Graphical representation of the SSH model. The coupling between the system and each bath mode is proportional to the bath spectral density, , at the frequency of the corresponding mode. At random times, the RDM of a given bath mode, here the seventh, is reset to its initial thermal state. These jumps simulate the energy exchange between the bath modes and an unresolved larger environment and progressively destroy the coherence.
Dynamics of a dimer system computed with the SSH approach (plain) and the Redfield equation (dashed). The dimer is initially prepared in |b⟩ and is characterized by e b − e a = 1 meV and α = 10 meV. The cutoff frequency of the bath is set at ω c = 1.5 and the reorganization energy is: λ = 2 meV (a), 5 meV (b), 7 meV (c), and 10 meV (d). The temperature of the bath was set to 300 K. The SSH dynamics has been solved using 6 modes, 100 realizations, and for Λ = 1.05.
Trajectory on the Bloch sphere of the dimer system for λ = 10 meV. The system undergoes a spiral trajectory to reach a mixed state located at the center of the Bloch sphere.
(a) The 7 BChl of the FMO complex labeled from a to g. Due to the weak interactions between each BChl and the differences in their on-site energies the excitonic states, labeled from 1 to 7, are mainly localized on one or two BChl. Two relaxation pathways have been experimentally observed driving an initial excitation to the lowest lying excitonic state (Ref. 8). (b) Bath spectral density used to compute the relaxation dynamics. The three oscillation frequencies of the red relaxation pathway are located near the maximum of . (c) The population oscillations obtained with the SSH algorithm show coherent oscillations lasting for almost 1 picosecond.
(a) The eight BChl constituting the FMO complex. BChl h, close to the base plate, is the initial state of the evolution. BChl c, close to the reaction center, is the target state of the evolution. The relaxation among the delocalised excitonic states, noted from 1 to 8, drives the initial excitation following different possible pathways represented on the left. (b) Bath spectral density used to compute the relaxation dynamics. The oscillation frequencies of the transition composing the red relaxation pathway are located near the maximum of . c) Population of the local BChl states starting from |h⟩ and showing only weak coherent oscillations.
(a) OBO spectral density with a cutoff frequency of ω c = 3 . The three oscillations frequencies correspond to the three transitions involved in the blue relaxation pathway of Fig. 5(a). Due to the weak system-bath interaction this combination leads to long living coherent oscillations but to an inefficient exciton transfer. (b) Gaussian spectral density centered on ω c = 16.5 and the three frequencies that correspond to the red relaxation pathway of Fig. 5(a). This leads to extremely weak system-bath interactions and suppresses the exciton transfer.
(a) OBO bath spectral density for different values of the cutoff frequency ω c . Depending on ω c the three oscillation frequencies involved in the red relaxation pathway shown in Fig. 5, more or less strong system-bath interactions are obtained. (b) Excitonic transfer efficiency with respect of the reorganization energy λ and for different values of the cutoff frequency ω c . The bath spectral density follows the model presented above. The dashed lines represent the exact numerical values obtained with the SSH algorithm and the plain line the best fit of these data.
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