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The Journal of Chemical Physics

Application of Redfield theory to optical dephasing and line shape of electronic transitions in molecular mixed crystals

Philippus de Bree, Douwe A. Wiersma

Published Jan 15, 1979• 105 citations
Publisher

Abstract

Redfield relaxation theory is used to study optical dephasing in molecular mixed crystals where pseudolocalized phonons play a dominant role. As a model an effective four-level system is defined which consists of the ground and excited electronic state of the guest impurity and one pseudolocalized phonon in each of these states. It is shown that coherence transfer between the purely electronic and the phonon-promoted transition is due to interference between the scattering amplitudes in the ground and excited state and only occurs when the transitions are near resonant. When the scattering amplitudes in the ground and excited state are identical the optical Redfield equations reduce to the modified Bloch equations and coherence transfer may appreciably contribute to optical dephasing. It further proves essential for coherence exchange to occur that next to electron–phonon coupling the phonon anharmonicity is taken into account. The stochastic and correlation function theories of line shape, using the same model system, have also been examined and we conclude that in these theories exchange of coherence is not properly taken into account. Next to the effect of pseudolocalized phonons the effect of band phonons on optical dephasing is also examined and within our model both effects are additive.

DOI
10.1063/1.437512

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Redfield relaxation theory is used to study optical dephasing in molecular mixed crystals where pseudolocalized phonons play a dominant role. As a model an effective four-level system is defined which consists of the ground and excited electronic state of the guest impurity and one pseudolocalized phonon in each of these states. It is shown that coherence transfer between the purely electronic and the phonon-promoted transition is due to interference between the scattering amplitudes in the ground and excited state and only occurs when the transitions are near resonant. When the scattering amplitudes in the ground and excited state are identical the optical Redfield equations reduce to the modified Bloch equations and coherence transfer may appreciably contribute to optical dephasing. It further proves essential for coherence exchange to occur that next to electron–phonon coupling the phonon anharmonicity is taken into account. The stochastic and correlation function theories of line shape, using the same model system, have also been examined and we conclude that in these theories exchange of coherence is not properly taken into account. Next to the effect of pseudolocalized phonons the effect of band phonons on optical dephasing is also examined and within our model both effects are additive.
The excitation line shape of a single terrylene molecule in a naphthalene crystal has been investigated. In addition to the conventional Lorentzian, it consists of a dispersive component in the core region and a sideband. This is due to a pseudolocal phonon caused by the substitution of a host molecule with the chromophore. When the pseudolocal phonon is excited, the resonance frequency of the chromophore slightly changes, resulting in the appearance of a second, quasiresonant transition. Coherence transfer between these two optical transitions causes the deviation from the purely Lorentzian line shape.
Picosecond optical coherence techniques are employed to study dynamical intermolecular interactions in low concentration mixed molecular crystals, i.e., pentacene in naphthalene at 1.4 K. A concentration-dependent broadening of the optical homogeneous line is observed. Stimulated photon echo measurements rule out excited state transport as the broadening mechanism. The photon echo results exhibit a linear concentration dependence and a theory is proposed that accounts for the broadening in terms of phonon-induced fluctuations in guest–guest dipole–dipole interactions. Detailed considerations indicate that the system is best described in terms of localized excitations rather than delocalized impurity band states. In the low concentration limit, there is additional broadening of the homogeneous line beyond that produced by the lifetime. A model is presented describing this broadening in terms of phonon-induced modulation of the guest–host van der Waals interactions, i.e., in terms of a fluctuating crystal shift.
A simple theoretical description of vibrational coherence decay in isotopically mixed molecular crystals at low temperatures is presented. Dephasing due to impurity scattering is shown to be a slower than exponential decay process for optically excited vibrons lying near band singularities, by analogy with the theory of coherence loss in weakly disordered crystals [I. I. Abram and R. M. Hochstrasser, J. Chem. Phys. 72, 3617 (1970)]. When the nature of the initially excited state is properly taken into account, the rate constant for population decay displays an unexpected interplay between trapping and self-relaxation which can, in principle, lead to a nonmonotonic dependence of the relaxation rate with impurity concentration. Our results are related to recent time resolved CARS measurements in low temperature molecular crystals.
The temperature-dependent optical dephasing of anthracene, 9-methylanthracene, and 2-methylanthracene monomers in phenanthrene host crystals has been measured using photon echo experiments. Despite large linear electron–acoustic phonon coupling, all three systems dephase because of coupling to pseudolocal modes (local motions of the guest molecule). Computer simulations of the three systems calculate the pseudolocal mode eigenvalues and eigenvectors. In contrast to previous discussions in the literature which describe pseudolocal modes as librations, the predicted eigenvalues are in reasonable agreement with the measured pseudolocal mode energies. The predicted eigenvectors are combinations of translational motion along the long molecular axis and rotational motion about the out-of-plane axis of the guest. Differences in site energies for various locations and orientations of the methyl group are calculated.
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.
We derive a quantum theory of the role of acoustic and optical phonons in modifying the optical absorption line shape, polarization dynamics, and population dynamics of a two-level atom (quantum dot) in the ``colored'' electromagnetic vacuum of a photonic band-gap (PBG) material. This is based on a microscopic Hamiltonian describing both radiative and vibrational processes quantum mechanically. We elucidate the extent to which phonon-assisted decay limits the lifetime of a single photon-atom bound state and derive the modified spontaneous emission dynamics due to coupling to various phonon baths. We demonstrate that coherent interaction with undamped phonons can lead to an enhanced lifetime of a photon-atom bound state in a PBG. This results in reduction of the steady-state atomic polarization but an increase in the fractionalized upper state population in the photon-atom bound state. We demonstrate, on the other hand, that the lifetime of the photon-atom bound state in a PBG is limited by the lifetime of phonons due to lattice anharmonicities (breakup of phonons into lower energy phonons) and purely nonradiative decay. We also derive the modified polarization decay and dephasing rates in the presence of such damping. This leads to a microscopic, quantum theory of the optical absorption line shapes. Our model and formalism provide a starting point for describing dephasing and relaxation in the presence of external coherent fields and multiple quantum dot interactions in electromagnetic reservoirs with radiative memory effects.