Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review B

Optically excited ruby as a saser: Experiment and theory

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

Published Jul 9, 2007• 19 citations
Publisher

Abstract

Avalanches of phonons are generated following population inversion of the Zeeman-split $\overline{E}(^{2}E)$ Kramers doublet in a single crystal of dilute ruby $({\mathrm{Al}}_{2}{\mathrm{O}}_{3}:{\mathrm{Cr}}^{3+})$ at $1.4\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. 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 $\overline{E}(^{2}E)$, while the angular divergence is determined by the geometry of the zone.

DOI
10.1103/physrevb.76.024302

Related papers

SASER action in optically excited ruby: Angular and spectral distribution

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

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.

Journal of Physics Conference Series•Dec 1, 2007•1 citation

Coherence of phonon avalanches in ruby

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

Phonon avalanches resonant with the optically inverted Zeeman-split $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ 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 $\ifmmode \bar{E}\else \={E}\fi{}{(}^{2}E)$ states, which indicates that dephasing primarily occurs by the spread in frequencies.

Physical review. B, Condensed matter•Oct 20, 2003•16 citations

Coherent phonons generated by stimulated emission in ruby

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

The Zeeman-split (2E) doublet of Cr3+ in a single crystal of 500-at.ppm ruby (Al2O3:Cr3+) is population inverted by selective transient optical pumping, and the resulting avalanches of resonant phonons are measured and analyzed. Coherent Bloch equations governing the acoustic wave and the transverse spin polarizations are found to provide an excellent description. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Physica status solidi. C, Conferences and critical reviews/Physica status solidi. C, Current topics in solid state physics•Nov 1, 2004•1 citation

Superfluorescence and amplified spontaneous emission of 29- cm−1 phonons in ruby

M.H.F. Overwijk, J. I. Dijkhuis, H. W. de Wijn

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{}${(}^{2}$E)-2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) acoustic transition of ${\mathrm{Cr}}^{3+}$ in ruby. The conditions for both of these manifestations of phonon avalanches are selected via the ${\mathrm{Cr}}^{3+}$ 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.

Physical Review Letters•Oct 15, 1990•11 citations

Optical detection and phonon bottleneck of the direct decay within the E¯(E2) state of ruby

J. I. Dijkhuis, K. Huibregtse, H. W. de Wijn

Direct relaxation within the optically excited $\overline{E}(^{2}E)$ 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 $\overline{E}$ 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 ${\mathrm{Cr}}^{3+}$ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the $\overline{E}$ 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 ${\mathrm{cm}}^{\ensuremath{-}1}$.

Physical review. B, Condensed matter•Sep 1, 1979•19 citations

Stimulated emission of phonons in an acoustical cavity

Peter A. Fokker, J. I. Dijkhuis, H. W. de Wijn

Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar${(}^{2}$E) 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.

Physical review. B, Condensed matter•Feb 1, 1997•45 citations
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.
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.
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.
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{}(2{(}^{2}(2E)-2A\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E) acoustic transition of Cr3+{\mathrm{Cr}}^{3+}Cr3+ in ruby. The conditions for both of these manifestations of phonon avalanches are selected via the Cr3+{\mathrm{Cr}}^{3+}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.
Direct relaxation within the optically excited E‾(2E)\overline{E}(^{2}E)E(2E) level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the ccc 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∗{N}^{*}N∗ is observed of the equilibrium population of the upper Zeeman level of E‾\overline{E}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+{\mathrm{Cr}}^{3+}Cr3+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the E‾\overline{E}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 ${\mathrm{cm}}^{\ensuremath{-}1}$.
Stimulated emission is studied of phonons resonant with the metastable Zeeman-split E-bar(2{(}^{2}(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.