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Physical Review Letters

Two-Exciton Collective Photon Echoes in Disordered Molecular Nanostructures

Vladimir Chernyak, Shaul Mukamel

Published Jun 12, 1995• 13 citations
Publisher

Abstract

A new disorder-induced two-exciton photon echo and its frequency-domain counterpart, a narrow four-photon extra resonance, are predicted in molecular aggregates. These effects are induced by the combined influence of aggregation and inhomogeneous broadening and provide a direct signature for the strong correlation between one- and two-exciton levels.

DOI
10.1103/physrevlett.74.4895

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A new disorder-induced two-exciton photon echo and its frequency-domain counterpart, a narrow four-photon extra resonance, are predicted in molecular aggregates. These effects are induced by the combined influence of aggregation and inhomogeneous broadening and provide a direct signature for the strong correlation between one- and two-exciton levels.
Two-pulse four-wave-mixing signals from molecular aggregates, including effects of two-exciton states, static disorder, and exciton-phonon interaction represented by arbitrary spectral densities are calculated. Three types of contributions to the signal are identified. The first, reflecting exciton self-correlation, is similar to the photon echo from disordered two-level systems and dominates the signal for long time-delays. The second is related to correlations of one-exciton states, whereas the third reflects correlations between one- and two-exciton states. The information gained by completely resolving the signal field (both amplitude and phase) is analyzed using Wigner spectrograms.
The disorder-induced transient optical four-wave mixing for a Frenkel exciton in a binary mixed crystal is theoretically investigated. We have clarified the role of static disorder in a wide range of disorder strength by using the coherent potential approximation. It is found that the weak disorder gives rise to exciton dephasing, and the strong disorder induces a photon echo signal. The crossover from homogeneous to inhomogeneous broadening with increasing disorder strength is systematically analyzed. In the case of off-resonant excitation, we find an oscillatory echolike signal inherent in the disorder-induced optical nonlinearity.
We study the nonlinear optical response of molecular assemblies consisting of coupled two-level molecules with arbitrary geometry including inhomogeneous broadening and exciton dephasing. An analytical expression for the third-order optical susceptibility is derived based on a certain closure of the equation-of-motion hierarchy. An exact expression for the third-order response of small crystalline aggregates with exciton population relaxation is derived, and used to show that for low relaxation rate \ensuremath{\Gamma} the cooperative part of the nonlinear response scales as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1/2}$ in d=1, and up to logarithmic corrections, as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}1}$ in d=2 and 3. We show that cooperative enhancement is caused by exciton scattering. This is to be contrasted to other cooperative effects such as superradiance, which are related to the size of molecular coherence domains and therefore scale as ${\mathrm{\ensuremath{\Gamma}}}^{\mathrm{\ensuremath{-}}\mathit{d}/2}$. In a numerical study for dipole-dipole interactions in d=1, 2, and 3 dimensions we find that the local-field approximation is valid only in selected cases, and in general fails to reproduce the magnitude and the resonance structure of ${\mathrm{\ensuremath{\chi}}}^{(3)}$.
The coherent response of excitons in semiconductor nanostructures measured in four-wave mixing (FWM) depends strongly on the inhomogeneous broadening of the exciton transition. We investigate GaAs/Al0.3Ga0.7As single quantum wells (SQW) and AlxGa1-xAs mixed crystals. Additional to the usual phase-space filling nonlinearity, excitation-induced dephasing (EID) and biexciton formation (BIF) are important. EID leads to a strong dependence of the signal on the angle between the linear input polarizations. We find that EID persists in inhomogeneous systems, showing that the mutual density-dependent dephasing rate difference between two subsystems within the inhomogeneous distribution is strongly dependent on their energy difference. BIF is strongly affecting the cross-linear polarized FWM response. The signal for positive delay is dominated by the transitions from the one-exciton state X to the two-exciton states. Here, the third-order polarization at X-XX is not at the same resonance as the first-order polarization at 0-X. Consequently, the rephasing of the microscopic third-order polarization to the macroscopic FWM photon echo is blurred by the non-perfect correlation of X and XX energies, leading to a fast and non-exponential signal decay in delay time. For inhomogeneous broadenings larger than the biexciton binding energy, we find an enhanced biexciton binding energy, and a quenching of the oscillator strength of the unbound biexciton.
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.