  Quantum light-matter interfaces (QLMIs) connecting stationary qubits to
photons will enable optical networks for quantum communications, precise global
time keeping, photon switching, and studies of fundamental physics.
Rare-earth-ion (REI) doped crystals are state-of-the-art materials for optical
quantum memories and quantum transducers between optical photons, microwave
photons and spin waves. Here we demonstrate coupling of an ensemble of
neodymium REIs to photonic nano-cavities fabricated in the yttrium
orthosilicate host crystal. Cavity quantum electrodynamics effects including
Purcell enhancement (F=42) and dipole-induced transparency are observed on the
highly coherent 4I9/2-4F3/2 optical transition. Fluctuations in the cavity
transmission due to statistical fine structure of the atomic density are
measured, indicating operation at the quantum level. Coherent optical control
of cavity-coupled REIs is performed via photon echoes. Long optical coherence
times (T2~100 microseconds) and small inhomogeneous broadening are measured for
the cavity-coupled REIs, thus demonstrating their potential for on-chip
scalable QLMIs.
