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.
Measurements of photon-echo decays in dilute ruby (
Cr2O3 concentration of 0.018 at. %) in magnetic fields up to 29.5 kG are reported. Echoes from the
4A2(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) and
4A2(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) transitions have dephasing times (
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
4A2(-1/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E(-1/2) echo are roughly a factor of 3 longer than for the
4A2(-3/2)${\mathrm{\ensuremath{\leftrightarrows}}}^{2}$E,E\ifmmode\bar\else\textasciimacron\fi{}(-1/2) echo. We attribute the lengthening of
T2 with increasing B/T to the suppression of Cr-Cr spin flip-flops as the population of the upper
4A2 levels decreases.
A large number of small but sharp changes (increases and decreases) of the R 1 fluorescence in ruby are observed as a function of applied magnetic field between 2 K and 77 K. At liquid helium temperatures, these signals have linewidths much narrower than the inhomogeneous linewidth (∼0.1 cm -1 ) of the R 1 line. All of these signals appear at the fields where the Zeeman splittings in the excited state \bar E ( 2 E ) and the ground state 4 A 2 satisfy an energy-matching condition for simultaneous transitions of two or more ions. Two distinct mechanisms are found to be responsible for the signals: spin-spin cross-relaxation between \bar E ( 2 E ) and 4 A 2 , and resonant self-trapping of the R 1 line. From the temperature dependence of the linewidths of the signals, thermal broadening of \bar E ( 2 E ) is measured below 77 K. Similar signals are observed in the N lines due to energy transfer from isolated ions to pairs.
Transition probabilities of spin-lattice relaxation (RTP) based on the Kronig-Van Vleck mechanism are calculated for ruby for the orientations θ = 90 and 54° and for magnetic fields up to 15 kG. Inversion ratios are evaluated on the basis of the RTP's for various pumping modes. Experimental measurements of the inversion ratio and pumping power at a signal frequency of fs = 22.2 GHz are carried out. The Kronig-Van Vleck mechanism is shown to be the principal mechanism of spin-lattice relaxation for high magnetic fields and low concentrations of paramagnetic ions.
A detailed experimental study is reported of the decay of circularly polarized photon echoes as a function of Cr concentration in samples ranging from 0.006 to 1.2 wt.%
Cr2O3 in
Al2O3. The decay is found to be independent of temperature in the liquid-helium range and generally depends on the pulse separation $\ensuremath{\tau}$ as $\mathrm{exp}(\ensuremath{-}K{\ensuremath{\tau}}^{\frac{1}{2}})$ with the decay constant
K proportional to the square root of the Cr concentration. The measured decay is independent of external magnetic field in the range 1.5-6 kG except at 1.06 kG, where modified decays are observed. A theoretical analysis is made of photon-echo decay in terms of spin flips of echo ions resulting from Cr-Cr magnetic interactions and yields good agreement with the observed decays. Spectral diffusion, modified for photon echoes, is shown not to be an important effect. However, anomalously slow decay is observed in some samples when the laser is tuned to the long-wavelength tail of the sample absorption line and the spectral-diffusion mechanism may apply here. The photon-echo-decay measurements are compared with spin-resonance and available spin-echo data in ruby. Also, it is inferred that resonant optical energy transfer is not an important photon-echo-decay mechanism even in the darkest sample studied.
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.