Ensembles of bismuth-donor spins in silicon are promising storage elements for microwave quantum memories due to their long coherence times, which exceed seconds. The operation of an efficient quantum memory requires the achievement of critical coupling between the spin ensemble and a suitable high-quality factor resonator—this in turn requires a thorough understanding of the line shapes for the relevant spin-resonance transitions, particularly considering the influence of the resonator itself on line broadening. Here, we present pulsed electron-spin-resonance measurements of ensembles of bismuth donors in natural silicon, above which niobium superconducting resonators have been patterned. By studying spin transitions across a range of frequencies and fields, we identify distinct line-broadening mechanisms and, in particular, those that can be suppressed by operating at magnetic-field-insensitive “clock transitions.” Given the donor concentrations and resonator used here, we measure a cooperativity $C\sim 0.2$ and based on our findings we discuss a route to achieve unit cooperativity, as required for a quantum memory.

中文翻译：

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硅与平面微谐振器耦合的铋供体的自旋共振线宽

硅中的铋供体自旋体的集合由于其长的相干时间（超过几秒）而成为微波量子存储器的有前途的存储元件。有效的量子存储器的操作要求实现自旋系综和合适的高质量因子谐振器之间的临界耦合，这又需要对相关自旋共振跃迁的线形有透彻的了解，尤其是考虑到谐振器本身在线扩宽。在这里，我们介绍了天然硅中铋供体集合体的脉冲电子自旋共振测量，在其上方已对铌超导共振器进行了图案化。通过研究频率和磁场范围内的自旋跃迁，我们确定了独特的线展宽机制，尤其是，可以通过对磁场不敏感的“时钟转换”来抑制的噪声。给定此处使用的供体浓度和谐振器，我们可以测量协同性$C〜0.2$ 根据我们的发现，我们讨论了实现量子存储所需的单位合作性的途径。