Quantum decoherence in finite size exciton–phonon systems

Abstract

Based on the operatorial formulation of the perturbation theory, the properties of a confined exciton coupled with phonons in thermal equilibrium is revisited. Within this method, the dynamics is governed by an effective Hamiltonian which accounts for exciton-phonon entanglement. The exciton is dressed by a virtual phonon cloud whereas the phonons are clothed by virtual excitonic transitions. Special attention is thus paid for describing the time evolution of the excitonic coherences at finite temperature. As in an infinite lattice, temperature-enhanced quantum decoherence takes place. However, it is shown that the confinement softens the decoherence. The coherences are very sensitive to the excitonic states so that the closer to the band center the state is located, the slower the coherence decays. In particular, for odd lattice sizes, the coherence between the vacuum state and the one-exciton state exactly located at the band center survives over an extremely long time scale. A superimposition involving the vacuum and this specific one-exciton state behaves as an ideal qubit insensitive to its environment.

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

“…The entanglement results from a dual dressing effect because a state |k defines an exciton dressed by a virtual phonon cloud whereas a number state |n p describes phonons clothed by virtual excitonic transitions. The behavior of the energy corrections has been studied in great details [56][57][58]. Owing to the dressing, we have shown that the excitonic eigenenergies are redshifted and the energy correction of a stationary wave |k scales as…”

“…As shown previously [57], the decoherence factor behaves as a gaussian function whose time evolution can be extracted from the short-time limit of Eq. (20).…”

“…(14). Provided that k = k ′ , F (kk ′ , t) defines a decaying function that tends to zero in the long-time limit [57]. It represents the way the phonon bath destroys the coherence of an excitonic state defined as the superimposition between two stationary waves |k and |k ′ .…”

“…The operatorial formulation of PT is based on the introduction of a unitary transformation U that diagonalizes the HamiltonianĤ = U HU † in the unperturbed basis [56,57]. It is written as U = exp(S), where S is an anti-Hermitian generator that is non-diagonal in the unperturbed basis.…”

“…Here, we use the operatorial formulation of the perturbation theory (PT) [55] recently introduced for studying the dynamics of the excitonic coherences [56][57][58]. In the nonadiabatic weak-coupling limit, this method is a powerful tool for describing the spectral properties of the exciton-phonon system over a broad energy scale.…”