  Nano-structuring impurity-doped crystals affects the phonon density of states
and thereby modifies the atomic dynamics induced by interaction with phonons.
We propose the use of nano-structured materials in the form of powders or
phononic bandgap crystals to enable or improve persistent spectral hole-burning
and coherence for inhomogeneously broadened absorption lines in
rare-earth-ion-doped crystals. This is crucial for applications such as
ultra-precise radio-frequency spectrum analyzers and optical quantum memories.
As an example, we discuss how phonon engineering can enable spectral hole
burning in erbium-doped materials operating in the convenient telecommunication
band, and present simulations for density of states of nano-sized powders and
phononic crystals for the case of Y2SiO5, a widely-used material in current
quantum memory research.
