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Physical review. B, Condensed matter

Accumulated photon echo in ruby under hydrostatic pressure: Ground-state splitting and spontaneous decay of 2A¯ (2 E)

M.H.F. Overwijk, J. I. Dijkhuis, H. W. de Wijn, Rob Vreeker, Rudolf Sprik, Ad Lagendijk

Published Jun 1, 1991• 1 citation
Publisher

Abstract

The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the $^{4}$${\mathit{A}}_{2}$ ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The $^{4}$${\mathit{A}}_{2}$ ground-state splitting is found to be 0.383\ifmmode\pm\else\textpm\fi{}0.001 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ at ambient pressure, and increases with a slope of +(6\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}${10}^{\mathrm{\ensuremath{-}}3}$ ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$/GPa. The spontaneous decay rate of 2A\ifmmode\bar\else\textasciimacron\fi{}${(}^{2}$E) increases only weakly with pressure. The pressure dependences of both quantities are accounted for in terms of the trigonal-field and spin-orbit-coupling parameters.

DOI
10.1103/physrevb.43.12744

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Physical review. B, Condensed matter•Nov 1, 1979•4 citations
The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the ^{4}$${\mathit{A}}_{2} ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The ^{4}$${\mathit{A}}_{2} ground-state splitting is found to be 0.383\ifmmode\pm\else\textpm\fi{}0.001 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1 at ambient pressure, and increases with a slope of +(6\ifmmode\pm\else\textpm\fi{}1)\ifmmode\times\else\texttimes\fi{}10\ensuremath−3{10}^{\mathrm{\ensuremath{-}}3}10\ensuremath−3 cm\ensuremath−1{\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}cm\ensuremath−1/GPa. The spontaneous decay rate of 2A\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E) increases only weakly with pressure. The pressure dependences of both quantities are accounted for in terms of the trigonal-field and spin-orbit-coupling parameters.
The technique of picosecond accumulated photon echo is applied to 700-at. ppm ruby and 2000-at. ppm alexandrite. The decay of the photon-echo intensity versus the probe-pulse delay displays a beat. A detailed analysis on the basis of Bloch equations shows that the beat frequency is associated with the zero-field splitting of the 4^{4}4A2{\mathit{A}}_{2}A2​ ground state, and that its phase and amplitude are determined by the amount of population communication within this state. Precise values for the spontaneous decay time of 2A\ifmmode\bar\else\textasciimacron\fi{}(2{(}^{2}(2E) and the 4^{4}4A2{\mathit{A}}_{2}A2​ zero-field splitting are derived.
Photon-echo techniques are widely applied nowadays to study optically active ions in solids. The first photon echoes were observed for the R1 transition in ruby (Al2O3: Cr3+) by Kurnit et al1 using the high-power pulses of a ruby laser. Very recently,2 phase relaxation of both the R1 and R2 transitions in ruby was studied at 1.5 K and ambient pressure. Here, use was ma.de of the technique of accun1ulated photon echo,3 which despite the low average laser power offers greatly enhanced detection sensitivity by virtue of the high repetition rate.
Measurements of photon-echo decays in dilute ruby (Cr2{\mathrm{Cr}}_{2}Cr2​O3{\mathrm{O}}_{3}O3​ concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and 4^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (T2{\mathit{T}}_{2}T2​) that are directly proportional to the ratio of the magnetic field (B) to the temperature (T), for the range 2.5B/T20 kG/K. A transition in the decay from exponential to nonexponential behavior for B/T>10 kG/K is observed. Decay times for the 4^{4}4A2{\mathit{A}}_{2}A2​(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the 4^{4}4A2{\mathit{A}}_{2}A2​(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of T2{\mathit{T}}_{2}T2​ with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper 4^{4}4A2{\mathit{A}}_{2}A2​ levels decreases.
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.
A detailed analysis of the photon-echo decay in dilute ruby is presented. The experimental results are in quantitative agreement with an echo-decay theory based on the magnetic interaction between the Cr electronic spin and neighboring Al nuclear magnetic moments. Specifically, the following photon-echo properties are explained by the Cr-Al interaction: (i) modulation of the echo as a function of pulse separation time, (ii) the rapid decay of the echo from the 4A(ms=32)^{4}A({m}_{s}=\frac{3}{2})4A(ms​=23​) to 2E(ms=12)^{2}E({m}_{s}=\frac{1}{2})2E(ms​=21​) transition, (iii) the dependence of the echo on the direction and magnitude of an external magnetic field, (iv) the echo behavior at the 2.06- and 4.12-kG level crossings, and (v) the photon-echo decay in low magnetic fields. In addition, the experiments presented here show that the Cr-Al magnetic interactions in the 2E^{2}E2E excited state are roughly the same as the corresponding interactions in the 4A2^{4}A_{2}4A2​ ground state. The relationship of the photon-echo results to recent fluorescence-linewidth measurements is discussed.
The population ratio $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ of the Zeeman states of E‾(2E)\overline{E}(^{2}E)E(2E) has been measured over five decades of metastable-state concentrations ${N}_{\ensuremath{-}}$ in 2500-ppm ruby at 28 kG and 1.5 K, i.e., in the absence of thermalization between ${\overline{E}}_{\ifmmode\pm\else\textpm\fi{}}$. Upon raising the pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ falls below the value corresponding to optical feeding only due to optically induced two-phonon processes via 2A‾(2E)2\overline{A}(^{2}E)2A(2E). Rate equations account for the findings under the assumption of marginal (ballistic regime) or moderate (spatially diffusive regime) trapping of these 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons. At high pumping, $\frac{{N}_{\ensuremath{-}}}{{N}_{+}}$ further drops to unity, reflecting disturbance of the Boltzmann equilibrium within the 4A2^{4}A_{2}4A2​ ground state.