Two-exciton excited states of J-aggregates in the presence of exciton-exciton annihilation

We study decay of two-exciton states of a J-aggregate that is collective in nature. We use mathematical formalism based on effective non-Hermitian Hamiltonian suggested in nuclear theory. We show that decay of two-exciton states is strongly affected by the interference processes in the exciton-exciton annihilation. Our evaluations of the imaginary part of the effective Hamiltonian show that it exceeds the spacing between real energies of the two-exciton states that gives rise to the transition to the regime of overlapping resonances supplying the system by the new collectivity - the possibility of coherent decay in the annihilation channel. The decay of two-exciton states varies from twice bimolecular decay rate to the much smaller values that is associated with population trapping. We have also considered the corresponding experiment in the framework of our approach, the picture of which appears to be more complex and richer than it was reasoned before.