Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing

A Time-Dependent Quantum Approach to Allostery and a Comparison With Light-Harvesting in Photosynthetic Phenomenon

The allosteric effect is one of the most important processes in regulating the function of proteins, and the elucidation of this phenomenon plays a significant role in understanding emergent behaviors in biological regulation. In this process, a perturbation, generated by a ligand in a part of the macromolecule (the allosteric site), moves along this system and reaches a specific (active) site, dozens of Ångströms away, with a great efficiency. The dynamics of this perturbation in the macromolecule can model precisely the allosteric process. In this article, we will be studying the general characteristics of allostery, using a time-dependent quantum approach to obtain rules that apply to this kind of process. Considering the perturbation as a wave that moves within the molecular system, we will characterize the allosteric process with three of the properties of this wave in the active site: (1) t_a, the characteristic time for reaching that site, (2) A_a, the amplitude of the wave in this site, and (3) B_a, its corresponding spectral broadening. These three parameters, together with the process mechanism and the perturbation efficiency in the process, can describe the phenomenon. One of the main purposes of this paper is to link the parameters t_a, A_a, and B_a and the perturbation efficiency to the characteristics of the system. There is another fundamental process for life that has some characteristics similar to allostery: the light-harvesting (LH) process in photosynthesis. Here, as in allostery, two distant macromolecular sites are involved—two sites dozens of Ångströms away. In both processes, it is particularly important that the perturbation is distributed efficiently without dissipating in the infinite degrees of freedom within the macromolecule. The importance of considering quantum effects in the LH process is well documented in literature, and the quantum coherences are experimentally proven by time-dependent spectroscopic techniques. Given the existing similarities between these two processes in macromolecules, in this work, we suggest using Quantum Mechanics (QM) to study allostery.

Angle-resolved coherent wave mixing using a 4 fs ultra-broad bandwidth laser

We demonstrate angle-resolved coherent (ARC) wave mixing using 4 fs light pulses derived from a laser source that spans 550-1000 nm. We believe this to be the shortest pulse duration used to date in coherent multi-dimensional spectroscopy. The marriage of this ultra-broad band, few-cycle coherent source with the ARC technique will permit new investigations of the interplay between energy transfers and quantum superposition states spanning 8200  cm^-1. We applied this configuration to measurements on the photosynthetic low light (LL) complex from Rhodopseudomonas palustris in solution at ambient temperature. We observe bi-exponential population dynamics for energy transfer across 5500  cm^-1 (0.65 eV), which we attribute to energy transfer from the Q_x transition of bacteriochlorophylls to the B850 pigment of the complex. We believe for the first time, to the best of our knowledge, we demonstrate that ARC maps can be recorded using a single laser pulse.

Competition between diagonal and off-diagonal coupling gives rise to charge-transfer states in polymeric solar cells

It has long been a puzzle on what drives charge separation in artificial polymeric solar cells as a consensus has yet to emerge among rivaling theories based upon electronic localization and delocalization pictures. Here we propose an alternative using the two-bath spin-boson model with simultaneous diagonal and off-diagonal coupling: the critical phase, which is born out of the competition of the two coupling types, and is neither localized nor delocalized. The decoherence-free feature of the critical phase also helps explain sustained coherence of the charge-transfer state. Exploiting Hamiltonian symmetries in an enhanced algorithm of density-matrix renormalization group, we map out boundaries of the critical phase to a precision previously unattainable, and determine the bath spectral densities inducive to the existence of the charge-transfer state.

