Artificial light harvesting by dimerized Möbius ring

We theoretically study artificial light harvesting by a Möbius ring. When the donors in the ring are dimerized, the energies of the donor ring are split into two subbands. Because of the nontrivial Möbius boundary condition, both the photon and acceptor are coupled to all collective-excitation modes in the donor ring. Therefore, the quantum dynamics in the light harvesting is subtly influenced by dimerization in the Möbius ring. It is discovered that energy transfer is more efficient in a dimerized ring than that in an equally spaced ring. This discovery is also confirmed by a calculation with the perturbation theory, which is equivalent to the Wigner-Weisskopf approximation. Our findings may be beneficial to the optimal design of artificial light harvesting.

Figure 1

Schematic of light harvesting by a dimerized ring with a Möbius boundary condition. $N$ donors form a dimerized ring with equal site energy. The green curve on the ring labels the Möbius boundary condition. Due to dimerization, there are two different kinds of alternative couplings between nearest neighbors, i.e., $g(1\pm \delta )$. An acceptor is located in the center of the ring with site energy ${\varepsilon }_A$. All donors are uniformly coupled to the acceptor with strength $\xi$. The fluorescence rate of the donor is $\kappa$, while the charge-separation rate on the acceptor is $\mathrm{\Gamma }$.

Figure 2

Energy spectrum ${\varepsilon }_k$ of $A_k$ modes vs dimerization $\delta$ with $N=800$, and $g/\xi =1$, and $\xi =10{\mathrm{ps}}^{-1}$. For any given $\delta , {\varepsilon }_k$ varies in the range $\left[2g\right|\delta |,2g]$.

Figure 3

Population dynamics of acceptor $P_a\left(t\right)={\left|{\alpha }_A\right|}^2$ with a Möbius ring for $\delta =0$ (red solid line), $\delta =0.3$ (blue dashed-dotted line), and $\delta =0.6$ (black dashed line). Other parameters are $N=8, \omega /\xi ={\varepsilon }_A/\xi =-6, J/\xi =1, g/\xi =1, \mathrm{\Gamma }/\xi =0.3$, and $\kappa /\mathrm{\Gamma }=1$ with $\xi =10{\mathrm{ps}}^{-1}$.

Figure 4

Transfer efficiency $\eta$ vs dimerization $\delta$ and detuning $\mathrm{\Delta }=\omega -{\varepsilon }_A$. Other parameters are $N=8, \omega /\xi ={\varepsilon }_A/\xi =-6, J/\xi =1, g/\xi =1, \mathrm{\Gamma }/\xi =0.3$, and $\kappa /\mathrm{\Gamma }=1$ with $\xi =10{\mathrm{ps}}^{-1}$.

Figure 5

Transfer efficiency $\eta$ vs detuning $\mathrm{\Delta }=\omega -{\varepsilon }_A$ by the perturbation theory. The parameters are the same as in Fig. 4.

Figure 6

Coupling constants (a) $|h_{Ak}|$ and (b) $|h_{Bk}|$ vs momentum $k$ for dimerization $\delta =0$ (blue solid line) and $\delta =0.6$ (red dashed line). Other parameters are $N=200$ and $g/\xi =1$.

Figure 7

Physical realization of a ring with a Möbius boundary condition. The zinc-phthalocyanine molecules are equally spaced in the circle with radius $R$. The $i\mathrm{th}$ molecular dipole is aligned in the $D_i-O-z$ plane, and it is rotated by an angle ${\theta }_i$ from the $z$ axis.