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Journal of the Physical Society of Japan

Theory of Indirect Dephasing for a Vibrating Molecule in Dense Mediums. I

Eiko Hiroike

Published Mar 1, 1982• 8 citations
Publisher

Abstract

The indirect dephasing model for a vibrating molecule in a dense medium is investigated by using the cumulant perturbation expansion method. The perturbation is taken as a sum of the anharmonic coupling between the high- and low-frequency modes and the interaction between the low-frequency mode and molecular surrounding. All the states of the low-frequency mode is taken into account in the calculation. Our model is available, only when the dephasing time of the high-frequency mode is shorter than the life-time of the low-frequency mode. This condition is satisfied in usual organic molecular crystals.

DOI
10.1143/jpsj.51.958

Related papers

Theory of Indirect Dephasing Model for a Vibrating Molecule in Dense Mediums. II

Eiko Hiroike

The indirect dephasing model for a vibrating molecule in a dense medium is succesively investigated by using the formulas obtained in the previous paper by the author. The line-shape function for the spectrum of the high-frequency mode is obtained, and the dependence of the line-width of the spectrum on the life-time of the excited state of the low-frequency mode is discussed.

Journal of the Physical Society of Japan•Jun 1, 1982•3 citations

Theory of Indirect Dephasing for a Vibrating Molecule in Dense Mediums. III

Eiko Hiroike

The dephasing of a high-frequency intramolecular vibrational mode in a molecular crystal is successively investigated by the cumulant perturbation expansion method as in the preceding papers in this series, I and II. The dephasing of the high-frequency mode is brought on by the thermal excitation of a low-frequency mode in the same molecule as in I and II. In this paper, however, the intramolecular vibrational modes are expressed by the bands of the exciton waves traveling through the crystal (in I and II, the intramolecular vibrational modes are expressed by the localized excitation in one molecule). The calculation shows that the spectrum becomes considerably broad as the temperature increases, while the narrowing is observed as the band widths of the exciton waves increases.

Journal of the Physical Society of Japan•Oct 1, 1983•3 citations

Quantum dynamics and control of vibrational dephasing

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This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.

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Mechanism of intermolecular dephasings on time-resolved anti-Stokes Raman scattering from a molecular ensemble

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Mechanisms of intermolecular dephasings revealed in the time-resolved coherent anti-Stokes Raman scattering (CARS) spectra of a molecular ensemble are theoretically studied by deriving the microscopical expression for the scattered photon intensity averaged over the heat-bath variables. The intermolecular dephasing means the decay of the intermolecular coherence created by the pumping process, i.e., a linear combination of the vibrational Raman transitions of the molecules at different sites. The intensity of the time-resolved CARS is expressed in terms of time-development matrix elements of the intermolecular coherence. An equation of motion for the intermolecular coherence is derived by using the projection operator method. The structure of the intermolecular-dephasing constant is clarified. The intermolecular-dephasing constant consists of the sum of population decay constants and the intermolecular pure dephasing constant that originates from an elastic interaction between the relevant molecules and a common heat-bath mode. The intermolecular pure dephasing constant is expressed in terms of the intramolecular pure dephasing constants and destructive interference of the intramolecular pure dephasings between the relevant two molecules. The intermolecular-dephasing constant is expressed as the sum of the intramolecular-dephasing constants of the relevant molecules when there is no common heat-bath mode. Inhomogeneous effects on the time-resolved CARS spectra are also investigated. A degree of the structural order is introduced to qualitatively express the inhomogeneity of local structures in the molecular ensemble. The microscopic expression derived in this paper has taken into account both incoherent and coherent optical processes in the thermally distributed molecular ensemble.

Physical Review A•Mar 1, 1991•15 citations

Theory of Absorption and Dispersion Profiles of Molecular Transitions in Dense Media

H. Paeeschke, K.‐E. Süsse, D.‐G. Welsch +1 more

Abstract Starting from quantum theoretical principles the phase relaxation is described of a molecule localized in a dense medium by an integro‐differential equation. Using this equation, which leads to a non‐exponential phase decay, general formulas are derived for calculating the absorption and dispersion profiles of vibronic and vibrational transitions of the guest molecule. In detail the calculations are performed for the case that the acoustic phonons of the medium are responsible for the phase relaxation. Especially it is shown, that in comparison with the Lorentz profile the wings of a real absorption profile become steeper with increasing ratio between dephasing rate y and Debye frequency wD‐ Only for γ/wD ≪ 1 the absorption profiles are expected to be Lorentz profiles. The dispersion is found to increase with increasing ratio γ/wD. Both the real absorption and dispersion curves are asymmetric ones.

