方案也适用于（反）质子、分子离子、宏观带电粒子和其他高带电离子种类，能够可靠地制备它们在陷阱中的运动量子基态。