Förster resonance energy transfer with transient coherent effects

Abstract

We formulate the weak intramolecular coupling Förster resonance energy transfer theory in a form suitable for calculating ultrafast non-linear response of molecular systems. We introduce a formally exact time-dependent factorization of the molecular statistical operator into the system and bath components. Combining this factorization with unperturbed environment evolution, we generalize the traditional Förster master equation for the state population probabilities into a complete master equation for the system's reduced statistical operator. The traditional Förster theory applies in the limit where the intermolecular coupling is weak and the system-bath coupling is strong. Our technique of derivation explicitly leads to a time non-local Förster type master equation which remains valid also in the limit of vanishing system-bath coupling. The theory predicts a rapid initial coherent evolution of populations arising from a transient initial coherence-dependent term, which induces a slippage of the initial condition that persists during subsequent rate-controlled transfer. Comparison with exact numerical results confirms the clear improvement of the present generalization over earlier formulations of the Förster theory and delineates its range of validity.

Figures (2)

• Figure 1: (a,b) Evolution of populations in a donor-acceptor system as obtained from gFT, Eqs. \ref{['eq:F_time_non_loc']} and \ref{['eq:ForsterIntDiff']} (solid lines), from the exact numerical results using HEOM (dashed lines) and neqFT (dotted lines). The dashed black line indicates the bath correlation time $t_c = 30\; \mathrm{fs}$. (c-e) Short time ($t < t_c$) evaluation of maximum population-only trace distance $\varepsilon_{pop}$ for a range of $\lambda$ and $J$. The results from HEOM are compared with (c) neqFT, (d) time localized gFT and (e) full gFT. (f) The distance $\varepsilon_{pop}$ for gFT and HEOM calculated density matrices at intermediate times ($t_c < t < t_s$, where $t_s$ indicates the time at which equilibrium is reached). All diagrams (c-f) are for $\Delta E = 50 \mathrm{cm}^{-1}$ with the star indicating the system parameters for the evolutions presented in (a,b): $J = 70\; \mathrm{cm}^{-1} \; \lambda=325\; \mathrm{cm}^{-1}$. The gray line indicates $J = \lambda$.
• Figure 2: Short time ($t < t_c$) evaluation of coherence-only trace distance $\varepsilon_{coh}$ in a donor-acceptor system as obtained from the derived EM Eqs. \ref{['eq:F_time_non_loc']}, \ref{['eq:ForsterIntDiff']} and HEOM at two different energy gaps $\Delta E$. At the gray line $J = \lambda$.