We report the first optical dephasing study of an inorganic impurity system possessing sharp, low frequency mode structure in its ground and excited state spectra. The total dephasing times T2 and population relaxation times T1 for the 1T2g and 1Eg d9s excited states of NaF:Cu+ are determined at a series of temperatures between 1.8 and 296 K. The T2 values are determined by extracting the Lorentzian components from one- and two-photon excitation line shapes. The T1 values caused by nonradiative decay rates are obtained by detecting very low quantum yield emission from the fast-relaxing excited states and applying the formula tnr=Qtr, where t’s are radiative and nonradiative lifetimes and Q is the quantum yield. T1(1T2g)=4.6 ps and T1(1Eg )=2.0 ps at 8 K. Significantly, these are very similar to the T1 values calculated from lowest temperature Lorentzian linewidths by the relationship 1/T2=1/T′2 +1/(2T1). The T1 values stay approximately constant over the temperature range 1.8–45 K, while the linewidths rapidly increase indicating that pure dephasing dominates. Using ground and excited state information on the low frequency modes, we test optical Redfield theory and the nonperturbative harmonic theory for pure dephasing by pseudolocal phonons against data for this system which displays strongly anhamonic progressions. The nonperturbative theory fits the line broadening data to higher temperatures than optical Redfield theory for the least anharmonic excited state potential, 1T2g. Both theories underpredict the broadening with temperature of the extremely anharmonic 1Eg state. A simple anharmonic theory including scattering to overtone levels also fails to predict the observed linewidth temperature behavior, although it is demonstrated these processes should be occurring.
We report the first optical dephasing study of an inorganic impurity system possessing sharp, low frequency mode structure in its ground and excited state spectra. The total dephasing times T2 and population relaxation times T1 for the 1T2g and 1Eg d9s excited states of NaF:Cu+ are determined at a series of temperatures between 1.8 and 296 K. The T2 values are determined by extracting the Lorentzian components from one- and two-photon excitation line shapes. The T1 values caused by nonradiative decay rates are obtained by detecting very low quantum yield emission from the fast-relaxing excited states and applying the formula tnr=Qtr, where t’s are radiative and nonradiative lifetimes and Q is the quantum yield. T1(1T2g)=4.6 ps and T1(1Eg )=2.0 ps at 8 K. Significantly, these are very similar to the T1 values calculated from lowest temperature Lorentzian linewidths by the relationship 1/T2=1/T′2 +1/(2T1). The T1 values stay approximately constant over the temperature range 1.8–45 K, while the linewidths rapidly increase indicating that pure dephasing dominates. Using ground and excited state information on the low frequency modes, we test optical Redfield theory and the nonperturbative harmonic theory for pure dephasing by pseudolocal phonons against data for this system which displays strongly anhamonic progressions. The nonperturbative theory fits the line broadening data to higher temperatures than optical Redfield theory for the least anharmonic excited state potential, 1T2g. Both theories underpredict the broadening with temperature of the extremely anharmonic 1Eg state. A simple anharmonic theory including scattering to overtone levels also fails to predict the observed linewidth temperature behavior, although it is demonstrated these processes should be occurring.
We have measured the optical dephasing time T2 of the $^{1}A_{1}\ensuremath{\leftrightarrow}^{1}E$ zero-phonon transition of the F3+ color center in NaF by optical free-induction decay. In this way we eliminate the effect of the 54-GHz inhomogeneous broadening, and find a homogeneous linewidth of 20 \ifmmode\pm\else\textpm\fi{} 5 MHz ${T}_{2}=16\ifmmode\pm\else\textpm\fi{}4$ nsec). We have also measured a spontaneous emission lifetime of ${T}_{1}=10\ifmmode\pm\else\textpm\fi{}2$ nsec. In the range 1.5-4 K, our results are consistent with the relation T2=2T1, indicating that optical dephasing is limited by population-decay processes. This relation was even more clearly demonstrated by performing the same experiment on the D lines of sodium vapor at 3 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}5}$ Torr, where the effects of collisions are negligible. We find that the dephasing is again limited by radiative decay, and that ${T}_{2}(32\ifmmode\pm\else\textpm\fi{}3 \mathrm{nsec})=2{T}_{1}(16.3\ifmmode\pm\else\textpm\fi{}0.4 \mathrm{nsec})$.
