Ultrafast energy relaxation in single light-harvesting complexes

Abstract

Energy relaxation in light-harvesting complexes has been extensively studied by various ultrafast spectroscopic techniques, the fastest processes being in the sub-100-fs range. At the same time, much slower dynamics have been observed in individual complexes by single-molecule fluorescence spectroscopy (SMS). In this work, we use a pump-probe-type SMS technique to observe the ultrafast energy relaxation in single light-harvesting complexes LH2 of purple bacteria. After excitation at 800 nm, the measured relaxation time distribution of multiple complexes has a peak at 95 fs and is asymmetric, with a tail at slower relaxation times. When tuning the excitation wavelength, the distribution changes in both its shape and position. The observed behavior agrees with what is to be expected from the LH2 excited states structure. As we show by a Redfield theory calculation of the relaxation times, the distribution shape corresponds to the expected effect of Gaussian disorder of the pigment transition energies. By repeatedly measuring few individual complexes for minutes, we find that complexes sample the relaxation time distribution on a timescale of seconds. Furthermore, by comparing the distribution from a single long-lived complex with the whole ensemble, we demonstrate that, regarding the relaxation times, the ensemble can be considered ergodic. Our findings thus agree with the commonly used notion of an ensemble of identical LH2 complexes experiencing slow random fluctuations.

Keywords: LH2; photosynthesis; single-molecule spectroscopy; ultrafast spectroscopy.

Fig. 1.

(A) The three-level scheme used for the data analysis. $k_L$ is the absorption and stimulated emission rate, $k_{FL}$ is the spontaneous emission rate, and $k_R$ is the relaxation rate that is measured. The Gaussian profile represents the laser pulse, resonant with state $|1\rangle$ and off-resonant with state $|2\rangle$. (B) Excited states available in LH2, schematically shown together with a measured absorption spectrum. The red peak represents the excitation spectrum at 800 nm; the arrows indicate possible relaxation channels.

Fig. 2.

First 1 min of a measured fluorescence intensity trace of a single LH2 complex, recorded while continuously scanning the delay between the two excitation pulses. Red lines: data fitted with the three-level model in Fig. 1A. At t = 55 s, the complex briefly switches to a dark state (“blinking”). (Inset) Magnification of one intensity dip with a fitted relaxation time of ${\tau }_R=\left(89\pm 25\right)\hspace{0.17em}\text{fs}$. The bottom axis gives the real recording time, whereas the top axis denotes the delay between the two pulses.

Fig. S1.

Numerical simulations of the intensity dip dependence on (A) the relaxation time, (B) the off-resonance of the relaxed level, and (C) the degree of saturation.

Fig. 3.

(A) Relaxation time distribution obtained from many measured complexes at three different excitation wavelengths. (B) Relaxation time trajectories of three stable complexes, under 800-nm excitation. The shaded regions indicate the standard error of the fits. (C) The relaxation time distribution obtained from a single complex, trace 1 in B, compared with the ensemble distribution at 800-nm excitation from A. (D) Modeled distribution of the relaxation times in a two-state model using Redfield theory. The distribution shape changes with the ratio of the coupling and energy gap (see text below Eq. 1 for description).

Fig. 4.

Testing the effect of Poissonian shot noise. The simulated parameters are as follows: a relaxation time of 100 fs, pulses of 200 fs, and a signal of around 1,000 cps. (A) The relaxation time distribution obtained from the simulation, fitted with a Gaussian distribution with a FWHM of 33 fs. (Inset) One of the simulated intensity dips, together with the fitted three-level model curve. The recovered relaxation time was ${\tau }_R=\left(90\pm 17\right)\hspace{0.17em}\text{fs}$. (B) A succession of simulated relaxation times that can be compared with Fig. 3B. The shaded area indicates the SE of the fits.

Fig. S3.

Cumulative distribution functions for the relaxation time distribution of the whole ensemble and a single complex. The K–S distance is also denoted.

Fig. S2.

Characterization of the pulses used for the 800-nm excitation measurement. (A) Intensity autocorrelation from using FRAC with vibrating mirror. Gaussian fit yields FWHM = 360 fs; using deconvolution factor $\sqrt{2}$ then gives 255-fs-long pulses. (B) Measured control spectrum (its parameters are not used for the relaxation time extraction). Gaussian fit gives FWHM = 3.8-nm spectral width.