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

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.

💡 Research Summary

This paper introduces a comprehensive theoretical framework for describing biexciton dynamics in molecular aggregates, explicitly incorporating populations and coherences across multiple excitation manifolds within a reduced density‑matrix formalism. The authors extend the kinetic description originally proposed by May, which was limited to weak electronic coupling and rapid decoherence, to regimes of intermediate and strong coupling where quantum coherence plays a decisive role. By employing a Lindblad‑type Markovian master equation, they include radiative decay from the first excited state (rate k), internal conversion from the higher‑energy state (rate r), and the exciton‑exciton annihilation (EEA) process mediated by a fusion coupling K. The Hamiltonian consists of three parts: H^(1) for the Frenkel exciton band, H^(2) for the second‑excited (higher) band, and V^(12) that couples the two bands via K, thereby enabling the formation of a biexciton state where one molecule is promoted to the higher level while its partner relaxes to the ground state.

A key methodological advance is the derivation of coupled equations of motion for diagonal (populations P_m, N_m) and off‑diagonal (coherences W_mn, Z_mn, R_mn) density‑matrix elements. The authors retain time‑dependent off‑diagonal terms by factorizing four‑body correlators in a mean‑field fashion, which yields a set of nonlinear equations (Eqs. 15‑17) that capture feedback between coherence and population dynamics. This goes beyond traditional rate‑law models that treat EEA as a simple bimolecular decay and neglect coherent transport effects.

To explore the impact of initial state preparation, the paper constructs biexciton wavefunctions from two single‑exciton wave packets ϕ^(1) and ϕ^(2). The spatial overlap S = ⟨ϕ^(1)|ϕ^(2)⟩ quantifies the degree of exchange‑induced coherence. Two families of initial conditions are examined: (i) standing‑wave packets with a Gaussian envelope and defined central momenta, and (ii) traveling‑wave packets with a complex phase factor. The antisymmetrized biexciton wavefunction Ψ_mn = ϕ^(1)_m ϕ^(2)_n – ϕ^(1)_n ϕ^(2)_m ensures hard‑core exclusion of double occupancy.

Simulation results reveal several distinct regimes. For incoherent (random‑phase) initial conditions, fluorescence intensity I(t) = Σ_n