Resonance radiation trapping with application to the phonon bottleneck in optically pumped ruby

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}$${\mathrm{s}}^{\ensuremath{-}1}$ is close to the theoretical estimate based on static experiments in ruby. When increasing optical pumping, the phonon-bath conduction is demonstrated to become the limiting process due to resonant trapping of the phonons. Following pulsed excitation, a prolonging of the decay time by a factor up to 13 is attained at excited-state concentrations ${N}^{*}\ensuremath{\sim}2\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. In stationary experiments, a nonlinear increase with ${N}^{*}$ is observed of the equilibrium population of the upper Zeeman level of $\overline{E}$ to over a decade above the nonbottlenecked value, corresponding to bottlenecking factors of over \ensuremath{\sim}200. Under the assumption of a constant phonon lifetime of the order of the flight time through the illuminated region, rate equations appear to consistently account for the experiments. A Gaussian-type resonance line, fully homogenized supposedly by magnetic interactions with the surrounding Al nuclei and ${\mathrm{Cr}}^{3+}$ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the $\overline{E}$ direct transition in ruby as a tunable phonon generator and detector with bandwidth 0.002 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the practical frequency range of 2-15 ${\mathrm{cm}}^{\ensuremath{-}1}$.Direct relaxation within the optically excited $\overline{E}(^{2}E)$ level of 700-ppm ruby is investigated in magnetic fields up to 65 kG making an angle to the $c$ axis. At low pump intensities, the experimental relaxation rates are found to be in excellent agreement with the theory by Blume et al., predicting a fifth-power dependence on field and a ${cos}^{3}\ensuremath{\theta}{sin}^{2}\ensuremath{\theta}$ dependence on orientation. The observed proportionality constant of 4.7 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}19}$ ${\mathrm{G}}^{\ensuremath{-}5}$${\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 matterSep 1, 197919 citations

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 ${\mathrm{cm}}^{\ensuremath{-}1}$.