D. Hsu

On the thermal broadening of zero‐phonon impurity lines in absorption and fluorescence spectra

We examine the problem of the absorption zero‐phonon line shape for dilute impurities in crystals. We consider the usual two level electronic model, where both the ground and excited state Born–Oppenheimer surfaces are harmonic in the phonon coordinates. The difference between the two surfaces (the electron–phonon interaction) has terms which are both linear and quadratic in the phonon coordinates. In contrast to the usual perturbative theories, we calculate the zero–phonon line broadening and shift to all orders in the electron–phonon interaction. We find that only the quadratic term is responsible for line broadening, and that at T=0 K this contribution vanishes. Our results are presented as integrals, which can be performed analytically or numerically, involving the weighted phonon density of states. We also show that within the model, the zero‐phonon lines in the absorption and fluorescence spectra coincide exactly for all temperatures. Our results resolve the theoretical controversy produced by the t...

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

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,...

Nonperturbative theory of temperature‐dependent optical dephasing in crystals. II. Pseudolocal phonons

We continue our discussion of the nonperturbative theory of zero‐phonon impurity lines in crystals formulated by Osad’ko and more recently by us. In Paper I of this series we evaluated our general results for the linewidth and shift for models of electronic coupling to both acoustic and optical phonons. Here we evaluate our general results for a simple model of electronic coupling to a pseudolocal phonon. The pseudolocal phonon is characterized by its frequency and lifetime in both the ground and excited electronic states. In addition to providing exact analytic expressions (reduced to quadrature) for the width and shift, we derive an approximate analytic expression for the linewidth that is bi‐Arrhenius, with activation energies corresponding to the ground and excited state pseudolocal phonon frequencies. We discuss how our theoretical approach and results are related to the exchange theory of Harris, the optical Redfield theory of deBree and Wiersma, and the perturbation theory of Small and Jones and Ze...

Nonperturbative theory of temperature‐dependent optical dephasing in crystals. III. Comparison with experiment

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.

General quantum mechanical theory of pure dephasing

Abstract We consider the pure dephasing of a two-level system interacting linearly and quadratically with a bath of harmonic oscillators; the system studied is the most general harmonic two-surface problem. The temperature-dependent pure dephasing rate is calculated exactly to all orders in the system-bath interaction. Often this interaction can be expressed in terms of a small number of collective coordinates (linear combinations of bath modes). For the case of two such coordinates, we provide explicit expressions for the dephasing rate. If there is only a single collective coordinate, we recover our result from previous publications.

Vibrational dephasing in crystals: Theory and experiment

Abstract Vibrational lineshapes of molecules in crystals are determined to a large extent by the vibration-phonon coupling. We show how our previously developed nonperturbative theory of optical pure dephasing can be applied to the vibrational dephasing problem. We consider two cases: dephasing in a pure crystal, and dephasing of a substitutional impurity. We compare our theoretical results to temperature-dependent linewidth and lineshift measurements on the 766 cm−1 mode in pure naphthalene, and the V3 mode of ReO4− in KI.

Temperature and frequency dependent optical dephasing of impurities in 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.

Optical and vibrational dephasing in crystals: Theory and experiment

The linewidths of both optical and vibrational transitions in crystals are often dominated by adiabatic coupling to phonons. We have recently developed a nonperturbative theory of dephasing due to the above, and have considered models for coupling to acoustic, optical, and pseudolocal phonons. We apply our theoretical results to optical experiments on NaF:Cu+ by Pack and McClure, and to vibrational experiments on the 766 cm-1ϵ8 mode of pure naphthalene by Hess and Prasad and Schosser and Dlott.