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The Journal of Chemical Physics

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

Thomas E. Orlowski, Ahmed H. Zewail

Published Feb 1, 1979• 124 citations
Publisher

Abstract

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.

DOI
10.1063/1.437579

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I. A new technique utilizing the electro-optic frequency switching of a single mode ( 6 Mhz) dye laser was used to observe free induction decay and optical nutation in iodine gas and optical nutation in an organic mixed crystal (pentacene in p-terphenyl) at low temperature. A new technique, incoherent resonance decay (IRO) was also developed. These experiments allow one to determine T_1 and T_2, the longitudinal and transverse relaxation times of the excited ensemble, in analogy with magnetic resonance. For I_2(g) at O∙C; T_l = 2.3 x 10^(-7) sec, T_2 ≃ 1 x 10^(-7) sec. These techniques are limited to a time scale > 10 nsec. II. The construction and characterization of cw, mode-locked dye laser capable of putting out a continuous train of reproducible sub-picosecond pulses is described. Experiments utilizing this laser for the measurement of picosecond coherent transients and time resolved absorption spectroscopy are proposed.

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High-resolution time resolved spectroscopy of collisionless molecular beams. II. Energy randomization and optical phase relaxation of molecules in crossed laser and molecular beams

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This paper outlines new ways for separating the different channels of optical dephasing of molecules in beams. It is shown that both the population loss and the optical phase relaxation rates can be obtained under collisionless conditions (molecular beams). These dephasing rates, which measure directly the homogeneous width of the prepared resonance, can be obtained with an energy resolution of better than one part in 108. Under these conditions the solution of the density matrix equations of motion is given for effusive and nozzle beams which represent a statistically open ensemble. The results, which we applied to our recent measurements of optical T1 and T2, are discussed in different limits of power broadening, beam geometry, detector characteristics, temperature of the oven (or material container), and the transit time the molecules of different velocities spend in the laser beam. Furthermore, we indicate that the treatment of coherent transients in beams utilizing conventional Bloch equations is not valid since there is a loss of optically excited molecules. Finally, we discuss possible differences between small and large molecules when they undergo radiationless (or reactive) processes following the selective laser excitation (∼10 kHz–10 MHz).

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Photon Echo of Pentacene Molecules Introduced in Crystals with High Concentration

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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.

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Coherent Transients by Laser-Acoustical Diffraction Spectroscopy

A. H. Zewail

Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.

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Spontaneous fluorescence has been used to measure the coherent femtosecond response of the organic, binary crystal pentacene/p-terphenyl. By using two-pulse excitation with phase-randomized pulses in an interferometric setup and analyzing the variance of the fluctuating intensity of correlated fluorescence photons, femtosecond beatings have been observed. The pattern of these terahertz oscillations is strongly dependent on the detuning frequency range of the exciting pulses, but is rather invariant with regard to the spectral position of the fluorescence probe window. In the interferometric regime of freely propagating pulses novel, ultrafast fluorescence carrier-wave oscillations superimposed to the beat structure have been obtained. The oscillatory signals evolve from a coherent superposition of optical free induction decays, caused by the different electronic transition energies of the pentacene absorber sites O1, O2, O3, and O4, respectively, are monitored as intrinsic, heterodyne beats by the fluorescence square detector. The major part of oscillations is thus considered to result from typical polarization interferences, but vibrational quantum beats are also extractable from the interferogram in the ultimate frequency regime of the pentacene S0→S1ν=1, S0→S1ν=2 resonances. The early picosecond-decay of the fluorescence beats reveals the mechanism of the loss of coherence to be mainly controlled by inhomogeneous dephasing at low phonon temperatures. A model of uncoupled two-level systems that includes Gaussian inhomogeneous broadening of the individual absorber sites and a Gaussian frequency distribution for the excitation pulses can account for the experimental data, quite adequately.

The Journal of Chemical Physics•Mar 1, 1999•19 citations

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 +1 more

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.

