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Efficient and reversible optical to microwave coherent transducers arerequired to enable entanglement transfer between superconducting qubits andlight for quantum networks. Rare-earth-doped crystals that possess narrowoptical and spin transitions are a promising way to implement these devices.Current approaches use ground-state electron spin transitions that havecoherence lifetimes ($T_2$) often limited by spin flip-flop processes and/orspectral diffusion, even at very low temperatures. Here, we investigate spincoherence in an optically excited state of an Er$^{3+}$:Y$_2$SiO$_5$ crystal attemperatures from 1.6 to 3.5 K and under a weak 8.7 mT magnetic field. Spincoherence and population lifetimes of up to 1.6 $\mu$s and 1.2 ms,respectively, are measured by 2- and 3-pulse optically-detected spin echoexperiments. Analysis of the dephasing processes suggest that ms $T_2$ can bereached at lower temperatures for the excited-state spins, whereas ground-statespin states could be limited to a few $\mu$s due to resonant interactions withthe other Er$^{3+}$ spins in the lattice (spin diffusion). We propose a quantumtransducer scheme with the potential for close to unit efficiency that exploitsthe specific advantages offered by the spin states of optically excitedelectronic energy levels.

Electron Spin Coherences in Rare-Earth Optically Excited States for Microwave to Optical Quantum Transducers