Förster resonance energy transfer, absorption and emission spectra in multichromophoric systems. I. Full cumulant expansions and system-bath entanglement

We study the Förster resonant energy transfer rate, absorption and emission spectra in multichromophoric systems. The multichromophoric Förster theory (MCFT) is determined from an overlap integral of generalized matrices related to the donor's emission and acceptor's absorption spectra, which are obtained via a full 2nd-order cumulant expansion technique developed in this work. We calculate the spectra and MCFT rate for both localized and delocalized systems, and calibrate the analytical 2nd-order cumulant expansion with the exact stochastic path integral method. We present three essential findings: (i) The role of the initial entanglement between the donor and its bath is found to be crucial in both the emission spectrum and the MCFT rate. (ii) The absorption spectra obtained by the cumulant expansion method are nearly identical to the exact spectra for both localized and delocalized systems, even when the system-bath coupling is far from the perturbative regime. (iii) For the emission spectra, the cumulant expansion can give reliable results for localized systems, but fail to provide reliable spectra of the high-lying excited states of a delocalized system, when the system-bath coupling is large and the thermal energy is small. This paper also provides a simple golden-rule derivation of the MCFT, reviews existing methods, and motivates further developments in the subsequent papers.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Noisy quantum cellular automata for quantum versus classical excitation transfer

We introduce a class of noisy quantum cellular automata on a qubit lattice that includes all classical Markov chains, as well as maps where quantum coherence between sites is allowed to build up over time. We apply such a construction to the problem of excitation transfer through 1D lattices, and compare the performance of classical and quantum dynamics with equal local transition probabilities. Our discrete approach has the merits of stripping down the complications of the open system dynamics, of clearly isolating coherent effects, and of allowing for an exact treatment of conditional dynamics, all while capturing a rich variety of dynamical behaviors.

Two-dimensional x-ray correlation spectroscopy of remote core states

Nonlinear all-X-ray signals that involve large core-atom separation compared to the X-ray wavelengths may not be described by the dipole approximation since they contain additional phase factors. Expressions for the rotationally averaged 2D X-ray photon echo signals from randomly oriented systems that take this position-dependent phase into account for arbitrary ratio between the core separation and the resonant wavelength are presented. Application is made to the Se K-edge of a selenium dipeptide system.

Carbon dioxide bio-fixation and wastewater treatment via algae photochemical synthesis for biofuels production

Utilizing the energy, nutrients and CO₂held within residual waste materials to provide all necessary inputs except for sunlight, the cultivation of algae becomes a closed-loop engineered ecosystem. Developing this green biotechnology is a tangible step towards a waste-free sustainable society.

Designs for molecular circuits that use electronic coherence

The mounting evidence of recent years regarding long-lived coherent dynamics of electronic excitations in several light-harvesting antenna proteins suggests the possibility of realizing and exploiting light-initiated quantum dynamics in synthetic molecular devices based on electronic energy transfer. Inspired by the field of molecular logic, we focus this discussion on the prospect of using quantum coherence to control the direction of energy flow in a molecular circuit. As a prototype system we consider a circuit consisting of three chromophores that deliver energy to two trap chromophores. Our aim is to control to which trap the energy is more likely to be delivered. This is achieved by switching one of the circuit chromophores ON and OFF from the system, such that the direction of energy flow substantially changes from the ON and OFF states of the circuit. We find that quantum coherence can allow a significant ability to direct energy transfer in the circuit. However, when realistic levels of noise are added, quantum coherence only slightly improves the ability to direct electronic energy in comparison to a classical hopping mechanism.

Dynamics of the sub-Ohmic spin-boson model: a comparison of three numerical approaches

Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local field. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D(1) ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.

Quantum dynamics experienced by a single molecular eigenstate excited by incoherent light

Contrary to conventional wisdom that all dynamics are a result of interference (or "dephasing") between many (at least two) energy eigenstates, we show that when a continuum of states is present, even a single molecular eigenstate undergoes "steady-state" quantum dynamics. Moreover, this type of dynamics can be initiated by incoherent (e.g., solar) light sources. Continua are invariably involved in molecular systems due to a variety of sources such as the ever present bath modes, spontaneously emitted photons; the detachment of electrons, or the dissociation of chemical bonds. Contrary to a single bound energy eigenfunction which is a real ("standing-waves") function that carries no flux and, hence, has no dynamics, a single (complex) continuum energy eigenfunction carries "steady-state" flux given by the group velocity of the energetically narrow wave packet it represents. When this energy eigenfunction is a multimode resonance embedded in a continuum via a chain of intramolecular couplings, this dynamics may be initiated by any (light) source, and is controlled, contrary to coherent wave packet dynamics, by the position of the resonance rather than its width.

