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Journal of the Physical Society of Japan

Optical Dephasing Due to Virtual Transfer of Excitation Energy as Observed in Photon Echo Experiments of Pentacene Molecules in Crystals

Yuzo Yoshikuni, Arao Nakamura, Shigeo Shionoya, Masaki Aihara

Published Aug 15, 1982• 12 citations
Publisher

Abstract

Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.

DOI
10.1143/jpsj.51.2604

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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.

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Radiationless relaxation and optical dephasing of molecules excited by wide- and narrow-band lasers. II. Pentacene in low-temperature mixed crystals

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One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.

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The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.

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Optical dephasing in multilevel systems. Bath-independent dephasing and breakdown of the two-level approximation

W. S. Warren, Ahmed H. Zewail

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
Optical dephasing due to intermolecular interaction is studied for pentacence molecules introduced in naphthalene and p -terphenyl crystals by measuring the ordinary photon echo and the accumulated three-pulse echo. It is found that the reciprocal of pure dephasing time increases linearly with the guest molecule concentration at low temperature where pure dephasing is known to be temperature-independent. A new model based on virtual transfer of excitation energy, i.e. energy transfer without phonon asistance, between guest molecules is presented to interpret this dephasing process. It is shown that observed linear dependence of the line width representing pure dephasing is well interpreted by this model, and that the calculated relationship between the line width and concentration agrees with the experimental one within a factor of about two.
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.
Abstract Photon echo decay time is measured for pentacence molecules introduced in naphthalene and p-terphenyl crystals with rather high concentrations (10−6–105 mol/mol) at temperatures between 1.6 K and 4.1 K, using a tunable picosecond laser system consisting of a mode-locked YAG laser and a parametric oscillator. In naphthalene echo decay time increases with lowering temperature approaching a constant value below 2 K, but in p-terphenyl it is almost constant. The phase relaxation time at very low temperature is much shorter than twice the population relaxation time in both crystals, indicating that pure dephasing processes exist. Analyzing the results it turns out that there exsists a pure dephasing process which is temperature-independent and is very probably due to interactions between pentacene molecules, in addition to the temperature-dependent dephasing process due to the scattering of pseudolocalized phonons.
One purpose of this paper is to present new studies on the effect of bandwidth and the coherence properties of the excitation source on the decay and the dephasing of isolated large molecules. A detailed study of the system pentacene in a p-terphenyl matrix is presented utilizing three different excitation sources, a single mode dye laser (60 KHz–6 MHz bandwidth depending on the time scale of the experiment) a multimode dye laser (240 GHz bandwidth), and an incoherent N2 flash lamp. Optical T1 (the longitudinal relaxation time) and T2 (the transverse relaxation time) are measured from the coherent and incoherent transients observed either in the forward direction of the laser or at right angles to the exciting beam. At 1.8 °K, the optical transition (1A1g→1B2u) of pentacene in p-terphenyl exhibits four sites, the lowest of which at 16 887 cm−1 has the following parameters: T2=44±2 nsec; T1=24.9±2 nsec, and μ=0.7±0.1 D. The transition moment μ, is obtained directly from the optical nutation, which exhibits a Rabi nutation time (h//μ⋅ε) of 27.3 nsec, and is corrected for the effect of the Lorentz local field inside the terphenyl crystal. The experiments presented here are categorized into two time regimes for theoretical analysis; a transient coherence regime where the observed decay is comparable with (h//μ⋅ε) and T2, and a steady-state coherence regime where transient dephasing is complete and the off-diagonal elements of the density matrix have decayed to their steady-state values in the presence of the field of amplitude ε. Using the Wilcox–Lamb method, rate equations (with T2 expressions) describing the population flow in the ’’complete’’ level structure of pentacene (ground‖0〉, singlet ‖p〉, and triplet {‖l}) are derived from the density matrix equations of motion. When these equations are averaged over the inhomogeneous width of the optical transition and the measured Gaussian transverse profile of our laser we obtain T1p0=24.9±2 nsec and T1pl=15.7 μsec, the time constants by which pentacene spontaneously decays to ‖0〉 or crosses over into l, as well as the averaged population at time t. In an effort to be complete, attention is placed upon the relationship between theory and the experimental findings. First, expressions for the OFID and nutation in the solid are presented for the pentacene case in order to relate T1, T2, and μ to the level structure. Second, at low temperatures (1.8 °K), the origin of dephasing is identified as spontaneous emission from p→0 since experimentally T2?2T1, in agreement with other work. At higher temperature, however, a strongly temperature dependent dephasing process with an onset at 3.7 °K takes place. Armed with these observations we present a theoretical treatment of these distinct dephasing channels and their temperature dependences. A discussion regarding the influence of ’’accepting’’ phonon modes (either optical or acoustic) on optical dephasing is also given. The results indicate that the treatment of Jones et al. can (1) explain the observed temperature dependence of T2 in pentacene; (2) distinguish dephasing as a result of scattering by acoustic phonons from that due to resonance or quasilocalized phonons with clear connections to gas and liquid state theories, but without invoking more than two approximation levels. (3) explain both the level shift and line width changes as a result of ’’conventional’’ dephasing or dephasing by exchange mechanisms; and (4) relate the pure dephasing term to an anisotropy in the scattering amplitudes (between the ground and excited states in the system) which contribute largely to the homogeneous width of the transition. Optical site selection of these transitions is also reported and discussed in relation to vibrational relaxation and to both homogeneous and inhomogeneous broadenings. The studies of the homogeneous broadening of the vibronic origin (267 cm−1) indicate that vibrational relaxation is fast (psec) in the excited singlet manifold of pentacene. Finally from more than ten independent experiments including single and multimode excitation, on- and off-resonance scattering, Zeeman effect and the transient decay as a function of excess energy in the molecule, a more complete picture of the pentacene level structure {‖l〉} is given. With this in mind, the influence of the laser bandwidth and coherence properties on state preparation and subsequent dephasing and decay is concluded. It is proposed that the slow decay, (∼15 μsec) observed during narrow-band excitation represents intersystem crossing to nearby triple manifolds after the transient coherence of the 0↔p subsystem is decayed. In addition, the decay of the primary state prepared in these experiments is not sensitive to the bandwidth or the correlation time of our excitation sources.
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.
The effects of optical density (OD) on photon echo experiments is examined both theoretically and experimentally. The theoretical treatment involves coupled Maxwell-Optical Bloch equations, and the experiments are picosecond photon echo studies of the mixed molecular crystal, pentacene in naphthalene. Under high power excitation (π/2, π) in high OD samples, the echo decays are predicted and observed to be faster than decays arising solely from the intrinsic molecular T2. The increase in the echo decay rate vanishes in the limit of low power or low OD, permitting the intrinsic molecular T2 to be measured. Previously reported concentration effects are shown to actually be optical density effects. The experimentally determined intrinsic molecular T2 of pentacene in naphthalene is shown to be independent of concentration and temperature (below ∼2 K) and T2≠2T1. It is suggested that the difference between T2 and 2T1 is due to the static multiplet level structure arising from the electronic state-phonon coupling.
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.