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AIP conference proceedings

Temperature and frequency dependent optical dephasing of impurities in crystals

David Hsu, Leslie J. Root, James L. Skinner

Published Jan 1, 1986• 0 citations
Publisher

Abstract

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.

DOI
10.1063/1.35710

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

David Hsu, James L. Skinner

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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/${T}_{2}$ 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/${T}_{2}$ becomes frequency independent. In the other limit when \ensuremath{\xi}/a\ensuremath{\rightarrow}0, and the site energies are uncorrelated (microscopic broadening), 1/${T}_{2}$ is proportional to the inhomogeneous line shape. We have compared our results to experiments by Macfarlane and Shelby on ${\mathrm{Y}}_{2}$${\mathrm{O}}_{3}$:${\mathrm{Eu}}^{3+}$ (2 at. %) and ${\mathrm{EuP}}_{5}$${\mathrm{O}}_{14}$. 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.

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A general description of zero-temperature pure dephasing in optical multilevel systems is presented. We derive expressions for the dephasing time due to transition multipole interactions. Specific application of the theory to mixed crystal systems predicts the dependence of the dephasing times on the concentration of guest molecules and transition dipole moments which is observed experimentally. Numerical estimates of the zero-temperature dephasing rates are in good agreement with experiments when the dependence on exciting pulse flip angle is included. Finally, our results suggest new experiments which are briefly discussed.

The Journal of Physical Chemistry•Aug 1, 1981•19 citations
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 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 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.
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.
For a crystal with both diagonal disorder (inhomogeneous broadening) and substitutional disorder we have calculated the contribution to the photon echo decay due to purely electronic intersite interactions. We have considered the two important limiting cases of macroscopic and microscopic inhomogeneous broadening. In the case of macroscopic broadening we find that the optical dephasing rate constant 1/T2∼f J, where f is the fractional concentration of impurities and J is the nearest-neighbor intersite interaction in frequency units. This result is valid for f≪1. In the opposite limit of microscopic inhomogeneous broadening, we find that 1/T2∼f J2/δ̄, where δ̄ is the width in frequency units of the inhomogeneous distribution. This result is valid for arbitrary f, including f=1, and for J≪δ̄. In the case that f≪1 and J≪δ̄, 1/T2 is much smaller for microscopic broadening than for macroscopic broadening. We discuss our results in relation to several experiments on mixed molecular crystals and to an experiment on the stoichiometric material EuP5O14.
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.
A general description of zero-temperature pure dephasing in optical multilevel systems is presented. We derive expressions for the dephasing time due to transition multipole interactions. Specific application of the theory to mixed crystal systems predicts the dependence of the dephasing times on the concentration of guest molecules and transition dipole moments which is observed experimentally. Numerical estimates of the zero-temperature dephasing rates are in good agreement with experiments when the dependence on exciting pulse flip angle is included. Finally, our results suggest new experiments which are briefly discussed.