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Atomic defects in the solid state are a key component of quantum repeaternetworks for long-distance quantum communication. Recently, there has beensignificant interest in rare earth ions, in particular Er$^{3+}$ for itstelecom-band optical transition, but their application has been hampered byoptical spectral diffusion precluding indistinguishable single photongeneration. In this work we implant Er$^{3+}$ into CaWO$_4$, a material thatcombines a non-polar site symmetry, low decoherence from nuclear spins, and isfree of background rare earth ions, to realize significantly reduced opticalspectral diffusion. For shallow implanted ions coupled to nanophotonic cavitieswith large Purcell factor, we observe single-scan optical linewidths of 150 kHzand long-term spectral diffusion of 63 kHz, both close to the Purcell-enhancedradiative linewidth of 21 kHz. This enables the observation of Hong-Ou-Mandelinterference between successively emitted photons with high visibility,measured after a 36 km delay line. We also observe spin relaxation times $T_1$= 3.7 s and $T_2$ > 200 $\mu$s, with the latter limited by paramagneticimpurities in the crystal instead of nuclear spins. This represents asignificant step towards the construction of telecom-band quantum repeaternetworks with single Er$^{3+}$ ions.

Indistinguishable telecom band photons from a single erbium ion in the solid state