Avalanches of phonons are generated following population inversion of the Zeeman-split
E(2E) Kramers doublet in a single crystal of dilute ruby
(Al2O3:Cr3+) at
1.4K. The inversion is achieved in a narrow zone of limited extent by selective pulsed optical pumping, and the phonons are detected via luminescence. The associated acoustic wave emanating from the zone propagates through the crystal, reverberates in the acoustic cavity formed by the crystalline end faces, and engages in further amplification each time it passes through the zone until the inversion becomes exhausted. The systems thus acts as a saser (sound amplification by stimulated emission of radiation). The avalanche is adequately described by coherent Bloch equations governing the acoustic wave and the interacting spin polarization, the losses being due to surface scattering and divergence. This conclusion holds good upon reducing the resonance length of the zone by a gradient magnetic field. Finally, the frequency and angular distributions of the avalanche are measured by using two disjunct zones located at opposite ends of the crystal, one serving as generator and the other as detector, in conjunction with a gradient field and lateral displacement. The frequency spread is found to be compatible with the inhomogeneously broadened transition within
E(2E), while the angular divergence is determined by the geometry of the zone.
Superfluorescence and amplified spontaneous emission of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons are observed following inversion of the E\ifmmode\bar\else\textasciimacron\fi{}
(2E)-2A\ifmmode\bar\else\textasciimacron\fi{}
(2E) acoustic transition of
Cr3+ in ruby. The conditions for both of these manifestations of phonon avalanches are selected via the
Cr3+ concentration. Superfluorescence is described in terms of a pendulum equation of the acoustic Bloch vector. Rate equations of the level and phonon populations account for amplified spontaneous emission.