Exciton level-structure of the Hamiltonian [Eq. (5)]. ∣0⟩ is the ground state, while means one of the one-exciton levels consisting of states. denotes one of the two-exciton states. and are eigenenergies for the single and double excitons, respectively. The exciton eigenenergies are numerically obtained by diagonalizing the first and second terms of the Frenkel-exciton Hamiltonian [Eq. (1)] (Ref. 19). Its monomer excitation energies are specified by the Gaussian distribution [Eq. (77)]. For example, the characteristic eigenenergy of B850 chlorophylls and the full width at half maximum .
Double-sided Feynman diagrams representing four-wave-mixing photon echo Liouville paths. The exciton-exciton coherence transfer (EECT) occurs during the time interval between second and third pulses. The diagram (a) includes only single exciton states, while (b) contains the double exciton state.
(Color) The time-resolved echo (TRE) signals vs and with with (a) and without (b) the EECT contribution. The fact that (b) is more elongated than (a) illustrates that EECT generates the fast decaying coherent state evolutions.
Photon echo peak shifts (PEPSs) estimated from the time-integrated photon echo signals [Eq. (83)] with respect to . The numerically calculated PEPSs with and without EECT are compared with the experimental results. The experimental data are measured in Ref. 14. The direct comparison shows that EECT is essential in accounting for the experimental data.
(Color) (a) Real part of the 2D photon echo spectrum in Eq. (84) at . The horizontal and vertical axes are and , respectively. Here, , given in Eq. (76). (b) The same as in (a), but without EECT. The width along the antidiagonal axis of (a) is broader than that of (b). This means that the decoherence (memory loss) of multiple quantum coherent states is another source of homogeneous dephasing process. EECT can cause the rapid diffusion of frequencies.
(Color) (a) Absolute magnitude of the 2D photon echo spectrum in Eq. (84) at . The horizontal and vertical axes are and , respectively. (b) The same as (a), but without EECT. The 2D correlation spectrum at an early time can be less diagonally elongated due to the decoherence of multiple quantum coherent states, i.e., hopping dephasing.
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