  The spectral addressing of many individual rare-earth dopants in optical
resonators offers great potential for realizing distributed quantum information
processors. To this end, it is required to understand and control the spectral
properties of the emitters in micron-scale devices. Here, erbium emitters are
investigated in a Fabry-Perot resonator which contains a ten-micrometer-thin
membrane of crystalline yttrium orthosilicate that is co-doped with europium.
The co-doping allows for tailoring the inhomogeneous distribution of the
emitter frequency, which enables high-fidelity spectral multiplexing of more
than 360 qubits with Purcell factors exceeding 35. At the same time, the
optical coherence is preserved up to 0.62(3) ms under dynamical decoupling.
Without decoupling, the coherence still reaches the lifetime limit for the
emitters with the strongest Purcell enhancement that leads up to a 110-fold
lifetime reduction, down to 0.104(9) ms. Future work may combine this with
long-lived nuclear spin memories, which makes the investigated co-doped
membranes a promising platform for quantum repeaters and distributed quantum
computers.
