LiY $_{1-x}$ Ho $_{x}$ F $_{4}$低能电子哈密顿量的精确测定
Precise determination of low energy electronuclear Hamiltonian for LiY$_{1-x}$Ho$_{x}$F$_{4}$
摘要：
我们使用互补光谱方法直接测量稀土量子磁体LiY $_{1-x}$ Ho $_{x}$ F $_{4}$的最低晶场能量，包括它们的超精细分裂，分辨率比以前的工作高10倍以上。我们能够观察到由于$^6\mathrm{Li}$和$^7\mathrm{Li}$同位素的能级分裂，以及源自偶极和四极超精细相互作用的非等距间隔的超精细跃迁。我们提供了精细的晶场参数和提取的偶极和四极超精细常数${A_J=0.02703\pm0.00003}$ $\textrm{cm}^{-1}$和${B= 0.04 \pm0.01}$ $\textrm{cm}^{-1}$，分别。因此，我们确定了所有的晶体场能级和磁矩的$^5I_8$基态流形，包括（非线性）超精细校正。后者与基于计量的估计数相符。非线性超精细校正的尺度为不均匀线宽设置了上限，该上限仍然允许对所选择的超精细过渡进行唯一寻址。例如用于量子信息应用。此外，我们建立了远红外，低温折射率的LiY $_{1-x}$ Ho $_{x}$ F $_{4}$。
英文摘要：
We use complementary optical spectroscopy methods to directly measure the lowest crystal-field energies of the rare-earth quantum magnet LiY$_{1-x}$Ho$_{x}$F$_{4}$, including their hyperfine splittings, with more than 10 times higher resolution than previous work. We are able to observe energy level splittings due to the $^6\mathrm{Li}$ and $^7\mathrm{Li}$ isotopes, as well as non-equidistantly spaced hyperfine transitions originating from dipolar and quadrupolar hyperfine interactions. We provide refined crystal field parameters and extract the dipolar and quadrupolar hyperfine constants ${A_J=0.02703\pm0.00003}$ $\textrm{cm}^{-1}$ and ${B= 0.04 \pm0.01}$ $\textrm{cm}^{-1}$, respectively. Thereupon we determine all crystal-field energy levels and magnetic moments of the $^5I_8$ ground state manifold, including the (non-linear) hyperfine corrections. The latter match the measurement-based estimates. The scale of the non-linear hyperfine corrections sets an upper bound for the inhomogeneous line widths that would still allow for unique addressing of a selected hyperfine transition. e.g. for quantum information applications. Additionally, we establish the far-infrared, low-temperature refractive index of LiY$_{1-x}$Ho$_{x}$F$_{4}$.
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