Journal of the Physical Society of Japan•Aug 15, 1982•12 citations
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.
I. A new technique utilizing the electro-optic frequency switching of a single mode ( 6 Mhz) dye laser was used to observe free induction decay and optical nutation in iodine gas and optical nutation in an organic mixed crystal (pentacene in p-terphenyl) at low temperature. A new technique, incoherent resonance decay (IRO) was also developed. These experiments allow one to determine T_1 and T_2, the longitudinal and transverse relaxation times of the excited ensemble, in analogy with magnetic resonance. For I_2(g) at O∙C; T_l = 2.3 x 10^(-7) sec, T_2 ≃ 1 x 10^(-7) sec. These techniques are limited to a time scale > 10 nsec. II. The construction and characterization of cw, mode-locked dye laser capable of putting out a continuous train of reproducible sub-picosecond pulses is described. Experiments utilizing this laser for the measurement of picosecond coherent transients and time resolved absorption spectroscopy are proposed.
This paper outlines new ways for separating the different channels of optical dephasing of molecules in beams. It is shown that both the population loss and the optical phase relaxation rates can be obtained under collisionless conditions (molecular beams). These dephasing rates, which measure directly the homogeneous width of the prepared resonance, can be obtained with an energy resolution of better than one part in 108. Under these conditions the solution of the density matrix equations of motion is given for effusive and nozzle beams which represent a statistically open ensemble. The results, which we applied to our recent measurements of optical T1 and T2, are discussed in different limits of power broadening, beam geometry, detector characteristics, temperature of the oven (or material container), and the transit time the molecules of different velocities spend in the laser beam. Furthermore, we indicate that the treatment of coherent transients in beams utilizing conventional Bloch equations is not valid since there is a loss of optically excited molecules. Finally, we discuss possible differences between small and large molecules when they undergo radiationless (or reactive) processes following the selective laser excitation (∼10 kHz–10 MHz).
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.
Recently we have reported[1] on the measurements of electronic dephasing (T_2) and radiationless decay (T_1) in molecules using emission spectroscopy as a probe for the detection of the photon echo. This right-angle photon echo utilizes a single mode of a narrow-band (~MHz) cw dye laser and an intracavity electro-optical (EO) element that modulates the frequency of the laser.[2] Applying voltage pulses into the EO crystal switches the laser frequency from ω_0 (the peak frequency of the transition resonance) into another frequency ω. This switching procedure introduced by Brewer et al. for the observation of transients in the forward direction of the laser allows one to observe coherent transients in gases,[1,2] solids[3-5] and molecular beams.[6] Typically, the dispersion of the nonlinear EO crystal (e.g., AD*P) gives a 60 MHz frequency shift within the inhomogeneous resonance of the optical transition (width ~GHz or larger). Therefore, to switch the laser frequency further, one must use high-voltage signals that are usually hard to obtain especially for multiple-pulse experiments. Secondly, there is a limit on the frequency shift which is conditioned by the mode spacing of the cavity. Thirdly, because the laser is switched into a new group of molecules some complications may arise in interpreting the transient spectra especially in large molecules. This is because in large molecules the density of excited states is high and thus the buildup of transients of w molecules (which could be complex) will be superimposed on the decay of ω_0 molecules. Finally, off-resonance effects (e.g., beats) between the molecules at frequency ω and ω_0 cannot be avoided.
Spontaneous fluorescence has been used to measure the coherent femtosecond response of the organic, binary crystal pentacene/p-terphenyl. By using two-pulse excitation with phase-randomized pulses in an interferometric setup and analyzing the variance of the fluctuating intensity of correlated fluorescence photons, femtosecond beatings have been observed. The pattern of these terahertz oscillations is strongly dependent on the detuning frequency range of the exciting pulses, but is rather invariant with regard to the spectral position of the fluorescence probe window. In the interferometric regime of freely propagating pulses novel, ultrafast fluorescence carrier-wave oscillations superimposed to the beat structure have been obtained. The oscillatory signals evolve from a coherent superposition of optical free induction decays, caused by the different electronic transition energies of the pentacene absorber sites O1, O2, O3, and O4, respectively, are monitored as intrinsic, heterodyne beats by the fluorescence square detector. The major part of oscillations is thus considered to result from typical polarization interferences, but vibrational quantum beats are also extractable from the interferogram in the ultimate frequency regime of the pentacene S0→S1ν=1, S0→S1ν=2 resonances. The early picosecond-decay of the fluorescence beats reveals the mechanism of the loss of coherence to be mainly controlled by inhomogeneous dephasing at low phonon temperatures. A model of uncoupled two-level systems that includes Gaussian inhomogeneous broadening of the individual absorber sites and a Gaussian frequency distribution for the excitation pulses can account for the experimental data, quite adequately.
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.