Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar
(2E) doublet in ruby. Initial population inversion of this two-level system is prepared by selective pulsed optical pumping, and the ensuing stimulated emission of resonant phonons is observed via an accelerated growth of the luminescence intensity emanating from the lower level. Under favorable conditions, a periodic recurrence of the process of stimulated emission is observed, which points to a phonon cavity formed by the end faces of the crystal in combination with a limited interaction length of the resonant phonons. To analyze these phenomena in detail, use is made of rate equations for the phonon occupation and the level populations with explicit account of their position dependences. With plausible assumptions an analytic solution of these equations is achieved, which excellently fits the data. The effect of lattice anharmonicity is shown to depend on the phonon energy in agreement with the theoretical prediction.
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.
Direct relaxation within the optically excited
E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the
c axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with
N∗ is observed of the equilibrium population of the upper Zeeman level of
E to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and
Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the
E direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.
Selective pulsed optical excitation is used in 500-at.ppm ruby (Al 2 O 3 :Cr 3+ ) at 1.4 K to prepare complete population inversion of the Zeeman-split Ē( 2 E ) doublet in a zone of limited size. The inversion results in prolific stimulated emission of phonons resonant with the one-phonon transition connecting the doublet states. The phonons are detected via the R 1 luminescence. The angular and spectral distributions of the associated acoustic wave are measured using a geometry with inverted zones at either end of the crystal, one serving as generator and the other as detector. The divergence appears to be governed by the geometry of the zone, while the spectral distribution is, within errors, in keeping with the inhomogeneously broadened phonon transition.