Theory of coherent transient spectroscopy in molecular aggregates: The effects of interacting excitons

Using a density matrix formalism we derive a general expression for the resonant response of an ensemble of molecular aggregates to two optical pulses. The aggregates, which can be of arbitrary geometry, are described by a Frenkel exciton Hamiltonian including exciton–exciton interactions. A hierarchy of resonant coherent transient signals is generated having wave vectors sk1+(1−s)k2, where ki is the wave vector of the ith pulse and s is an integer. General expressions for the differential pump–probe absorption spectrum D(ω;tD) (s=0) and the photon echo Iecho(tD) (s=−1) are presented for arbitrary pulse intensities. Applications are made to a linear chain of interacting Frenkel excitons with nearest neighbor exciton–exciton interaction A and exciton transfer J. Analytical expressions for D(ω;tD) and Iecho(tD) are obtained which are valid to third order in the aggregate-field interaction. The influence of the optically active red (blue) biexciton which detaches from the bottom (top) of the two-exciton band when A<−2‖J‖ (A≳2‖J‖) is investigated. Biexcitons appear as extra peaks in D(ω;tD) and as oscillations in Iecho(tD). Finite size effects are responsible for quantum beat oscillations in D(ω;tD) and long time oscillations in the echo decay. Quantum beats arise predominantly from the difference between the lowest one-exciton frequencies. Our theory successfully describes the salient spectral features in the pump–probe spectra of J-aggregates.