Coherent Biexciton Transport in the Presence of Exciton-Exciton Annihilation in Molecular Aggregates

Abstract

We present a theoretical framework for biexciton dynamics in molecular aggregates that explicitly treats populations and coherences across excitation manifolds within a reduced density-matrix formalism. By extending kinetic descriptions beyond the weak-coupling limit, the approach captures the influence of exciton delocalization and exciton-exciton annihilation while remaining computationally tractable within a Markovian description of environmental relaxation. Using this framework, we investigate how the spatial profile and momentum composition of the initial biexciton state govern fluorescence decay and transport. Incoherent initial conditions lead to strongly non-exponential relaxation and time-dependent diffusion driven by nonlinear population kinetics. In contrast, coherently prepared biexciton states exhibit pronounced early-time coherent transport, whose character depends sensitively on whether the initial state is prepared as a standing-wave or traveling-wave superposition of single-exciton modes. Despite nearly identical emission dynamics for J and H aggregate, biexciton transport properties differ markedly due to band structure-dependent interference effect. Our results demonstrate that biexciton dynamics remains strongly influenced by initial-state coherence and momentum composition. Besides initial-state preparation, the coherent-to-incoherent crossover and the diffusive spreading of the exciton density are sensitive to internal conversion processes such as exciton fusion and the decay to the first excited state. The present work establishes initial-state preparation as a key control parameter for many-exciton transport in excitonic systems and provides a general framework for interpreting nonlinear optical experiments beyond population-based descriptions.

Figures (4)

• Figure 1: Biexciton dynamics in linear chain of three-level systems with nearest neighbor interaction. $J$ is the interaction between first excited state, $\mathcal{J}$ refers to second excited state interaction and $K$ denotes fusion due to exciton-exciton annhiliation.
• Figure 2: For a linear chain of three-level systems with nearest neighbor interaction with $J=\mathcal{J}=-0.1$ and decay from first excited state $k=0.1$ semi-log plot of time dependent emission, mean squared displacement and time dependent diffusivity are plotted, with varying decay rate $r$ from second excited state in panels (a) to (c) at fixed $K=1$ and with varying fusion $K$ at fixed decay rate $r=1$ in panels (d) to (f). Initially biexcitons are placed symmetrically with respect to the center of the 21-site molecular aggregates. The dynamics is propagated with population-only kinetic equations.
• Figure 3: Same system specifications as in Fig. \ref{['fig:fig2']} but for initial biexciton state corresponding to two exciton gaussian wavepackets with $k_1=\frac{\pi}{N_{mol}+1}$ and $k_2=\frac{2\pi}{N_{mol}+1}$ with the width $w=3$, described in main text. The dynamics is propagated with fully coherent description. The inset highlights the short-time MSD and $D_t$.
• Figure 4: Same setup as in Fig. \ref{['fig:fig3']} with $r=1$. Panels (a) to (c) are for fixed $K=1$ and in panels (d) to (f) $K=0.1$. Here the initial biexciton states are standing wave (SW) packets with $k_1=\frac{\pi}{N_{mol}+1}$ and $k_2=\frac{2\pi}{N_{mol}+1}$ and traveling wave (TW) packets with $k_1=\frac{2\pi}{N_{mol}+1}$ and $k_2=\frac{N_{mol}\pi}{N_{mol}+1}$ for J and H aggregate, respectively.