Efficiency of energy transfer in a light-harvesting system under quantum coherence

We investigate the role of quantum coherence in the efficiency of excitation transfer in a ring-hub arrangement of interacting two-level systems, mimicking a light-harvesting antenna connected to a reaction center as it is found in natural photosynthetic systems. By using a quantum jump approach, we demonstrate that in the presence of quantum coherent energy transfer and energetic disorder, the efficiency of excitation transfer from the antenna to the reaction center depends intimately on the quantum superposition properties of the initial state. In particular, we find that efficiency is sensitive to symmetric and asymmetric superposition of states in the basis of localized excitations, indicating that initial-state properties can be used as an efficiency control parameter at low temperatures.

Figure 1

(Color online) Schematic of the LH1-RC core of purple bacteria Rodobacter Sphaeroides. (a) Arrangement of the 32 bacterioclorophylls (Bchls) molecules surrounding the RC. The RC has two accessory Bchls and two acceptors forming a special pair responsible for charge separation. (b) Diagram of the induced dipole moments in (a). The arrows indicate the dipole moment directions corresponding to data taken from Hu and Schulten (Ref. 18). (c) Toy model: the RC is assumed to be a single two-level system.

Figure 2

Numerical results for (a) $\eta$, (b) $t_f$, and and (d) $\tau$ versus $m$ for the toy model with three different interaction mechanisms. For nearest-neighbor interactions $(◇)$ the coupling is 100 meV, while for the pairwise case $(+)$ it is 10 meV and equals the average dipole-dipole coupling $(●)$. In each case, the donor-RC coupling $\gamma$ equals 1 meV, $\Gamma =1{\text{ns}}^{-1}$, and $\kappa =4{\text{ps}}^{-1}$. (c) No-jump probability for the case of dipole-dipole interactions as a function of time and for different $m$ values.

Figure 3

(Color online) Top view of the directions of the transition dipole moments in the LH1-RC complex corresponding to the simulated data in Ref. 18. The numbers indicate total dipole-dipole interaction between individual donors and the special pair (filled circles) ${\gamma }_j={\sum }_{c=1}^2{\gamma }_{jc}$ in units of ${\text{cm}}^{-1}$. Locations A and B indicate dimmer subunits whose total coupling strengths with the special pair are maximum and minimum, respectively, i.e., ${\gamma }_{\text{A}}=-0.95-0.76=-1.71$ and ${\gamma }_{\text{B}}=0.17–0.22=-0.05$.

Figure 4

(Color online) Numerical results for initial symmetric states of the form $|{\Psi }_m^s⟩=\left(1/\sqrt{m}\right){\sum }_{j=1}^m|j⟩$ satisfying ${\left|B_0\right|}^2=m$. (a) Efficiency and (b) transfer time versus $m$ for different $\sigma -$ values. Results shown are averaged over an ensemble of 1000 aggregates for each standard deviation $\sigma$. Single-site energies and electronic couplings for the LH1-RC core have been taken from Ref. 18. For donors in the LH1 complex $E_j\left(0\right)=12911{\text{cm}}^{-1}$ while for the special pair at the RC $E_c\left(0\right)=12748{\text{cm}}^{-1}$ and for the accessory Bchl $E_a\left(0\right)=12338{\text{cm}}^{-1}$. In all cases $\Gamma =1{\text{ns}}^{-1}$ and $\kappa =4{\text{ps}}^{-1}$.

Figure 5

(Color online) Numerical results for initial asymmetric states of the form $|{\Psi }_m^{as}⟩=\left(1/\sqrt{m}\right){\sum }_{j=1}^m{\left(-1\right)}^j|j⟩$ satisfying ${\left|B_0\right|}^2=0$. (a) Efficiency and (b) transfer time versus $m$ for different $\sigma -$ values. Results shown are averaged over an ensemble of 1000 aggregates for each standard deviation $\sigma$. Single-site energies and electronic couplings for the LH1-RC core have been taken from Ref. 18. For donors in the LH1 complex $E_j\left(0\right)=12911{\text{cm}}^{-1}$ while for the special pair at the RC $E_c\left(0\right)=12748{\text{cm}}^{-1}$ and for the accessory Bchl $E_a\left(0\right)=12338{\text{cm}}^{-1}$. In all cases $\Gamma =1{\text{ns}}^{-1}$ and $\kappa =4{\text{ps}}^{-1}$.