Coherent spin dynamics of rare-earth doped crystals in the high-cooperativity regime

Abstract

Rare-earth doped crystals have long coherence times and the potential to provide quantum interfaces between microwave and optical photons. Such applications benefit from a high cooperativity between the spin ensemble and a microwave cavity---this motivates an increase in the rare-earth ion concentration which in turn impacts the spin coherence lifetime. We measure spin dynamics of two rare-earth spin species, $^{145}\mathrm{Nd}$ and Yb, doped into ${\mathrm{Y}}_{\text{2}}{\mathrm{SiO}}_{\text{5}}$, coupled to a planar microwave resonator in the high-cooperativity regime, in the temperature range $1.2\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ to $14\phantom{\rule{0.16em}{0ex}}\mathrm{mK}$. We identify relevant decoherence mechanisms, including instantaneous diffusion arising from resonant spins and temperature-dependent spectral diffusion from impurity electron and nuclear spins in the environment. We explore two methods to mitigate the effects of spectral diffusion in the Yb system in the low-temperature limit, first, using magnetic fields of up to 1 T to suppress impurity spin dynamics and, second, using transitions with low effective $g$ factors to reduce sensitivity to such dynamics. Finally, we demonstrate how the ``clock transition'' present in the $^{171}\mathrm{Yb}$ system at zero field can be used to increase coherence times up to ${T}_{2}=6(1)\phantom{\rule{0.16em}{0ex}}\mathrm{ms}$.