Radiative and non-radiative transitions of excited Ti3+ cations in sapphire

Abstract

We have measured the fluorescence quantum efficiency in Ti3+:sapphire single crystals between 150 K and 550 K. Using literature-given effective fluorescence lifetime temperature dependence, we show that the zero temperature radiative lifetime is (4.44 ± 0.04) μs, compared to the 3.85 μs of the fluorescence lifetime. Fluorescence lifetime thermal shortening resolves into two parallel effects: radiative lifetime shortening, and non-radiative transition rate enhancement. The first is due to thermally enhanced occupation of a ΔE = 1,700 cm−1 higher (top) electronic state of the upper multiplet, exhibiting a transition oscillator strength of f = 0.62, compared to only 0.013 of the bottom electronic state of the same multiplet. The non-radiative rate relates to multi-phonon decay transitions stimulated by the thermal phonon occupation. Thermal enhancement of the configuration potential anharmonicity is also observed. An empiric expression for the figure-of-anharmonicity temperature dependence is given as (T) = (0)(1 + β exp(−ℏωco /kBT )), where (0) = 0.276, β = 5.2, ℏωco = 908 cm−1, and kB is the Boltzmann constant.

Suppressing Non‐Radiative Relaxation through Single‐Atom Metal Modification for Enhanced Fluorescence Efficiency in Molybdenum Disulfide Quantum Dots

“…Thus, we assume that the single‐atom metal modification enhanced fluorescence emission is probably due to the introduction of a new defect energy level in the forbidden band of MoS 2 QDs, and this level serves as a deep impurity, which can trap excess electrons in n‐type MoS 2 , [45, 46] passivating multi‐particle non‐radiative surface states, [47] and thus increasing the radiative recombination efficiency to enhance the fluorescence emission [48] . Transient fluorescence measurements show a slight decrease in fluorescence lifetime at 460 nm upon single‐atom metal modification (Figures 2c, S17 and Table S1), which is probably attributed to the fact that the non‐radiative dissipation from the defect energy level to valence band of MoS 2 is a little faster than the exciton radiation process [49] . The more obvious enhancement observed in s Au/MoS 2 QDs compared with other s M/MoS 2 QDs can be visualized by the best matched degenerate electron energy of the 5 d atomic orbital of s Au with the 3 p atomic orbital of S (Figures 2b, S18 and Table S2), which is calculated from the orbital number divided by the sum of each electron energy originating from density functional theory (DFT) calculations, and the best match favors the electron transfer from MoS 2 QDs to s Au.…”

“…[48] Transient fluorescence measurements show a slight decrease in fluorescence lifetime at 460 nm upon single-atom metal modification (Figures 2c, S17 and Table S1), which is probably attributed to the fact that the non-radiative dissipation from the defect energy level to valence band of MoS 2 is a little faster than the exciton radiation process. [49] The more obvious enhancement observed in s Au/MoS 2 QDs compared with other s M/MoS 2 QDs can be visualized by the best matched degenerate electron energy of the 5d atomic orbital of s Au with the 3p atomic orbital of S (Figures 2b, S18 and Table S2), which is calculated from the orbital number divided by the sum of each electron energy originating from density functional theory (DFT) calculations, and the best match favors the electron transfer from MoS 2 QDs to s Au. The enhanced fluorescence efficiency is significantly decreased on increasing the density of Au atoms on MoS 2 QDs (Figure S19), as indicated by the control experiment of Au nanoclusters modified MoS 2 QDs (Au NCs/MoS 2 QDs) (Figure S20) synthesized by using a method similar to that for s Au/MoS 2 QDs except that the deposition potential was set at À 0.200 V. [50] The fluorescence emission enhancement of MoS 2 QDs by single-atom Au modification is also observed from the fluorescence spectra of individual QDs at 395 nm excitation (Figures 2d and S21).…”

Saturation, Allowed Transitions and Quantum Interference in Laser Cooling of Solids

“…Other quantized absorption transitions are possible at longer wavelengths from the occupied sub-levels of other modes and other electronic sub-levels of the ground state. Figure 6 depicts a more detailed picture of the vibrational and electronic sub-levels of the 2 T 2 ground state of Ti 3+ :Al 2 O 3 [21,22].…”

“…The three 2 Au electronic levels are labeled 0, 1, 2 in order of increasing energy, following Ref. [22]. The four vibrational sublevels labeled a, b, c, d correspond to four allowed modes for 𝜋-polarization [21].…”

“…The validity of these two perspectives explains why two forms of quantum interference are possible in this system, namely Although the observed resonances were grouped into sets of four perturbed site transitions for the purpose of making transition assignments, the tabulations were based purely on unperturbed host vibrational modes and electronic splitting of the ground state. Absorption transitions at wavelengths on the low energy side of the mean fluorescence wavelength 760 nm were calculated by subtracting the vibrational mode frequencies [21] or electronic splitting [22] (in cm −1 ) for the listed transitions from the mean fluorescence wavenumber 13,158 cm −1 (π-polarization only). The mean fluorescence wavelength for σ-polarization was 763 nm.…”