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The nature of the low energy band of the Fenna-Matthews-Olson complex: Vibronic signatures
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View: Figures


Image of FIG. 1.
FIG. 1.

In (a) fluorescence intensity from solution of stationary state in Eq. (4). Dashed and continuous lines correspond to Huang-Rhys factors s = 0.5 and s = 0.12, at T = 4 K, drawn with the same scale. The arrows point the frequency of the zero-phonon (0 cm−1), phono sideband (36 cm−1), and overtone (72 cm−1). The inset shows the fluorescence intensity at T = 77 K, s = 0.12. In (b) A(ω) is normalized for the three resonances and correspond in continuous, dashed, and dotted lines, to the Δ = 0, 36, and 72 cm−1 resonances, that have a FWHM of {γ0, γ1, γ2} = {1.6, 3.5, 5.6} cm−1 at 4 K, from a fit with lorentzian functions. Inset (b) shows the variation of the lorentzian widths with temperature for the ZPL (γ0, circles), sideband at 36 (γ1, boxes) and overtone 72 cm−12, diamonds), that yields to values of {γ0, γ1, γ2} = {6.2, 8.1, 11.2} cm−1 at 77 K. If otherwise not stated Γ = 7.9 × 10−2 cm−1, γ = 2.36 cm−1, γ z0 = 3 × 10−3 cm−1, s = 0.12 , ω = 36 cm−1, Ω = 10−3 cm−1.

Image of FIG. 2.
FIG. 2.

In (a) and (b) we present the second order expansion for rephasing and non-rephasing paths, respectively. (c) The addition of rephasing and non-rephasing contributions, while (d) subtraction FT[R 2 + R 3 − (R 1 + R 4)]. In plots (a)–(b) an arcsinh scale has been used in order to discuss the sideband features, while (c)–(d) use a linear scale for purposes of comparison and t 2 = 450 fs. In all plots the zero phonon emission line is shown in continuous line to guide the eye. Exciton 1 energy 12 121 cm−1,37 vibrational mode energy ω = 36 cm−1, and Huang-Rhys factor s = 0.12.

Image of FIG. 3.
FIG. 3.

In (a) and (b), rephasing and non-rephasing 2D spectra of exciton 1 diagonal peak of FMO complex, broadened by excitonic energy inhomogeneities. In (c), (d), and (e) are presented the real (continuous, blue) and imaginary (dashed, red) contributions to the inhomogeneous signal at points , and respectively, for complexes whose energy differ from the ensemble average as explained in the text. In (f) and (g), rephasing and non-rephasing 2D spectra of exciton 1 diagonal peak of FMO complex, broadened by both excitonic and vibrational mode energy inhomogeneities. σ E = 102 cm−1, σω = 10 cm−1, t 2 = 2 ps.

Image of FIG. 4.
FIG. 4.

In (a), Feynman diagrams involving the phonon sideband. Letters label electronic states, the superscript the boson state. In (b) are shown the waiting time domain signals at the homogeneously broadened peak at , for the set {γ0, γ1, γ2} = {6.2, 8.1, 11.2} (left panel) and {γ0, γ1γ2} = {50, 136, 156} cm −1 (right panel). In (c) are presented the results for inhomogeneous broadened peaks with σ E = 102 cm−1, σω = 10 cm−1: in the left panel are shown the signals resolved in waiting time of the ZPL (top), sideband (middle) and overtone (bottom) peaks; in the right panel the slope (long enough to avoid overlap with the second pulse t 2 ⩾ 16 fs, the equality fulfilled for the pulses duration achieved in Ref. 38) is presented; arrows highlight the positions of the ZPL, sideband and overtone. In all plots non-rephasing (continuous, black) and rephasing (dashed, blue) path signals.

Image of FIG. 5.
FIG. 5.

Excitonic coherence ρ2, 1(t) = Tr{|ψ1〉〈ψ2|ρ(t)}. In (a) full numerical calculation (continuous) and electronic coherence analytical result (dotted). In (b) are shown the Feynman diagrams that contribute to oscillating terms at frequencies concerning the excited electronic states on the response function. In (c) the result of the homogeneously broadened signal is presented for the addition of both paths, at a waiting time t 2 = 20 fs. In (d)–(e), the waiting time resolved signal at points and respectively, is presented. Thick continuous line represent the real part of these oscillatory contributions. For comparison purposes, we show the absolute value of the rephasing signal (dotted) and the amplitude envelope from electronic coherence solution Eq. (11) (thin, continuous) scaled in amplitude and shifted in phase as described in the text.

Image of FIG. 6.
FIG. 6.

In (a), the result of averaging homogeneous contributions with independent energy variations equal to those reported17 of cm−1 (dashed) and with excitonic energy variation with cm−1 (real part, continuous; absolute value dotted). In (b) the additional inhomogeneity arising from the vibronic ensemble is included, and the result of the averaging using gaussian distributions with standard deviations σω = {1, 10} cm−1 are presented in continuous and dashed lines, respectively. Dotted line is the absolute value for σω = 10 cm−1. In all plots s = 0.24 (see text).


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The nature of the low energy band of the Fenna-Matthews-Olson complex: Vibronic signatures