Spatially correlated fluctuations and coherence dynamics in photosynthesis

Recent multicolor photon-echo experiments revealed a long-lasting quantum coherence between excitations on the donor and acceptor in photosynthetic systems. Identifying the origin of the quantum coherence is essential to fully understand photosynthesis. Here we present a generic model in which a strong intermolecular steric restoring force in densely packed pigment-protein complexes results in a spatial correlation in conformational (static) variations of chromophores, which in turn induces an effective coupling between high-frequency (dynamic) fluctuations in donor and acceptor. The spatially correlated static and dynamic fluctuations provide a favorable environment to maintain quantum coherence, which can consistently explain the photon-echo measurements.

Figure 1

Total energy of two benzene molecules, represented by the two solid bars in the schematic drawing, as a function of $\Theta$ with $d=2.55\mathrm{\AA }$ (squares) and $d=1.85\mathrm{\AA }$ (triangles). ${\phi }_1$ $\left({\phi }_2\right)$ is the orientation change of the upper (lower) benzene molecule from its equilibrium (dashed bars), around the $C_2^{\prime }$ axis between 1,4 C atoms of benzene, and $\Theta =\mid {\phi }_1-{\phi }_2\mid$. Solid and dashed lines delineate $\Delta E=8.634{\Theta }^2$ and $24.62{\Theta }^2$, respectively. The inset shows $\sqrt{\overline{{\left(\delta \omega \right)}^2}}$ as a function of $\Theta$, where the straight lines are plotted to guide the eye.

Figure 2

Temporal correlation functions (left panels) and dynamic dephasing functions (right panels) for different dynamic correlation strengths $\left(\xi \right)$. Solid and dashed lines are $k_{12}\left(t\right)$ and $k_{11}\left(t\right)$ in the left panels, and ${\tilde{g}}_{+-}^d\left(t\right)$ and $g_{++}^d\left(t\right)$ in the right panels. Panels (a)–(c) correspond to $\xi =0$, 0.36, and 0.72, respectively. The in-phase frequency is fixed, $\hslash {\omega }_{+}=250{\mathrm{cm}}^{-1}$, $\hslash \gamma =40{\mathrm{cm}}^{-1}$, $c_1=c_2=2.6{\left({\mathrm{cm}}^{-1}\right)}^{1∕2}{\mathrm{fs}}^{-1}$, $\cos \theta =0.92$, and $T=77\mathrm{K}$. These values are consistent with those used in Ref. 3.

Figure 3

Photon-echo signal as a function of $t_2$ with a fixed $t_1=30\mathrm{fs}$ (left panels) and as a function of $t_1$ with a fixed $t_2=100\mathrm{fs}$ (right panels) for different static and dynamic correlation strengths, $\zeta$ and $\xi$. Panels (a)–(c) correspond to $(\xi ,\zeta )=(0,0)$, (0.36,0.45), and (0.72,0.90), respectively. Parameters are $\hslash \sqrt{{\Delta }_{11}}=\hslash \sqrt{{\Delta }_{22}}=20{\mathrm{cm}}^{-1}$. Other parameters are the same as in Fig. 2.