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AIP conference proceedings

Statistical fine structure in inhomogeneously broadened absorption lines in solids

W. E. Moerner, T. P. Carter

Published Jan 1, 1988• 0 citations
Publisher

Abstract

By using laser FM spectroscopy, we have observed statistical fine structure (SFS) in the inhomogeneously broadened zero‐phonon S1←S0 (0–0) absorption of pentacene molecules in crystals of p‐terphenyl at liquid helium temperatures. SFS results from variations in the spectral density of absorbers with optical wavelength due to statistics, illustrating that the inhomogeneous line profile is not a simple, smooth Gaussian function as has been previously assumed but rather contains significant fine structure. Theoretical analysis of the SFS spectra using autocorrelation techniques can be used to estimate the underlying value of the homogeneous linewidth. This new observation not only provides a novel way to study the statistics of inhomogeneous broadening, but it also allows estimation of the homogeneous width without requiring spectral hole‐burning or coherent transient techniques.

DOI
10.1063/1.37439

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By using laser FM spectroscopy, we have observed statistical fine structure (SFS) in the inhomogeneously broadened zero‐phonon S1←S0 (0–0) absorption of pentacene molecules in crystals of p‐terphenyl at liquid helium temperatures. SFS results from variations in the spectral density of absorbers with optical wavelength due to statistics, illustrating that the inhomogeneous line profile is not a simple, smooth Gaussian function as has been previously assumed but rather contains significant fine structure. Theoretical analysis of the SFS spectra using autocorrelation techniques can be used to estimate the underlying value of the homogeneous linewidth. This new observation not only provides a novel way to study the statistics of inhomogeneous broadening, but it also allows estimation of the homogeneous width without requiring spectral hole‐burning or coherent transient techniques.
Using laser frequency-modulation spectroscopy, we have observed statistical fine structure (SFS) in the inhomogeneously broadened optical absorption of pentacene in ppp-terphenyl at liquid-helium temperatures. SFS is time-independent structure on the inhomogeneous line profile caused by statistical variations in the spectral density of absorbers in each frequency interval. The size of the SFS varies as the square root of the number of centers, and the autocorrelation of the SFS yields an estimate of the homogeneous linewidth without the requirement of spectral hole burning or coherent transients.
Recently, we reported the first observation of the statistical fine structure (SFS) on an inhomogeneously broadened optical absorption line, the 0-0 origin transition of pentacene molecules in p-terphenyl crystals at liquid helium temperatures.1 SFS is a time-independent spectral structure resulting from number fluctuations in the spectral density of absorbers that we have detected directly using laser frequency modulation (FM) techniques. In our samples where the number of molecules per homogeneous linewidth N¯ H is large, a zero-background technique such as FM spectroscopy is optimal for detection of SFS because only the deviations of the absorption coefficient from the background value produce FM signals. In addition, for extremely low signal levels, we use double modulation with a Stark field to remove the effects of residual amplitude modulation in the modulator. Our goal is to describe the systematics and analysis of SFS spectra at a fixed low temperature, 1.6 K. For example, we show that the rms value of the SFS grows as the square root of N¯ H . More important, by computing the autocorrelation of the measured frozen noise spectra, the homogeneous linewidth can be determined to good accuracy without requiring spectral hole-burning or coherent transients. Since the source for SFS is fundamental statistical fluctuations in the absorber spectral density, SFS should occur for all inhomogeneously broadened lines; furthermore, the effect imposes a fundamental limit on the detectability of shallow spectral features in solids.
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.
Using two different double-modulation techniques, we have observed the optical-absorption spectrum of single dopant molecules of pentacene in a p-terphenyl host crystal at liquid-helium temperatures. To achieve this, frequency-modulation spectroscopy was combined either with Stark or ultrasonic modulation to remove interfering background signals from residual amplitude modulation, and the number of molecules in resonance was reduced to one by operating in the wings of the inhomogeneous line. Triplet bottleneck saturation appears to be suppressed in the single-molecule regime.
Remarkably narrow optical homogeneous linewidths of the order of 1 kHz have now been observed in low temperature zero‐phonon transitions of dilute impurity ion crystals, such as Pr3+ in LaF3. Novel nonlinear optical resonance techniques have been devised for this purpose using ultrastable phase locked cw dye lasers where the measurements are performed either in the frequency domain (hole burning) or in the time domain (coherent optical transients). These studies effectively bring the Mossbauer effect into the optical region. Hence, the observed linewidths are no longer limited by inhomogeneous strain broadening (∼5 GHz) or even by static local fields due to neighboring spins (∼100 kHz). However, weak magnetic field fluctuations from local spins are readily detected. As an example, spin decoupling and line narrowing, which are well known in NMR, are observed in an optical transition of Pr3+:LaF3 at 2 K where the 19F– 19F dipolar interaction is quenched and the optical linewidth drops from 10 to 2 kHz, clearly demonstrating the spin broadening mechanism. Results will be discussed in terms of a Monte Carlo line broadening theory.
We have succeeded in observing finely resolved spectra in the spectral regions of absorption and emission bands of cresyl violet in ethanol, by means of population-grating spectroscopy based on four-photon parametric mixing. The inhomogeneous width is investigated in terms of the excitation frequency dependence. The energy separation and the homogeneous width are also analyzed by assuming that the observed fine bands consist of several Lorentzian lines. It is revealed that the observed spectra reflect the detailed vibrational and vibronic structures of molecules. This high-resolution spectroscopy can be readily applied to more general disordered systems in the condensed phase.