Physical Review Letters

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

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

Published Oct 15, 1990• 11 citations

Abstract

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.

DOI: 10.1103/physrevlett.65.2015

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Physical Review Letters

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

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

Published Oct 15, 1990• 11 citations

Publisher

Abstract

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.

DOI: 10.1103/physrevlett.65.2015

Related papers

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.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.

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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.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.

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Trapping of point-contact-generated 29- cm−1 phonons in ruby

Kars Troost, J. I. Dijkhuis, H. W. de Wijn

Trapping of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons by optically excited ${\mathrm{Cr}}^{3+}$ ions in ruby is studied at phonon occupations of up to order unity. The 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons are supplied by transient excitation of a metallic point contact and subsequent conversion of the injected phonons to resonance. The growth and the decay of the trapped phonon population are markedly non-single-exponential quantities, particularly at higher phonon populations. A quantitative analysis of these effects is made on the basis of phenomenological rate equations of the ion and phonon populations. These equations make explicit allowance for the line shape of the E\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E)-2A\ifmmode\bar\else\textasciimacron\fi{} ${(}^{2}$ E) phonon transition as well as for feeding and loss of resonant phonons by mediation of weakly exchange-coupled ${\mathrm{Cr}}^{3+}$ pairs. At the higher phonon occupations, the transition appears to be dynamically broadened by stimulated phonon emission, which reduces the trapping efficiency.Trapping of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons by optically excited ${\mathrm{Cr}}^{3+}$ ions in ruby is studied at phonon occupations of up to order unity. The 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons are supplied by transient excitation of a metallic point contact and subsequent conversion of the injected phonons to resonance. The growth and the decay of the trapped phonon population are markedly non-single-exponential quantities, particularly at higher phonon populations. A quantitative analysis of these effects is made on the basis of phenomenological rate equations of the ion and phonon populations. These equations make explicit allowance for the line shape of the E\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E)-2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) phonon transition as well as for feeding and loss of resonant phonons by mediation of weakly exchange-coupled ${\mathrm{Cr}}^{3+}$ pairs. At the higher phonon occupations, the transition appears to be dynamically broadened by stimulated phonon emission, which reduces the trapping efficiency.

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Stimulated emission of phonons in a ruby fiber

Peter A. Fokker, W. D. Koster, J. I. Dijkhuis +4 more

Physical review. B, Condensed matterAug 1, 19975 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.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 matterFeb 1, 199745 citations

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+}

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.

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+})

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.

Trapping of 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons by optically excited

{\mathrm{Cr}}^{3+}

ions in ruby is studied at phonon occupations of up to order unity. The 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons are supplied by transient excitation of a metallic point contact and subsequent conversion of the injected phonons to resonance. The growth and the decay of the trapped phonon population are markedly non-single-exponential quantities, particularly at higher phonon populations. A quantitative analysis of these effects is made on the basis of phenomenological rate equations of the ion and phonon populations. These equations make explicit allowance for the line shape of the E\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E)-2A\ifmmode\bar\else\textasciimacron\fi{}

{(}^{2}

E) phonon transition as well as for feeding and loss of resonant phonons by mediation of weakly exchange-coupled

{\mathrm{Cr}}^{3+}

pairs. At the higher phonon occupations, the transition appears to be dynamically broadened by stimulated phonon emission, which reduces the trapping efficiency.

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.