Coherent Behavior and the Bound State of Water and K(+) Imply Another Model of Bioenergetics: Negative Entropy Instead of High-energy Bonds

Observations of coherent cellular behavior cannot be integrated into widely accepted membrane (pump) theory (MT) and its steady state energetics because of the thermal noise of assumed ordinary cell water and freely soluble cytoplasmic K(+). However, Ling disproved MT and proposed an alternative based on coherence, showing that rest (R) and action (A) are two different phases of protoplasm with different energy levels. The R-state is a coherent metastable low-entropy state as water and K(+) are bound to unfolded proteins. The A-state is the higher-entropy state because water and K(+) are free. The R-to-A phase transition is regarded as a mechanism to release energy for biological work, replacing the classical concept of high-energy bonds. Subsequent inactivation during the endergonic A-to-R phase transition needs an input of metabolic energy to restore the low entropy R-state. Matveev's native aggregation hypothesis allows to integrate the energetic details of globular proteins into this view.

Two-dimensional electronic spectroscopy using incoherent light: theoretical analysis

Electronic energy transfer in photosynthesis occurs over a range of time scales and under a variety of intermolecular coupling conditions. Recent work has shown that electronic coupling between chromophores can lead to coherent oscillations in two-dimensional electronic spectroscopy measurements of pigment-protein complexes measured with femtosecond laser pulses. A persistent issue in the field is to reconcile the results of measurements performed using femtosecond laser pulses with physiological illumination conditions. Noisy-light spectroscopy can begin to address this question. In this work we present the theoretical analysis of incoherent two-dimensional electronic spectroscopy, I((4)) 2D ES. Simulations reveal diagonal peaks, cross peaks, and coherent oscillations similar to those observed in femtosecond two-dimensional electronic spectroscopy experiments. The results also expose fundamental differences between the femtosecond-pulse and noisy-light techniques; the differences lead to new challenges and new opportunities.

Coherence and decoherence in biological systems: principles of noise-assisted transport and the origin of long-lived coherences

The quantum dynamics of transport networks in the presence of noisy environments has recently received renewed attention with the discovery of long-lived coherences in different photosynthetic complexes. This experimental evidence has raised two fundamental questions: firstly, what are the mechanisms supporting long-lived coherences; and, secondly, how can we assess the possible functional role that the interplay of noise and quantum coherence might play in the seemingly optimal operation of biological systems under natural conditions? Here, we review recent results, illuminate them by means of two paradigmatic systems (the Fenna-Matthew-Olson complex and the light-harvesting complex LHII) and present new progress on both questions.

Exciton diffusion length in complex quantum systems: the effects of disorder and environmental fluctuations on symmetry-enhanced supertransfer

Symmetric couplings among aggregates of n chromophores increase the transfer rate of excitons by a factor n(2), a quantum-mechanical phenomenon called 'supertransfer'. In this work, we demonstrate how supertransfer effects induced by geometrical symmetries can enhance the exciton diffusion length by a factor n along cylindrically symmetric structures, consisting of arrays of rings of chromophores, and along spiral arrays. We analyse both closed-system dynamics and open quantum dynamics, modelled by combining a random bosonic bath with static disorder. In the closed-system case, we use the symmetries of the system within a short-time approximation to obtain a closed analytical expression for the diffusion length that explicitly reveals the supertransfer contribution. When subject to disorder, we show that supertransfer can enhance excitonic diffusion lengths for small disorders and characterize the crossover from coherent to incoherent motion. Owing to the quasi-one-dimensional nature of the model, disorder ultimately localizes the excitons, diminishing but not destroying the effects of supertransfer. When dephasing effects are included, we study the scaling of diffusion with both time and number of chromophores and observe that the transition from a coherent, ballistic regime to an incoherent, random-walk regime occurs at the same point as the change from supertransfer to classical scaling.

