We propose an optical scheme for generating entanglement between co-trapped identical or dissimilar alkaline-earth atomic ions (${}^{40}\mathrm{Ca}^{+}$, ${}^{88}\mathrm{Sr}^{+}$, ${}^{138}\mathrm{Ba}^{+}$, ${}^{226}\mathrm{Ra}^{+}$) which exhibits fundamental error rates below ${10}^{-4}$ and can be implemented with a broad range of laser wavelengths spanning from ultraviolet to infrared. We also discuss straightforward extensions of this technique to include the two lightest group-2 ions (${\text{Be}}^{+}$, ${\text{Mg}}^{+}$) for multispecies entanglement. The key elements of this wavelength-insensitive geometric phase gate are the use of a ground ($S_{1/2}$) and a metastable ($D_{5/2}$) electronic state as the qubit levels within a ${\sigma }^z{\sigma }^z$ light-shift entangling gate. We present a detailed analysis of the principles and fundamental error sources for this gate scheme which includes photon scattering and spontaneous emission decoherence, calculating two-qubit-gate error rates and durations at fixed laser beam intensity over a large portion of the optical spectrum (300 nm to $2\mu \text{m}$) for an assortment of ion pairs. We contrast the advantages and disadvantages of this technique against previous trapped-ion entangling gates and discuss its applications to quantum information processing and simulation with like and multispecies ion crystals.

中文翻译：

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波长不敏感的多族纠缠门，用于第2组原子离子

我们提出了一种光学方案，用于在同陷的相同或不同的碱土原子离子之间产生纠缠（${}^{40}钙^{+}$， ${}^{88}r^{+}$， ${}^{138}巴^{+}$， ${}^{226}镭^{+}$），其基本错误率低于 ${10}^{-4}$可以用从紫外到红外的各种波长的激光来实现。我们还将讨论此技术的直接扩展，以包括两个最轻的2族离子（${\text{是}}^{+}$， ${\text{镁}}^{+}$）用于多物种纠缠。这种对波长不敏感的几何相位门的关键要素是使用接地（${\mathrm{小号}}_{\mathrm{1个}/\mathrm{2个}}$）和亚稳（$d_{5/\mathrm{2个}}$）电子状态作为一个内部的量子位 ${\sigma }^{ž}{\sigma }^{ž}$光移纠缠门。我们对该门方案的原理和基本误差源进行了详细分析，包括光子散射和自发发射退相干，在很大的光谱范围内计算了两个量子位门的误差率和固定激光束强度下的持续时间（300纳米至$\mathrm{2个}\mu \text{米}$）用于各种离子对。我们对比了该技术与以前的俘获离子纠缠门的优缺点，并讨论了其在类似和多物种离子晶体的量子信息处理和模拟中的应用。