Tomáš Mančal

Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems

Photosynthetic complexes are exquisitely tuned to capture solar light efficiently, and then transmit the excitation energy to reaction centres, where long term energy storage is initiated. The energy transfer mechanism is often described by semiclassical models that invoke ‘hopping’ of excited-state populations along discrete energy levels. Two-dimensional Fourier transform electronic spectroscopy has mapped these energy levels and their coupling in the Fenna–Matthews–Olson (FMO) bacteriochlorophyll complex, which is found in green sulphur bacteria and acts as an energy ‘wire’ connecting a large peripheral light-harvesting antenna, the chlorosome, to the reaction centre. The spectroscopic data clearly document the dependence of the dominant energy transport pathways on the spatial properties of the excited-state wavefunctions of the whole bacteriochlorophyll complex. But the intricate dynamics of quantum coherence, which has no classical analogue, was largely neglected in the analyses—even though electronic energy transfer involving oscillatory populations of donors and acceptors was first discussed more than 70 years ago, and electronic quantum beats arising from quantum coherence in photosynthetic complexes have been predicted and indirectly observed. Here we extend previous two-dimensional electronic spectroscopy investigations of the FMO bacteriochlorophyll complex, and obtain direct evidence for remarkably long-lived electronic quantum coherence playing an important part in energy transfer processes within this system. The quantum coherence manifests itself in characteristic, directly observable quantum beating signals among the excitons within the Chlorobium tepidum FMO complex at 77 K. This wavelike characteristic of the energy transfer within the photosynthetic complex can explain its extreme efficiency, in that it allows the complexes to sample vast areas of phase space to find the most efficient path.

Phase-stabilized two-dimensional electronic spectroscopy

Two-dimensional (2D) spectroscopy is a powerful technique to study nuclear and electronic correlations between different transitions or initial and final states. Here we describe in detail our development of inherently phase-stabilized 2D Fourier-transform spectroscopy for electronic transitions. A diffractive-optic setup is used to realize heterodyne-detected femtosecond four-wave mixing in a phase-matched box geometry. Wavelength tunability in the visible range is accomplished by means of a 3 kHz repetition-rate laser system and optical parametric amplification. Nonlinear signals are fully characterized by spectral interferometry. Starting from fundamental principles, we discuss the origin of phase stability and the precise calibration of excitation-pulse time delays using movable glass wedges. Automated subtraction of undesired scattering terms removes experimental artifacts. On the theoretical side, the response-function formalism is extended to describe molecules with three electronic levels, and the shape of 2D spectral features is discussed. As an example for this technique, experimental 2D spectra are shown for the dye molecule Nile Blue in acetonitrile at 595 nm, recorded for a series of population times. Simulations explore the influence of different model parameters and qualitatively reproduce the experimental results. We show that correlations between different electronically excited states can be determined from the spectra. The technique described here can be used to measure the third-order response function of complex systems covering several electronic transitions.

Origin of Long-Lived Coherences in Light-Harvesting Complexes

A vibronic exciton model is applied to explain the long-lived oscillatory features in the two-dimensional (2D) electronic spectra of the Fenna–Matthews–Olson (FMO) complex. Using experimentally determined parameters and uncorrelated site energy fluctuations, the model predicts oscillations with dephasing times of 1.3 ps at 77 K, which is in a good agreement with the experimental results. These long-lived oscillations originate from the coherent superposition of vibronic exciton states with dominant contributions from vibrational excitations on the same pigment. The oscillations obtain a large amplitude due to excitonic intensity borrowing, which gives transitions with strong vibronic character a significant intensity despite the small Huang–Rhys factor. Purely electronic coherences are found to decay on a 200 fs time scale.

Two-dimensional electronic spectroscopy of the B800–B820 light-harvesting complex

Emerging nonlinear optical spectroscopies enable deeper insight into the intricate world of interactions and dynamics of complex molecular systems. 2D electronic spectroscopy appears to be especially well suited for studying multichromophoric complexes such as light-harvesting complexes of photosynthetic organisms as it allows direct observation of couplings between the pigments and charts dynamics of energy flow on a 2D frequency map. Here, we demonstrate that a single 2D experiment combined with self-consistent theoretical modeling can determine spectroscopic parameters dictating excitation energy dynamics in the bacterial B800–B820 light-harvesting complex, which contains 27 bacteriochlorophyll molecules. Ultrafast sub-50-fs dynamics dominated by coherent intraband processes and population transfer dynamics on a picosecond time scale were measured and modeled with one consistent set of parameters. Theoretical 2D spectra were calculated by using a Frenkel exciton model and modified Förster/Redfield theory for the calculation of dynamics. They match the main features of experimental spectra at all population times well, implying that the energy level structure and transition dipole strengths are modeled correctly in addition to the energy transfer dynamics of the system.

Cross-peak-specific two-dimensional electronic spectroscopy

Intermolecular electronic coupling dictates the optical properties of molecular aggregate systems. Of particular interest are photosynthetic pigment–protein complexes that absorb sunlight then efficiently direct energy toward the photosynthetic reaction center. Two-dimensional (2D) ultrafast spectroscopy has been used widely in the infrared (IR) and increasingly in the visible to probe excitonic couplings and observe dynamics, but the off-diagonal spectral signatures of coupling are often obscured by broad diagonal peaks, especially in the visible regime. Rotating the polarizations of the laser pulses exciting the sample can highlight certain spectral features, and the use of polarized pulse sequences to elucidate cross-peaks in 2D spectra has been demonstrated in the IR for vibrational transitions. Here we develop 2D electronic spectroscopy using cross-peak-specific pulse polarization conditions in an investigation of the Fenna–Matthews–Olson light harvesting complex from green photosynthetic bacteria. Our measurements successfully highlight off-diagonal features of the 2D spectra and, in combination with an analysis based on the signs of features arising from particular energy level pathways and theoretical simulation, we characterize the dominant response pathways responsible for the spectral features. Cross-peak-specific 2D electronic spectroscopy provides insight into the interchromophore couplings, as well as into the energetic pathways giving rise to the signal. With femtosecond resolution, we also observe dynamical processes that depend on these couplings and interactions with the protein environment.