Efficient estimation of energy transfer efficiency in light-harvesting complexes

The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their realistic with surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second order time-convolution (TC2) master equation and examine its reliability beyond extreme Markovian and perturbative limits. In particular, we present a derivation of TC2 without making the usual weak system-bath coupling assumption. Using this equation, we explore the long-time behavior of exciton dynamics of Fenna-Matthews-Olson (FMO) portein complex. Moreover, we introduce a constructive error analysis to estimate the accuracy of TC2 equation in calculating energy transfer efficiency, exhibiting reliable performance for system-bath interactions with weak and intermediate memory and strength. Furthermore, we numerically show that energy transfer efficiency is optimal and robust for the FMO protein complex of green sulfur bacteria with respect to variations in reorganization energy and bath correlation time scales.

Topology and energy transport in networks of interacting photosynthetic complexes

We address the role of topology in the energy transport process that occurs in networks of photosynthetic complexes. We take inspiration from light-harvesting networks present in purple bacteria and simulate an incoherent dissipative energy transport process on more general and abstract networks, considering both regular structures (Cayley trees and hyperbranched fractals) and randomly generated ones. We focus on the the two primary light-harvesting complexes of purple bacteria, i.e., the LH1 and LH2, and we use network-theoretical centrality measures in order to select different LH1 arrangements. We show that different choices cause significant differences in the transport efficiencies, and that for regular networks, centrality measures allow us to identify arrangements that ensure transport efficiencies which are better than those obtained with a random disposition of the complexes. The optimal arrangements strongly depend on the dissipative nature of the dynamics and on the topological properties of the networks considered, and depending on the latter, they are achieved by using global versus local centrality measures. For randomly generated networks, a random arrangement of the complexes already provides efficient transport, and this suggests the process is strong with respect to limited amount of control in the structure design and to the disorder inherent in the construction of randomly assembled structures. Finally, we compare the networks considered with the real biological networks and find that the latter have in general better performances, due to their higher connectivity, but the former with optimal arrangements can mimic the real networks' behavior for a specific range of transport parameters. These results show that the use of network-theoretical concepts can be crucial for the characterization and design of efficient artificial energy transport networks.

Elucidation of the timescales and origins of quantum electronic coherence in LHCII

Photosynthetic organisms harvest sunlight with near unity quantum efficiency. The complexity of the electronic structure and energy transfer pathways within networks of photosynthetic pigment-protein complexes often obscures the mechanisms behind the efficient light-absorption-to-charge conversion process. Recent experiments, particularly using two-dimensional spectroscopy, have detected long-lived quantum coherence, which theory suggests may contribute to the effectiveness of photosynthetic energy transfer. Here, we present a new, direct method to access coherence signals: a coherence-specific polarization sequence, which isolates the excitonic coherence features from the population signals that usually dominate two-dimensional spectra. With this polarization sequence, we elucidate coherent dynamics and determine the overall measurable lifetime of excitonic coherence in the major light-harvesting complex of photosystem II. Coherence decays on two distinct timescales of 47 fs and ~800 fs. We present theoretical calculations to show that these two timescales are from weakly and moderately strongly coupled pigments, respectively.

Quantitative investigations of quantum coherence for a light-harvesting protein at conditions simulating photosynthesis

Recent measurements using two-dimensional electronic spectroscopy (2D ES) have shown that the initial dynamic response of photosynthetic proteins can involve quantum coherence. We show how electronic coherence can be differentiated from vibrational coherence in 2D ES. On that basis we conclude that both electronic and vibrational coherences are observed in the phycobiliprotein light-harvesting complex PC645 from Chroomonas sp. CCMP270 at ambient temperature. These light-harvesting antenna proteins of the cryptophyte algae are suspended in the lumen, where the pH drops significantly under sustained illumination by sunlight. Here we measured 2D ES of PC645 at increasing levels of acidity to determine if the change in pH affects the quantum coherence; quantitative analysis reveals that the dynamics are insensitive to the pH change.

