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The Journal of Chemical Physics

Optical Hartmann–Hahn resonance and the spatial correlation of inhomogeneous broadening in molecular solids

Jeffrey A. Cina, R. Silbey

Published Sep 1, 1986• 1 citation
Publisher

Abstract

We propose the use of optical Hartmann–Hahn resonance between guest molecules in a solid in order to study the extent of spatial correlation of site energies in the inhomogeneous distribution. The correlation length and the form of the interaction which mediates the resonance between guest molecules can be determined from the time development of fluorescence.

DOI
10.1063/1.451053

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We propose the use of optical Hartmann–Hahn resonance between guest molecules in a solid in order to study the extent of spatial correlation of site energies in the inhomogeneous distribution. The correlation length and the form of the interaction which mediates the resonance between guest molecules can be determined from the time development of fluorescence.
The study of optical relaxation processes in solids at low temperature has progressed tremendously in the last 20 years due to the development of coherent optical techniques. The latter would not have been possible without the advent of narrow-band tunable lasers, on the one hand, and lasers with very short pulses (picoseconds, femtosecoods) on the other hand. Such coherent techniques are necessary because spectral line shapes of solids doped with guest molecules are seldom determined by dynamical interactions but principally by strain or structural disorder. This gives rise to inhomogeneous broadening, rlOh, which in crystalline hosts at low temperature varies between ' 0.1 and 10 cm -I, whereas in glasses it may amount to � 100-500 em-I. One of the techniques to achieve narrowing of spectral lines is site­ selection spectroscopy (1-3). A sub-ensemble of molecules within thc inhomogeneously broadened absorption band is selectively excited by mcans of a narrow-band laser, and the fluorescence or phosphoresccnce signal is detected with a high-resolution monochromator and/or a Fabry­ Perot interferometer. Fluorescence line-narrowing ( I) is a special case of this technique (for a review see 3). The intrinsic or homogeneous spectral linewidth, r hom, which yields information on the relaxation processes of the excited state, is given by the effective optical dephasing time, T2:
Optical spectroscopy provides a useful tool for probing the structure and dynamics of solids. Over the years, optical methods have evolved from absorption spectroscopy to more complex methods such as spectral hole burning, photon echoes, and luminescence line narrowing. The absorption spectrum provides information about inhomogeneous broadening, while the latter approaches provide information about the systematics of the homogeneous line shape information that is often obscured by inhomogeneous broadening. When external perturbations such as strain or electric fields are applied, details of the local site can be obtained. Recently, the ultimate limit of optical spectroscopy has been attained, in which the spectral properties of individual single impurity molecules in a solid can be measured, with all ensemble averaging removed. This novel regime has provided additional, previously unobtainable, information on a highly local scale, such as the direct observation of the spectral shifting of a single molecule produced by configurational transitions of the host. It is to be expected that further surprises await us in this new frontier of single-molecule spectroscopy in solids.
We present a theory of frequency-dependent optical dephasing as measured by narrow-band photon-echo experiments. We consider a substitutionally disordered crystal with inhomogeneous broadening (diagonal disorder) and electronic interactions between occupied sites. We include the possibility of site-energy correlations. We find that the frequency dependence of the dephasing rate 1/T2{T}_{2}T2​ is very sensitive to the ratio \ensuremath{\xi}/a, where \ensuremath{\xi} is the correlation length and a is the lattice spacing. When \ensuremath{\xi}/a\ensuremath{\rightarrow}\ensuremath{\infty}, and there are macroscopic domains of resonant ions, 1/T2{T}_{2}T2​ becomes frequency independent. In the other limit when \ensuremath{\xi}/a\ensuremath{\rightarrow}0, and the site energies are uncorrelated (microscopic broadening), 1/T2{T}_{2}T2​ is proportional to the inhomogeneous line shape. We have compared our results to experiments by Macfarlane and Shelby on Y2{\mathrm{Y}}_{2}Y2​O3{\mathrm{O}}_{3}O3​:Eu3+{\mathrm{Eu}}^{3+}Eu3+ (2 at. %) and EuP5{\mathrm{EuP}}_{5}EuP5​O14{\mathrm{O}}_{14}O14​. We find reasonable agreement with experiment when \ensuremath{\xi} is less than a few lattice sites. Thus, for these systems the model of microscopic broadening is more appropriate than that of macroscopic broadening.
Experiments with single quantum systems are at the frontier of modern physics. Probing single molecules allows for very precise control of light-matter interaction and for quantum optical studies. Moreover, a single guest molecule in a solid host matrix is a very sensitive probe of local dynamics in its nano-environment. Fluorescence excitation spectroscopy on single molecules is a powerful tool for spectroscopic characterizations at highest resolution, as information can be revealed that is not accessible in experiments on ensembles of molecules. The detection of the fluorescence signal of a single absorber is achieved by exploiting the high spectral selectivity given by the ratio (10 10) of homogeneous to inhomogeneous linewidths of optical transitions at cryogenic temperatures (zero-phonon transitions). Two-photon fluorescence excitation, a fundamental nonlinear optical process, was observed on a single quantum system [1]. Single diphenyl-octatetraene molecules trapped in an n-tetradecane matrix were excited from the 1Ag ground to the lowest excited singlet state by simultaneous absorption of two photons using a single-mode cw laser. Excited molecules were observed through weak one-photon emission resulting from a symmetry breaking induced by the crystal field. The fundamental principles and the experimental technique of single molecule spectroscopy will be introduced briefly and some particular single molecule experiments presented. This work was done in collaboration with T. Plakhotnik, A. Renn and U.P. Wild
Abstract Inhomogeneous broadening is often considered a nuisance in solid state spectroscopy, and the usual treatment of it is phenomenological. In fact, the inhomogeneous broadening of absorption spectra, coupled with a microscopic theory, can provide one with interesting information about the nature of disorder in different systems. More sophisticated experiments can provide more detailed information about disorder by probing certain correlations between energy levels. For example, flourescence line narrowing spectra of isolated impurities involve correlations among three different vibronic levels. Pressure effects on hole burning spectra probe correlations of impurity transition energies before and after the pressure change. For interacting impurity systems, photon echo experiments involve transition energy correlations between different impurities. Efforts to understand these effects within a microscopic framework are discussed.
Recent advances in absorption1 and fluorescence2 detection now allow high-quality measurement of the optical absorption spectrum of individual single-impurity molecules in both crystals and polymers at liquid-helium temperatures. Here, the solid may be viewed as a trap for the defect center similar to the well-known electromagnetic single-ion traps, except that Doppler and recoil effects are replaced by (static) inhomogeneous broadening and host-guest interactions. Most importantly, molecular rotation is absent because of steric effects at low temperatures.