Coherence of phonon avalanches in ruby
L. G. Tilstra, A. F. M. Arts, and H. W. de Wijn
Faculty of Physics and Astronomy, and Debye Institute, Utrecht
University, P.O. Box 80000, 3508 TA Utrecht, The Netherlands
Phonon avalanches resonant with the optically inverted Zeeman-split
E(2E) doublet of Cr3+ have been measured and
analyzed in a single crystal of 500-at.ppm ruby
(Al2O3:Cr3+) 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 E(2E) states, which indicates that dephasing
primarily occurs by the spread in frequencies.