Which-way interference within ringlike unit cells for efficient energy transfer

We show that which-way interference within ringlike unit cells enhances the propagation of electronic excitations (excitons) along linear arrays made upon these basic units. After providing an analytic approximate solution of the eigenvalue problem for such aggregates, we show that the constructive interference of wave packets leads to an excitonic population transferred across the array which is not a monotonic function of the coupling between nearest-neighbor rings. The nonmonotonicity depends on an interesting trade-off between the exciton transfer speed and the amount of energy transferred, arising from the interplay between paths within the ringlike cells and the interring coupling strength across the array.

Figure 1

(a) Geometry of the B850-mimetic ring. The intersection of the dot-dashed lines is the location of the centrosymmetry point. (b) Linear aggregate model with $N_R=4$ and $N_D=8$. The pigment-to-pigment coupling between nearest-neighbor rings is represented by a solid wavy line. The figure exemplifies the site numbering adopted in the paper. The centrosymmetry point of the Hamiltonian (9) is located at the intersection of the dot-dashed lines.

Figure 2

Comparison between the exact (numerical) and approximate perturbative diagonalization for an aggregate of $N_R=4$ rings of $N_D=8$ dimers for different values of the interring coupling strength $\xi =W/J_2$; each ring is parametrized as in Fig. 1. (a) Eigenvalues of the $\rho =1$ block of the Hamiltonian (10). (b) Amplitudes ${\varphi }_{n,s}$ of the eigenstate $|\varphi \rangle ={\sum }_{n,s}{\varphi }_{n,s}|n,s\rangle$ of the same $\rho =1$ block of the Hamiltonian (10) corresponding to the lowest energy (ground state of the $\rho =1$ block) for the index mapping $j=N_D(n-1)+s$.

Figure 3

Time evolution of populations in an aggregate of $N_R=4$ rings, when initially the excitation is in the leftmost site of the first ring ($|\varphi \rangle =|n=4,s=1\rangle$) for different values of the interring coupling $\xi =W/J_2$: (a) $\xi =\frac{1}{16}$, (b) $\xi =\frac{1}{4}$, and (c) $\xi =1$. (d) Result of the perturbative analysis for $\xi =\frac{1}{16}$. In all the panels a rescaled time $\xi t$ (ps) is used.

Figure 4

Transfer efficiency as a function of time for different values of the rescaled interring coupling $\xi =W/J_2$ in an array of four rings: (a) exciton in the leftmost site of the first ring of the array, i.e., $|\varphi \rangle =|n=4,s=1\rangle$; (b) delocalized initial condition $|\varphi \rangle =|k=1,\sigma =1\rangle$; (c) and (d) effect of dephasing ($\mathrm{\Gamma }=0.1J_2$) on the dynamics of the transfer efficiency $P_4\left(t\right)$ for the same initial state as in (a) and (b), respectively; and (e) and (f) effect of static disorder ($\mathrm{\Delta }=0.1J_2$, with ${10}^3$ stochastic realizations) on the dynamics of the transfer efficiency $P_4\left(t\right)$ for the same initial state as in (a) and (b), respectively. In all cases, the system is initialized in the first ring: $|{\psi }_0\rangle =|r=1\rangle |\varphi \rangle$.