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The Journal of Chemical Physics

Theory of vibrational coherence and population decay in isotopically mixed crystal

Stephan P. Velsko, Robin M. Hochstrasser

Published Mar 1, 1985• 34 citations
Publisher

Abstract

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.

DOI
10.1063/1.448360

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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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The Journal of Chemical Physics•Feb 9, 2006•23 citations
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.
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.
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.
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 technique of COIN (coherence observation by interference noise) relies on the measurement of correlated fluorescence fluctuations subsequent to two-pulse excitation with randomized relative phase [Kinrot et al., Phys. Rev. Lett. 75, 3822 (1995)]. In this paper, a comprehensive theoretical study on the use of random-phase fluorescence interferometry in the measurement of solid-state, molecular coherence is given. Optical response functions in terms of populations expanded to second order in a perturbational approach are presented for a guest/host system that are based on a generalized Bloch–Liouville formalism including inhomogeneous site broadening and harmonic vibrational modes. The theoretical treatment is intended to explain the coherence and coherence loss mechanisms measured, very recently, in the pentacene/p-terphenyl mixed crystal at low phonon temperatures. The expressions derived within the limits of the usual approximations are quite general and valid for both δ- and finite-width pulses. The perturbative solutions reproduce the temperature variation of the experimental COIN interferograms and reveal the effects of inhomogeneous dephasing and impurity–bath coupling, quite satisfactorily.
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.
In this paper, we present simulations of the decay of quantum coherence between vibrational states of I(2) in its ground (X) electronic state embedded in a cryogenic Kr matrix. We employ a numerical method based on the semiclassical limit of the quantum Liouville equation, which allows the simulation of the evolution and decay of quantum vibrational coherence using classical trajectories and ensemble averaging. The vibrational level-dependent interaction of the I(2)(X) oscillator with the rare-gas environment is modeled using a recently developed method for constructing state-dependent many-body potentials for quantum vibrations in a many-body classical environment [J. M. Riga, E. Fredj, and C. C. Martens, J. Chem. Phys. 122, 174107 (2005)]. The vibrational dephasing rates gamma(0n) for coherences prepared between the ground vibrational state mid R:0 and excited vibrational state mid R:n are calculated as a function of n and lattice temperature T. Excellent agreement with recent experiments performed by Karavitis et al. [Phys. Chem. Chem. Phys. 7, 791 (2005)] is obtained.