By using far-infrared laser spectroscopy we have studied the temperature dependence of the absorption that is due to transitions between the E ((2)E) and 2A ((2)E) levels of excited Cr(3+) ions in ruby. From the temperature dependence of the linewidth we determined the inhomogeneous and the homogeneous contributions to line broadening. From the homogeneous width the lifetime of the 2A level was obtained. We found that, for emperatures up to 70 K, the lifetime is due mainly to one-phonon relaxation, whereas at higher temperatures another relaxation process, probably a two-phonon Raman process, becomes strong.
These datasets have been used to produce Figures 2A, 3 and 4 of the manuscript: " Twin-field quantum key distribution without optical frequency dissemination". The spreadsheet file "Figure Data except 2a and 3d.xlxs" contains multiple tabs, each of which contains data for a figure panel or a figure, including Figure 3a Figure 3b Figure 3c Figure 3d Figure 3e Figure 3f Figure 3g Figure 4 Supplementary Figure 2a Supplementary Figure 2b Supplementary Figure 2c Supplementary Figure 2d Supplementary Figure 3. The file "Figures_2a and 3d.zip" contains the following raw data: (1) "Figure_2a.txt": XY data for Figure 2a in text format. (2) "Fig3_d_purple line.txt": XY data for the purple curve in Figure 3d. (3) "Fig3_d_green line.txt": XY data for the green curve in Figure 3d. (4) "Fig3_d_yellow line.txt": XY data for the yellow circles in Figure 3d.
The technique of accumulated photon echo is used in combination with a high-pressure diamond anvil cell to measure the splitting of the
4A2 ground state and the one-phonon spontaneous decay rate of the 2A\ifmmode\bar\else\textasciimacron\fi{}
(2E) level at 1.5 K in ruby up to 4.3 GPa of hydrostatic pressure. The
4A2 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{}
(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.