Electronic coherence lifetimes of the Fenna-Matthews-Olson complex and light harvesting complex II

Abstract

The study of coherence between excitonic states in naturally occurring photosynthetic systems offers tantalizing prospects of uncovering mechanisms of efficient energy transport. However, experimental evidence of functionally relevant coherences in wild-type proteins has been tentative, leading to uncertainty in their importance at physiological conditions. Here, we extract the electronic coherence lifetime and frequency using a signal subtraction procedure in two model pigment-protein-complexes (PPCs), light harvesting complex II (LH2) and the Fenna-Matthews-Olson complex (FMO), and find that the coherence lifetimes occur at the same timescale (<100 fs) as energy transport between states at the energy level difference equal to the coherence energy. The pigment monomer bacteriochlorophyll a (BChla) shows no electronic coherences, supporting our methodology of removing long-lived vibrational coherences that have obfuscated previous assignments. This correlation of timescales and energy between coherences and energy transport reestablishes the time and energy scales that quantum processes may play a role in energy transport.

Fig. 1. Methodology of extracting electronic coherence from the light harvesting complex II. (a) A slice of the real rephasing LH2 3DES spectrum is shown at T = 43 fs. (b) An example point from (a) is chosen at the star with population dynamics subtracted using global analysis. The residual (blue) is fit for later time points (red) and projected back to the early time points (purple). (c) The short lifetime coherences are revealed once the projected coherences are subtracted. (d) A Fourier transform is performed on (c) to reveal the line width and coherence frequency.

Fig. 2. Sum of the electronic coherences over the entire 2D spectrum. (a) The BChla spectra contains only vibrational coherences. With the long-lived coherences subtracted, no additional peaks are observed. Both (b) FMO and (c) LH2 have multiple electronic states within the bandwidth of the pulse and display fast decaying coherences. For FMO, excitonic energy level differences are drawn as a stick spectrum for differences between 330–550 cm^–1. The closest excitonic energy level difference to the main peak is between excitons 7 and 2 at 400 cm^–1, with the energy levels taken from ref. 22.

Fig. 3. DAS beatmaps of BChla (left) and LH2 (right). The BChla assignments are aided by only having one electronic state within the bandwidth of the laser and simpler dynamic processes. The BChla 13 fs component indicates a global shift energy and is attributed to a Stokes shift convolved with instrument response. The 76 fs component appears to be an internal relaxation process with signal growth at the low energy side of the spectra (highlighted in the circle). The 74 fs LH2 component most likely has similar internal relaxation processes, but also appears to have amplitude at the downhill cross-peak [ω_τ, ω_τ] = [–12 400, 11 700] cm^–1, located in the hexagon, at roughly the electronic coherence energy. Grey bands are located on the energies of the B800 and B850 states.