Microcavity-Enhanced Exciton Dynamics in Light-Harvesting Complexes: Insights from Redfield Theory

Abstract

We investigated the exciton transfer dynamics in photosynthetic light-harvesting complex 2 (LH2) coupled to an optical microcavity. Using computational simulations based on Redfield theory, we analyzed how microcavity coupling influences energy relaxation and transfer within and between LH2 aggregates. Our results show that the exciton transfer rate between B850 rings follows a square dependence on the light-matter coupling strength, in agreement with Fermi's golden rule. Interestingly, the energy transfer rate remains almost independent of the number of LH2 complexes. This behavior is explained by the molecular components of the polaritonic wavefunction overlaps. These findings highlight the crucial role of cavity-induced polaritonic states in mediating energy transport and provide a theoretical framework for optimizing microcavity environments to enhance exciton mobility in light-harvesting systems and related photonic applications.

Figures (10)

• Figure 1: (a) Population decay of the initially excited B800 (blue) and the corresponding excitation population rise of the B850. The inset shows long timescale dynamics. (b) The energy level structure of LH2 showing a single B800 level as blue (we only included one B800 Bchl) and 18 B850 exciton levels, beige. On the left, the grey plot is the temperature weighted spectral density function used in Equation \ref{['wrates']} where both the upwards and downwards rate contributions are included.
• Figure 2: (a) Relaxation simulation with a single LH2 containing an initially excited B800 and the B850 ring, and three external B850 rings each with 18 Bchls; (b) relaxation rate from the initially excited LH2 to the external B850s as a function of square of the coupling; (c): overlap sums between the initially excited B850 and the polariton (red), the polariton and the external B850s (purple), and the initially excited B850 and the external B850s (black) as a function of the square of the coupling. Coupling constant $g_0$ in the simulation in (a) is set to 2 cm$^{-1}$. Transfer rate for each coupling in (b) was obtained by fitting the initial rise of the population of the external B850s with a single exponential. The overlap sums in (c) were calculated as described in the main text, and the populations in (a) similarly as in Equations \ref{['b800pop']}-\ref{['b850pop']}. Dashed lines are linear fits.
• Figure 3: Relaxation simulations using a single LH2 and three extra B850 rings (B850 External) with ($g_0$)$^2$ = 80 cm$^{-2}$ (a) and ($g_0$)$^2$ = 400000 cm$^{-2}$ (b); positions of LP, MP, and UP maxima as a function of coupling (c); and B850$\rightarrow$B850 transfer rates as a function of coupling (d-f). The B800 level becomes resonant with the MP at 20000 cm$^{-2}$ (vertical dashed grey line). Transfer rate for each coupling was obtained by fitting the initial rise of the external B850 population plot with a single exponential. The maximum in (e) is at 16000 cm$^{-2}$. The energy of the cavity was set to 850 nm.
• Figure 4: Relaxation simulations with two (a) and seven (b) LH2s, i.e. with one and six external B850s, respectively, using $g_0$ = 0.8 cm$^{-1}$ in both simulations; and B850$\rightarrow$B850 transfer rate $k$ as a function of the number of LH2s with $g_0 = 0.2$ cm$^{-1}$ (c) and $g_0 =$ 0.8 cm$^{-1}$ (d), showing also the external B850 population (p$_{850}$) in steady state. Transfer rate $k$ was evaluated by fitting the initial rise of the external B850 population with a single exponential. $N_\text{B850}$ is the number of external B850 rings.
• Figure 5: (a) Wavefunction overlap between the initially excited B850 and polaritons (orange), and between the initially excited B850 and the external B850s (black); (b) wavefunction overlap between the polaritons and the external B850s. An external B850 state close to resonance with the polariton is present with $N_\text{LH2}$$>$ 4. The overlaps were calculated as described in the main text with $g_0$=0.2 cm$^{-1}$.