Coherent optical-microwave interface for manipulation of low-field electronic clock transitions in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$

The coherent interaction of solid-state spins with both optical and microwave fields provides a platform for a range of quantum technologies, such as quantum sensing, microwave-to-optical quantum transduction and optical quantum memories. Rare-earth ions with electronic spins are interesting in this context, but it is challenging to simultaneously and efficiently drive both optical and microwave transitions over a long crystal. In this work, we use a loop-gap microwave resonator to coherently drive optical and microwave clock transitions in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$, at close to zero external magnetic field. The low magnetic field regime is particularly interesting for interfacing these spin transitions with superconducting circuits. We achieve a Rabi frequency of 0.56 MHz at 2.497 GHz, over a 1-cm long crystal. Furthermore, we provide new insights into the spin dephasing mechanism at very low fields, showing that superhyperfine-induced collapse of the Hahn echo signal plays an important role at low fields. Our calculations and measurements reveal that the effective magnetic moment can be manipulated in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$, allowing to suppress the superhyperfine interaction at the clock transition. At a doping concentration of 2 ppm and a temperature of $3.4$ K, we achieve the longest spin coherence time of $10.0 \pm 0.4 ~\text{ms}$ reported in $^{171}$Yb$^{3+}$:Y$_2$SiO$_5$.