Phonon avalanches resonant with the optically inverted Zeeman-split $Ē{(}^{2}E)$ doublet of ${\mathrm{Cr}}^{3+}$ have been measured and analyzed in a single crystal of 500-at. ppm ruby $({\mathrm{Al}}_2{\mathrm{O}}_3:{\mathrm{Cr}}^{3+})$ with a geometry adapted to the study of coherence. A set of coherent Bloch equations governing the interacting acoustic wave and spin polarizations is found to provide an excellent description of the results, and to be far superior to incoherent rate equations for the phonon and level populations. The dephasing time conforms with the width of the inhomogeneously broadened transition connecting the $Ē{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.

• Received 9 June 2003

DOI:https://doi.org/10.1103/PhysRevB.68.144302