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Chinese Journal of Physics

Nature of the Phonon Beam Emitted by the Ruby Saser

Lieuwe Gijsbert Tilstra, A. F. M. Arts, H. W. de Wijn

Published Feb 1, 2011• 0 citations
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Abstract

The properties of the phonon beam emitted by the optically pumped ”hot zone” in the ruby saser are examined. The phonons generated are detected via the R1 luminescence and analyzed by the use of coherent Bloch-type equations. The phonons are found to reach occupations p of order 3000, which at the relevant phonon frequency of 50.4 GHz corresponds to temperatures of order 5000 K. The spectral and angular distributions of the beam have been measured in experiments involving pumped zones at either end of the crystal, one serving as generator, the other one as detector. The spectral distribution is 54±10 MHz wide at half value, or 0.1% of the phonon frequency. Within errors, this is in conformity with the inhomogeneous Gaussian frequency spread inherent to the sasering one-phonon transition. The angular divergence appears to be governed by the geometry of the hot zone. Under the prevailing conditions it measures 3 degrees of arc to either side.

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The properties of the phonon beam emitted by the optically pumped ”hot zone” in the ruby saser are examined. The phonons generated are detected via the R1 luminescence and analyzed by the use of coherent Bloch-type equations. The phonons are found to reach occupations p of order 3000, which at the relevant phonon frequency of 50.4 GHz corresponds to temperatures of order 5000 K. The spectral and angular distributions of the beam have been measured in experiments involving pumped zones at either end of the crystal, one serving as generator, the other one as detector. The spectral distribution is 54±10 MHz wide at half value, or 0.1% of the phonon frequency. Within errors, this is in conformity with the inhomogeneous Gaussian frequency spread inherent to the sasering one-phonon transition. The angular divergence appears to be governed by the geometry of the hot zone. Under the prevailing conditions it measures 3 degrees of arc to either side.
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.
Avalanches of phonons are generated following population inversion of the Zeeman-split E‾(2E)\overline{E}(^{2}E)E(2E) Kramers doublet in a single crystal of dilute ruby (Al2O3:Cr3+)({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})(Al2​O3​:Cr3+) at 1.4K1.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}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)\overline{E}(^{2}E)E(2E), while the angular divergence is determined by the geometry of the zone.
Phonon avalanches resonant with the optically inverted Zeeman-split $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ doublet of Cr3+{\mathrm{Cr}}^{3+}Cr3+ have been measured and analyzed in a single crystal of 500-at. ppm ruby (Al2O3:Cr3+)({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})(Al2​O3​: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 $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.
The ruby R2{R}_{2}R2​-line intensity at 2.1 K is observed to be nearly quadratically depedent on the R1{R}_{1}R1​ intensity, indicative of strongly bottlenecked 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons generated by the $2\overline{A}(^{2}E)\ensuremath{\rightarrow}\overline{E}(^{2}E)$ decay in the optical pumping cycle. The spectral width of the phonon excitation is probed by separating the degenerate phonon packets in a magnetic field and monitoring the decrease of the bottlenecking.
We introduce a technique utilizing the evanescent field of an optical waveguide to examine the dynamics of nonequilibrium high-frequency phonons resonant with optically excited centers in zones of submicrometer dimension. The technique is used to create a nearly saturated zone of excited Cr3+{\mathrm{Cr}}^{3+}Cr3+ ions at the surface of a 700-at. ppm ruby crystal at 1.5 K by optical pumping through the broad bands. At the same time, the optical pumping serves to generate resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons. The decay of the combined spin-phonon system, measured via the R2{\mathit{R}}_{2}R2​ luminescence following interruption of the optical pumping, is explained by elastic spatial diffusion in parallel with spectral wipeout. The time constant for loss by spatial diffusion is derived rigorously from rate equations. Spectral wipeout is treated according to the model developed by Goossens et al. based on one-site inelastic scattering by weakly exchange-coupled Cr3+{\mathrm{Cr}}^{3+}Cr3+ pairs, but modified to include the appreciable elastic diffusion remaining after wipeout under the present extreme conditions. Spectral wipeout turns out to predominate at high excited-state concentration. The optical feeding into 2A\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E) is found to result mainly from excited-state absorption starting from E\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E), despite the low probability of the latter at the light wavelength used (514.5 nm).