Following a brief review of laser frequency and time domain techniques for overcoming inhomogeneous broadening of optical transitions in solids, recent studies on the failure of the optical Bloch equations (OBE) in describing saturation and coherent transient phenomena in ruby will be discussed. Experiments using free induction decay (FID), as in the original work on the system Pr3+:LaF3 by DeVoe and Brewer1, as well as extensions to rotary echos2 and hole-burning3 will be described. At low fields (~ 0.4 T), the time and frequency domain linewidth variation with Rabi frequency agree provided care is taken to avoid line broadening caused by spectral diffusion4. Recent work at high fields (~ 5 T), where Cr-Cr electron spin flipping is suppressed5, shows that spectral diffusion decreases and the dephasing time increases. Observed frequency domain hole widths as narrow as 18 kHz (FWHM) have been obtained for the 4 A2(−1/2)→E¯(−1/2) optical transition in dilute ruby using a pump-probe technique4. Work with such narrow holes emphasizes the fundamental limits imposed by the uncertainty principle and as an aside, a thought experiment where single photons are transmitted through "frequency slits" will be discussed.
We report experimental and theoretical studies of optical hole burning in the inhomogeneous
R1 line of ruby at low temperatures. Both Stark-shifting and pump-probe techniques using narrow-band single-frequency lasers were employed. In addition to the observation of narrow holes, we have found that a large (up to 70%) decrease in absorption occurs outside the hole and that the relative size of this decrease is constant over the entire inhomogeneous line. This effect is ascribed to fast resonant cross-spin relaxation in the ground-state levels which drives all spins within the optically pumped volume to a common spin temperature. A theoretical model is formulated which describes the power-broadened hole shapes as well as the off-resonance decrease in the absorption coefficient. Fair agreement with experiment is obtained for the case of a magnetic field applied along the
c axis; however, sizable deviations from the theory are seen for zero field. We conclude that further studies are needed to elucidate the nature of the Al superhyperfine-broadening mechanism. An upper limit of 1200 nm is deduced for the size of macroscopically broadened regions in ruby.
The spin-lattice relaxation time in the 4 A 2 ground state of C r 3 + in ruby can be on the order of magnitude of seconds at liquid helium temperatures in low magnetic fields B | | c . This allows for highly efficient optical pumping of the spin levels in this system. Such pumping can then in turn be employed to drastically increase the optical density of the inhomogeneously broadened R 1 ( ± 3 / 2 ) or R 1 ( ± 1 / 2 ) lines and also to narrow the spectral hole width because Cr–Cr electron-spin flips (cross relaxation) are suppressed in the ground state, leading to longer dephasing times T 2 ∗ . Both effects can be employed to further reduce the group velocity of light pulses propagating through a transient spectral hole.
Spatial and, additionally, spectral diffusion of 29-${\mathrm{cm}}^{\ensuremath{-}1}$ phonons trapped in an excited cylindrical region with diameter \ensuremath{\sim}0.1 mm has been investigated under continuous optical pumping of ruby. For 130- and 700-ppm ruby, phonon decay strictly limited by spatial diffusion is reflected in a quadratic dependence of the bottlenecking factor $\ensuremath{\sigma}$ on the excited-state concentration
N∗ up to ${N}^{*}\ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}{10}^{17}/{\mathrm{cm}}^{3}$. At higher
N∗, attainable in 700- and 2500-ppm ruby, the observed reduction of $\ensuremath{\sigma}$ relative to the second-power dependence, as well as the increased width of the dependence of $\ensuremath{\sigma}$ on magnetic field, reveal that spectral diffusion from inhomogeneous packet to packet is operative. In the spatially diffusive regime, evidence for Zeeman-induced spectral diffusion is found in a characteristic narrowing of the magnetic-field dependence of the
R2 fluorescence upon raising $\ensuremath{\sigma}$. At full separation of the Zeeman transitions $2\overline{A}(^{2}E)\ensuremath{\leftrightarrow}\overline{E}(^{2}E)$, $\ensuremath{\sigma}$ is reduced to 15-40% relative to zero field, depending on
N∗ and ground-state concentration. Rate equations governing the
Cr3+ populations in the two-level scheme (
2A,
E) with inclusion of spatial diffusion and anharmonic decay of the phonons account for the second-power dependence. Diffusive phonon decay turns out to dominate from ${N}^{*}R\ensuremath{\sim}4\ifmmode\times\else\texttimes\fi{}{10}^{13}/{\mathrm{cm}}^{2}$ up to at least ${N}^{*}{R}^{2}\ensuremath{\sim}{10}^{14}/\mathrm{cm}$, with
R the characteristic dimension of the excited region. Spectral diffusion, treated as a perturbation, satisfactorily fits the data at higher $\ensuremath{\sigma}$, yielding a diffusive step of \ensuremath{\sim}2% of the linewidth. At low bottlenecking, the functional form of the magnetic field dependence of $\ensuremath{\sigma}$, including its width and level at full separation, is closely described by use of rate equations, taking the line shape to be Gaussian-type, and assuming the phonons associated with spin flip and those with non spin flip to belong to distinct classes.
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.
We report on the observation of slow light induced by transient spectral hole-burning in a solid, that is based on excited-state population storage. Experiments were conducted in the R1-line (2E←4A2 transition) of a 2.3 mm thick pink ruby (Al2O3:Cr(III) 130 ppm). Importantly, the pulse delay can be controlled by the application of a low external magnetic field B||c≤9 mT and delays of up to 11 ns with minimal pulse distortion are observed for ~55 ns Gaussian pulses. The delay corresponds to a group velocity value of ~c/1400. The experiment is very well modelled by linear spectral filter theory and the results indicate the possibility of using transient hole-burning based slow light experiments as a spectroscopic technique.