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The Journal of Chemical Physics

Nonperturbative theory of temperature-dependent optical dephasing in crystals. I. Acoustic or optical phonons

David Hsu, James L. Skinner

Published Dec 15, 1984• 85 citations
Publisher

Abstract

We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.

DOI
10.1063/1.447648

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We continue the discussion of the nonperturbative theory of zero-phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In that paper, a diagrammatic analysis was undertaken which led to analytic results for the thermal width and shift of the zero-phonon line. Here we evaluate these results for two model phonon densities of states: the Debye model for acoustic phonons, and a sharply peaked density of states appropriate for optical phonons. For Debye phonons we find that at low temperatures the standard (perturbative) theory of optical dephasing is qualitatively correct, but at high temperatures it becomes very inaccurate. Moreover, if one of the excited state phonon frequencies tends to zero (a soft mode), then perturbation theory breaks down completely. For optical phonons our results give an Arrhenius temperature dependence for the linewidth and place an upper bound on the value of the preexponential. In paper II of this series we will discuss dephasing by pseudo-local phonons, and in paper III we will compare our results to absorption, photon echo, and hole burning experiments.
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.
The optical dephasing in frozen amorphous toluene doped with octaethylporphine zinc is investigated using the photon echo technique over a wide range of temperatures (0.4–100 K) up to the Debye temperature of solid toluene (T D=100.7 K). The contributions of different mechanisms to the broadening of the zero-phonon line (ZPL) are reliably separated owing to the measurements performed over such a wide range of temperatures. Analysis of the experimental data demonstrates that, at low temperatures, the main contribution to the optical dephasing is determined by the interaction of impurities with fast tunneling transitions in two-level systems. The temperature dependence of the linewidth exhibits a quasi-linear behavior at temperatures below 3–4 K. At higher temperatures, the dominant contribution to the dephasing is made by the interaction of impurities with quasi-local phonons, which leads to a quasi-exponential temperature dependence of the linewidth. It is shown that the latter contribution can be described in the framework of the soft-potential model allowing for a broad spectrum of low-frequency phonon vibrations in the matrix. The temperature of the crossover between the aforementioned two mechanisms of line broadening is determined.
The optical dephasing, caused by a quadratic interaction with acoustic phonons, is studied on the basis of the nonperturbative theory. The effect of a strong weakening of the elastic springs on the electronic transition is studied. It is found that, if the weakening brings the system close to the dynamical instability, then the usual ∝ T7 dependence of the homogeneous width of a zero-phonon line (ZPL) is replaced by the ∝ T3 dependence in a broad temperature interval. An equation is derived which describes the additional broadening of a ZPL caused by the dynamical instability of the final state. The model explains the temperature broadening and shift of the zero-phonon lines of some nitrogen-containing centers in diamond crystals.
We present a nonperturbative theory of the thermal line broadening of optical transitions due to pure dephasing by phonons. The theory extends previous perturbative results of McCumber and Sturge. The theory is applied to experimental results on mixed organic crystals and ruby. We also present a theory of dephasing at T=0 K due to interacting impurities. Our results predict a frequency dependence to 1/T2. We analyze experiments on Y2O3:Eu3+ by Macfarlane and Shelby with this theory, and are able to comment on the nature of inhomogeneous broadening in this system.
We present a joint experiment-theory analysis of the temperature-dependent emission spectra, zero-phonon linewidth, and second-order correlation function of light emitted from a single organic molecule. We observe spectra with a zero-phonon line together with several additional sharp peaks, broad phonon sidebands, and a strongly temperature dependent homogeneous broadening. Our model includes both localized vibrational modes of the molecule and a thermal phonon bath, which we include nonperturbatively, and is able to capture all observed features. For resonant driving we measure Rabi oscillations that become increasingly damped with temperature, which our model naturally reproduces. Our results constitute an essential characterization of the photon coherence of molecules, paving the way to their use in future quantum information applications.
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.