Abstract
We explore the mechanism for the long-lived quantum coherence by considering the discrete phonon modes: these vibrational modes effectively weaken the exciton-environment interaction, due to the new composite (polaron) formed by excitons and vibrons. This subsequently demonstrates the role of vibrational coherence which greatly contributes to long-lived feature of the excitonic coherence that has been observed in femtosecond experiments. The estimation of the timescale of coherence elongated by vibrational modes is given in an analytical manner. To test the validity of our theory, we study the pigment-protein complex in detail by exploring the energy transfer and coherence dynamics. The ground-state vibrational coherence generated by incoherent radiations is shown to be long-survived and is demonstrated to be significant in promoting the excitation energy transfer. This is attributed to the nonequilibriumness of the system caused by the detailed-balance-breaking, which funnels the downhill migration of excitons.
Highlights
In (b) the excitons in pigments couple to a vibrational mode and the radiation energy with temperature T1 is absorbed by such joint system and dissipated into the noisy protein environment with temperature T2
To elucidate this issue in detail, we consider the phonon dynamics being restricted to the space spanned by |{mn}〉, |{mn + 1}〉, where mn = {mn} dn†dn {mn} represents the occupation number of phonons on each vibrational mode
The bare exciton is surrounded by a cloud consisting of discrete vibrational modes
Summary
The 2nd and exciton-exciton interaction (intermediated by phonons) and the free Hamiltonian of discrete vibrational modes, respectively. The last term in HS quantifies the electronic coupling renormalized by exciton-vibrational (discrete phonon modes) coupling. The exciton-phonon interaction strength fqs is replaced by λn where λn = fq′s′ for those discrete modes. The vibrational operator is χijn = eλn(γi−γ j)dn†e−λn(γi−γ j)dn. Those discrete vibrational modes are denoted by the operator dn’s. Equation (2) shows that the effective coupling strength between exciton and phonon is renormalized by the polaron effect, which leads to the weak interaction of the new composite (exciton +vibron) with the environmental modes, as will be illustrated in details in the section of Results.
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