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.
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.
The optical response of a two-site system driven by a pair of optical pulses in an interferometric set up has been studied theoretically by applying the density operator formalism. The one-exciton approach is taken for modeling two coupled two-level systems (TLS), the external field is presented semiclassically and bath-induced dissipative processes are included. In the δ-pulse limit the population of the excited state has been formulated to the lowest order perturbation expansion in the external field. In the limit of slow luminescence the interferogram of time-integrated total fluorescence has been calculated for pulses with constant relative phase. For phase-randomized pulses the variance of the correlated fluorescence signal as a function of the pulse delay allows direct interrogation of coherent transients and dephasing processes. Our analysis follows the principle of coherence observation by interference noise, COIN [O. Kinrot, I. Sh. Averbukh, and Y. Prior, Phys. Rev. Lett. 75, 3822 (1995)], but is a generalization of this concept to expand on electronically interacting TLS. The theoretical results demonstrate that analysis of fluorescence interference fluctuations may provide a powerful diagnostic tool for probing the initial quantum coherence of energy transfer, i.e., excitation oscillations by employing fs-fluorescence correlation measurements in stable interferometric configurations.
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.
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.
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.
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 two-dimensional (2D) temporal shape of the (degenerate) three-pulse photon-echo (3-PPE) polarization P(3)(t′,τ12,τ23=0) has been theoretically analyzed for a weakly interacting two-site system (TSS) in the presence of site inhomogeneous broadening. The TSS has been modeled in terms of two identical, energy-degenerate, excitonically coupled pairs of electronic states in the site-representation (i.e., two S0 and S1 states forming a 4-level system). The 2D time-domain signal S(t′,τ12,τ23=0) has been derived in a closed-form solution which allowed to formulate the analytical Fourier transform analog under sequential δ-pulse excitation. The resulting 2D PE signal in frequency–frequency space S(ωt′,ωτ12) is formed in the region of the resonant, optical carrier frequency by, generally, four peaks, arranged at the edges of a square with distances determined by the excitonic coupling. The two diagonal peaks are of one-exciton origin, while the two off-diagonal (cross) peaks involve two-exciton effects, too. The relative heights of the four peaks are in distinct relation with the mutual orientation of the site-localized transition dipoles, thus these 2D line shapes serving as a structural probe for resonantly interacting molecules. The shapes of the peaks reflect the ratio between homogeneous and inhomogeneous dephasings and can be used for structural studies of statically disordered systems of TSS. The semiclassical two-site model is intended to provide a preparatory platform for mimicking electronically coupled segmental pairs dispersed in energy and space along the strongly disordered main chain contour. The results of the model calculation are taken to discuss the potential and the limitations of 2D line shape echo-spectroscopy in the study of short-range coherences and electronic coupling in π-conjugated polymers.