Energy transfer in finite-size exciton-phonon systems: confinement-enhanced quantum decoherence

Based on the operatorial formulation of the perturbation theory, the exciton-phonon problem is revisited for investigating exciton-mediated energy flow in a finite-size lattice. Within this method, the exciton-phonon entanglement is taken into account through a dual dressing mechanism so that exciton and phonons are treated on an equal footing. In a marked contrast with what happens in an infinite lattice, it is shown that the dynamics of the exciton density is governed by several time scales. The density evolves coherently in the short-time limit, whereas a relaxation mechanism occurs over intermediated time scales. Consequently, in the long-time limit, the density converges toward a nearly uniform distributed equilibrium distribution. Such a behavior results from quantum decoherence that originates in the fact that the phonons evolve differently depending on the path followed by the exciton to tunnel along the lattice. Although the relaxation rate increases with the temperature and with the coupling, it decreases with the lattice size, suggesting that the decoherence is inherent to the confinement.