physica status solidi (b)•Aug 1, 1977•2 citations

Theory of vibrational coherence and population decay in isotopically mixed crystal

Stephan P. Velsko, Robin M. Hochstrasser

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 Journal of Chemical Physics•Mar 1, 1985•34 citations
The indirect dephasing model for a vibrating molecule in a dense medium is investigated by using the cumulant perturbation expansion method. The perturbation is taken as a sum of the anharmonic coupling between the high- and low-frequency modes and the interaction between the low-frequency mode and molecular surrounding. All the states of the low-frequency mode is taken into account in the calculation. Our model is available, only when the dephasing time of the high-frequency mode is shorter than the life-time of the low-frequency mode. This condition is satisfied in usual organic molecular crystals.
The dephasing of a high-frequency intramolecular vibrational mode in a molecular crystal is successively investigated by the cumulant perturbation expansion method as in the preceding papers in this series, I and II. The dephasing of the high-frequency mode is brought on by the thermal excitation of a low-frequency mode in the same molecule as in I and II. In this paper, however, the intramolecular vibrational modes are expressed by the bands of the exciton waves traveling through the crystal (in I and II, the intramolecular vibrational modes are expressed by the localized excitation in one molecule). The calculation shows that the spectrum becomes considerably broad as the temperature increases, while the narrowing is observed as the band widths of the exciton waves increases.
This review emphasizes the physical principles underlying the dephasing of nonstationary vibrational states of molecules with multiple vibrational degrees of freedom. The motion of atoms within molecules can be described to a very good approximation by a many-level system of coupled anharmonic quantized oscillators. The separation of electronic and nuclear timescales, combined with weak symmetry breaking inherent in molecular structures, guarantees that the Hamiltonian can always be cast in a form that is local in the quantum state space of the molecular vibrations. The resulting nonexponential dephasing dynamics can be controlled with external fields to stabilize nonstationary quantum states, and both quantum–classical and fully quantum control formalisms are described. Coupled molecular vibrations interacting with external fields also offer prospects for quantum computing because vibrational level spacings can be made very large compared to thermal noise, and relaxation mechanisms such as infrared fluorescence are many orders of magnitude slower than the timescales required for coherence transfer. Finally, a toy model that provides insights into the interaction of vibrational degrees of freedom with 'solvent' modes is also discussed, and exhibits nonexponential dynamics in certain regimes.
Mechanisms of intermolecular dephasings revealed in the time-resolved coherent anti-Stokes Raman scattering (CARS) spectra of a molecular ensemble are theoretically studied by deriving the microscopical expression for the scattered photon intensity averaged over the heat-bath variables. The intermolecular dephasing means the decay of the intermolecular coherence created by the pumping process, i.e., a linear combination of the vibrational Raman transitions of the molecules at different sites. The intensity of the time-resolved CARS is expressed in terms of time-development matrix elements of the intermolecular coherence. An equation of motion for the intermolecular coherence is derived by using the projection operator method. The structure of the intermolecular-dephasing constant is clarified. The intermolecular-dephasing constant consists of the sum of population decay constants and the intermolecular pure dephasing constant that originates from an elastic interaction between the relevant molecules and a common heat-bath mode. The intermolecular pure dephasing constant is expressed in terms of the intramolecular pure dephasing constants and destructive interference of the intramolecular pure dephasings between the relevant two molecules. The intermolecular-dephasing constant is expressed as the sum of the intramolecular-dephasing constants of the relevant molecules when there is no common heat-bath mode. Inhomogeneous effects on the time-resolved CARS spectra are also investigated. A degree of the structural order is introduced to qualitatively express the inhomogeneity of local structures in the molecular ensemble. The microscopic expression derived in this paper has taken into account both incoherent and coherent optical processes in the thermally distributed molecular ensemble.
Abstract Starting from quantum theoretical principles the phase relaxation is described of a molecule localized in a dense medium by an integro‐differential equation. Using this equation, which leads to a non‐exponential phase decay, general formulas are derived for calculating the absorption and dispersion profiles of vibronic and vibrational transitions of the guest molecule. In detail the calculations are performed for the case that the acoustic phonons of the medium are responsible for the phase relaxation. Especially it is shown, that in comparison with the Lorentz profile the wings of a real absorption profile become steeper with increasing ratio between dephasing rate y and Debye frequency wD‐ Only for γ/wD ≪ 1 the absorption profiles are expected to be Lorentz profiles. The dispersion is found to increase with increasing ratio γ/wD. Both the real absorption and dispersion curves are asymmetric ones.
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.