Direct relaxation within the optically excited
E(2E) 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
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+ ions, explains the lattice-bath equilibration. Finally, the prospect is discussed of using the
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 ${\mathrm{cm}}^{\ensuremath{-}1}$.
The relaxation of resonant 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ phonons trapped in a laser-excited cylinder of submillimeter diameter is investigated under the conditions of modulated pumping in ruby of 130, 700, and 2500 at. ppm
Cr3+ at 1.5 K. The decay time
Teff of the 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) population, which is a measure of the phonon relaxation time, appears to depend on the metastable population
N∗ and the cylinder diameter L as the product
N∗L only, establishing boundary-limited phonon decay. At
N∗L below 5\ifmmode\times\else\texttimes\fi{}
1015 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$, pure spatial diffusion prevails.At higher
N∗L, where the measured
Teff levels off at about 1 \ensuremath{\mu}s, dependent on the ground-state concentration, the phonon relaxation is adequately accounted for by the assumption of enhancement by mediation of frequency-shifting Orbach processes at metastable
Cr3+ subject to diagonal exchange with ground-state
Cr3+. Shifts away from resonance to the extent that the phonons escape the zone by ballistic flight are considered active, which predominantly involve distant
Cr3+ neighbors.Furthermore, a random distribution of
Cr3+ is assumed, while the exchange is calibrated with reference to pair spectra. The spin-nonflip transitions of metastable
Cr3+ that are part of the pairs remain at resonance with the phonons because the exchange splittings of \ifmmode \bar{E}\else \={E}\fi{}
(2E) and 2\ifmmode \bar{A}\else \={A}\fi{}
(2E) are comparable. This is borne out by a separate calculation based on a perturbative molecular field. In addition, experiments have been performed as a function of an external magnetic field up to 4 T parallel to the c axis to disclose the effects of successive separation of the spin-flip and spin-nonflip transitions. The resultant complex development of
Teff with field as well as similar data on the
R2 luminescent intensity taken with continuous optical pumping are consistent with exchange-invoked relaxation and, further, yield effective spectral widths of the 29-${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$ transitions of the weakly coupled metastable
Cr3+ of order 1 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$.
Abstract Ruby (α-Al2O3 doped with Cr3+) has been an archetypal material in the development of optical spectroscopy of the solid state for the last 150 years and was the first material that was demonstrated to lase. Notwithstanding the vast literature on ruby, one effect was somehow missed: in a magnetic field B ∥c ∼ 235 mT, the spin-lattice relaxation time T 1 for the |+3/2⟩ level in the 4A2 ground state is massively lengthened to ∼12 s at 1.4 K as demonstrated in this study. This very long relaxation time enables optical pumping of the |+3/2⟩ level via the R 1(±1/2) lines and a considerable +3/2 spin polarization of ∼95% is readily achieved. The observed magnetic field dependence can be quantitatively described using the one-phonon relaxation process.
Techniques for the measurement of non-radiative decay rates between the optically excited states in solid-state laser materials are described. Two crystals have been investigated, ruby (Cr3+:Al2O3) and Sm2+:CaF2. A review of the spectroscopy of these materials is presented with particular emphasis on aspects relevant to non-radiative decay. An experiment is described using a second harmonic Nd3+ Nd:glass Q-switched laser to pump ruby crystals. Limiting non-radiative relaxation times were derived from the rise of fluorescence. Rubies varying in concentration between 0.05% and 0.4% were studied over a range of temperatures, 77 -> 7000 K. 4T2 -> 2E(E + 2A), 4T2 -> 2T1 (Eb) and 4T2 -> 2T1 (2A + Ea) non-radiative relaxations were all found to be <4ns in good agreement with the experimental results of other workers. Two experiments employing a ruby laser to pump Sm2+ :CaF2 are described. The first used a Q-switched laser and, apart from some improvements was similar to the ruby experiment. An upper limit of 4f5 5d pump -> metastable non-radiative decay of 2ns was found for Sm2+:CaF2, The fluorescence decay constant at 295 K was also measured to be 63ns. The second experiment employed a mode-locked laser and the Sm2+:CaF2 non-radiative decay time was <0.5ns. A new effect - provisionally called 'surface emission' - discovered during the ruby measurements, has been examined in detail and the results of this investigation are presented. A phase-shift technique for the measurement of non-radiative decay times is examined in detail. A pilot experiment using a self-mode-locked He-Ne laser at 633 nm to pump Sm2+:CaF2 is described. The non-radiative relaxation time found by this method was <33ps. Suggestions for improved experiments, both pulsed and phase-shifts, are made and the application of the techniques to other materials is discussed.
Paramagnetic ions in solid state crystals form the basis for many advanced technologies like lasers, masers, frequency standards, and quantum-enhanced sensors. One of the most-studied examples is the Cr3+ ion in sapphire (Al2O3), also known as ruby, which has been intensely studied in the 1950s and 1960s. However, despite decades of research on ruby, some of its fundamental optical and spin properties have not been characterized at ultra low-temperatures, yet. In this article, we present optical measurements on a ruby crystal in a dilution refrigerator at ultra-low temperatures down to 20 mK. Analysing the relative populations of its 4A2 ground state spin levels, we extract a lattice temperature of 143(7) mK under continuous laser excitation. We perform spin lattice relaxation T1 measurements in excellent agreement with the direct, one-phonon model. Furthermore, we perform optically detected magnetic resonance measurements showing magnetically driven transitions between the ground state spin levels for various magnetic fields. Our measurements characterize some of ruby's low temperature spin properties, and lay the foundations for more advanced spin control experiments.