Enhancement of vibronic and ground-state vibrational coherences in 2D spectra of photosynthetic complexes.

A vibronic-exciton model is applied to investigate the recently proposed mechanism of enhancement of coherent oscillations due to mixing of electronic and nuclear degrees of freedom. We study a dimer system to elucidate the role of resonance coupling, site energies, vibrational frequency and energy disorder in the enhancement of vibronic-exciton and ground-state vibrational coherences, and to identify regimes where this enhancement is significant. For a heterodimer representing two coupled bachteriochloropylls of the FMO complex, long-lived vibronic coherences are found to be generated only when the frequency of the mode is in the vicinity of the electronic energy difference. Although the vibronic-exciton coherences exhibit a larger initial amplitude compared to the ground-state vibrational coherences, we conclude that, due to the dephasing of the former, both type of coherences have a similar magnitude at longer population time.

Two-dimensional optical three-pulse photon echo spectroscopy. II. Signatures of coherent electronic motion and exciton population transfer in dimer two-dimensional spectra

Using the nonperturbative approach to the calculation of nonlinear optical spectra developed in a foregoing paper [Mancal et al., J. Chem. Phys. 124, 234504 (2006), preceding paper], calculations of two-dimensional electronic spectra of an excitonically coupled dimer model system are presented. The dissipative exciton transfer dynamics is treated within the Redfield theory and energetic disorder within the molecular ensemble is taken into account. The manner in which the two-dimensional spectra reveal electronic couplings in the aggregate system and the evolution of the spectra in time is studied in detail. Changes in the intensity and shape of the peaks in the two-dimensional relaxation spectra are related to the coherent and dissipative dynamics of the system. It is shown that coherent electronic motion, an electronic analog of a vibrational wave packet, can manifest itself in two-dimensional optical spectra of molecular aggregate systems as a periodic modulation of both the diagonal and off-diagonal peaks.

Two-Dimensional Electronic Spectroscopy Reveals Ultrafast Energy Diffusion in Chlorosomes.

Chlorosomes are light-harvesting antennae that enable exceptionally efficient light energy capture and excitation transfer. They are found in certain photosynthetic bacteria, some of which live in extremely low-light environments. In this work, chlorosomes from the green sulfur bacterium Chlorobaculum tepidum were studied by coherent electronic two-dimensional (2D) spectroscopy. Previously uncharacterized ultrafast energy transfer dynamics were followed, appearing as evolution of the 2D spectral line-shape during the first 200 fs after excitation. Observed initial energy flow through the chlorosome is well explained by effective exciton diffusion on a sub-100 fs time scale, which assures efficiency and robustness of the process. The ultrafast incoherent diffusion-like behavior of the excitons points to a disordered energy landscape in the chlorosome, which leads to a rapid loss of excitonic coherences between its structural subunits. This disorder prevents observation of excitonic coherences in the experimental data and implies that the chlorosome as a whole does not function as a coherent light-harvester.

System-Dependent Signatures of Electronic and Vibrational Coherences in Electronic Two-Dimensional Spectra.

In this work, we examine vibrational coherence in a molecular monomer, where time evolution of a nuclear wavepacket gives rise to oscillating diagonal- and off-diagonal peaks in two-dimensional electronic spectra. We find that the peaks oscillate out-of-phase, resulting in a cancellation in the corresponding pump-probe spectra. Our results confirm the unique disposition of two-dimensional electronic spectroscopy (2D-ES) for the study of coherences. The oscillation pattern is in excellent agreement with the diagrammatic analysis of the third-order nonlinear response. We show how 2D-ES can be used to distinguish between ground- and excited-state wavepackets. On the basis of our results, we discuss coherences in coupled molecular aggregates involving both electronic and nuclear degrees of freedom. We conclude that a general distinguishing criterion based on the experimental data alone cannot be devised.

Exciton dynamics in photosynthetic complexes: excitation by coherent and incoherent light

In this paper, we consider the dynamics of a molecular system subjected to external pumping by a light source. Within a completely quantum mechanical treatment, we derive a general formula, which enables us to assess the effects of different light properties on the photo-induced dynamics of excitations in a molecular system. We show that, once the properties of light are known in terms of a certain two-point correlation function, the only information needed to reconstruct the system dynamics is the reduced evolution superoperator. The latter quantity is, in principle, accessible through ultrafast nonlinear spectroscopy. Considering a direct excitation of a small molecular antenna by incoherent light, we find that excitation of coherences is possible due to the overlap of homogeneous line shapes associated with different excitonic states. In Markov and secular approximations, the amount of coherence is significant only under fast relaxation, and both the populations and coherences between exciton states become static at long times. We also study the case when the excitation of a photosynthetic complex is mediated by a mesoscopic system. We find that such a case can be treated by the same formalism with a special correlation function characterizing ultrafast fluctuations of the mesoscopic system. We discuss bacterial chlorosome as an example of such a mesoscopic mediator and propose that the properties of energy-transferring chromophore–protein complexes might be specially tuned to the fluctuation properties of their associated antennae.