We report results of an optical and picosecond photon echo study on the zero-phonon line of photosite I of pentacene in benzoic acid. The results show that optical dephasing in this system proceeds via uncorrelated phonon scattering processes from the ground and optically excited state to singly excited librational levels. It is also shown that the data can not be consistently interpreted using coherence exchange theory. The librational frequencies and lifetimes at low temperature are determined to be 12 cm−1 and 18 ps in the ground state and 16.7 cm−1 and 2.5 ps in the singlet excited state. It is argued that population decay of librational overtones proceeds in single quantum steps down the librational ladder which excludes these modes from playing a role in optical dephasing. From a temperature-dependent line shape study of the libronic transition in absorption, it is concluded that the low-temperature librational lifetime is primarily due to resonant decay into acoustic phonons. At elevated temperature, cubic libration-phonon anharmonicity dominates the librational lifetime. These lifetime shortening processes are reflected in the temperature dependent dephasing of the origin. Finally, with the dephasing model presented in this paper for photosite I, existing controversies concerning optical dephasing in the unburned origin of pentacene in benzoic acid can be resolved.
Redfield relaxation theory is used to study optical dephasing in molecular mixed crystals where pseudolocalized phonons play a dominant role. As a model an effective four-level system is defined which consists of the ground and excited electronic state of the guest impurity and one pseudolocalized phonon in each of these states. It is shown that coherence transfer between the purely electronic and the phonon-promoted transition is due to interference between the scattering amplitudes in the ground and excited state and only occurs when the transitions are near resonant. When the scattering amplitudes in the ground and excited state are identical the optical Redfield equations reduce to the modified Bloch equations and coherence transfer may appreciably contribute to optical dephasing. It further proves essential for coherence exchange to occur that next to electron–phonon coupling the phonon anharmonicity is taken into account. The stochastic and correlation function theories of line shape, using the same model system, have also been examined and we conclude that in these theories exchange of coherence is not properly taken into account. Next to the effect of pseudolocalized phonons the effect of band phonons on optical dephasing is also examined and within our model both effects are additive.
We have observed extremely fast nonradiative relaxation (picosecond to femtosecond) between closely spaced crystal field states derived from the 4G5/2,2G7/2 Stark manifold of Nd3+ in glassy media. The relaxation is significantly faster than that predicted by an indiscriminate application of the energy-gap law, and it is highly wavelength-dependent. Femtosecond accumulated-photon-echo techniques were used at 13 K, revealing single and nonexponential echo decays. Relaxation was found to involve single phonon processes. Generally, the dephasing rate increased as higher-lying crystal field states were excited, reflecting the larger number of available terminal levels for the relaxation and the phonon density of states. However, a detailed plot of the dephasing rate versus wavelength revealed considerable unexpected structure. As higher-lying states were excited, the relaxation rate did not increase in the expected monotonic fashion. Surprisingly, the relaxation rate decreased in various spectral regions as the excitation energy was increased. By using T2-selective dynamic-excitation spectroscopy, we assigned these regions to the spectral locations of the inhomogeneously broadened crystal field states in the Stark manifold. Site-dependent electron-phonon interaction and a strong correlation between the inhomogeneous broadening of the crystal field states are deduced from the data.
One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.
We have applied the results of the nonperturbative theory of zero-phonon linewidths of impurities in crystals discussed by Osad’ko and us, and further developed by us in papers I and II of this series, to the analysis of several absorption, photon echo, and hole burning experiments. Two (relatively) high temperature absorption experiments on 1,3-diazaazulene in naphthalene and dilute ruby were analyzed with a model of Debye acoustic phonons. In both cases the Debye temperature was obtained from independent experiment or theory, and a one-parameter fit was performed on the temperature-dependent linewidth. It was found that (especially for diazaazulene) the systems are not in the weak coupling limit. For several low temperature experiments, where the dephasing is presumably due to pseudolocal phonons, the nonperturbative theory, coupled with the results of deBree and Wiersma, provides a reasonably complete understanding of the observed dephasing rates.