The role of the environment in electronic energy transfer: a molecular modeling perspective

The key role of the environment in electronic energy transfer has been underscored in recent experimental and theoretical studies. In this perspective, we provide an overview of novel quantum-mechanical methodologies aimed at describing environment effects in energy transfers. The techniques described include continuum dielectric and atomistic descriptions of the surroundings. We discuss the advantages and limitations of each technique, as well as the main insights that have emerged from their application to solvated dyads and photosynthetic pigment-protein complexes. We finally highlight the aspects that still need to be solved in order to provide a full theoretical route to the study of energy transfer phenomena in complex environments.

Towards a scientific concept of free will as a biological trait: spontaneous actions and decision-making in invertebrates

Until the advent of modern neuroscience, free will used to be a theological and a metaphysical concept, debated with little reference to brain function. Today, with ever increasing understanding of neurons, circuits and cognition, this concept has become outdated and any metaphysical account of free will is rightfully rejected. The consequence is not, however, that we become mindless automata responding predictably to external stimuli. On the contrary, accumulating evidence also from brains much smaller than ours points towards a general organization of brain function that incorporates flexible decision-making on the basis of complex computations negotiating internal and external processing. The adaptive value of such an organization consists of being unpredictable for competitors, prey or predators, as well as being able to explore the hidden resource deterministic automats would never find. At the same time, this organization allows all animals to respond efficiently with tried-and-tested behaviours to predictable and reliable stimuli. As has been the case so many times in the history of neuroscience, invertebrate model systems are spearheading these research efforts. This comparatively recent evidence indicates that one common ability of most if not all brains is to choose among different behavioural options even in the absence of differences in the environment and perform genuinely novel acts. Therefore, it seems a reasonable effort for any neurobiologist to join and support a rather illustrious list of scholars who are trying to wrestle the term 'free will' from its metaphysical ancestry. The goal is to arrive at a scientific concept of free will, starting from these recently discovered processes with a strong emphasis on the neurobiological mechanisms underlying them.

Real-time mapping of electronic structure with single-shot two-dimensional electronic spectroscopy

Electronic structure and dynamics determine material properties and behavior. Important time scales for electronic dynamics range from attoseconds to milliseconds. Two-dimensional optical spectroscopy has proven an incisive tool to probe fast spatiotemporal electronic dynamics in complex multichromophoric systems. However, acquiring these spectra requires long point-by-point acquisitions that preclude observations on the millisecond and microsecond time scales. Here we demonstrate that imaging temporally encoded information within a homogeneous sample allows mapping of the evolution of the electronic Hamiltonian with femtosecond temporal resolution in a single-laser-shot, providing real-time maps of electronic coupling. This method, which we call GRadient-Assisted Photon Echo spectroscopy (GRAPE), eliminates phase errors deleterious to Fourier spectroscopies while reducing the acquisition time by orders of magnitude using only conventional optical components. In analogy to MRI in which magnetic field gradients are used to create spatial correlation maps, GRAPE spectroscopy takes advantage of a similar type of spatial encoding to construct electronic correlation maps. Unlike magnetic resonance, however, this spatial encoding of the nonlinear polarization along the excitation frequency axis of the two-dimensional spectrum results in no loss in signal while simultaneously reducing overall noise. Correlating the energy transfer events and electronic coupling occurring in tens of femtoseconds with slow dynamics on the subsecond time scale is fundamentally important in photobiology, solar energy research, nonlinear spectroscopy, and optoelectronic device characterization.

Coherently wired light-harvesting in photosynthetic marine algae at ambient temperature

Photosynthesis makes use of sunlight to convert carbon dioxide into useful biomass and is vital for life on Earth. Crucial components for the photosynthetic process are antenna proteins, which absorb light and transmit the resultant excitation energy between molecules to a reaction centre. The efficiency of these electronic energy transfers has inspired much work on antenna proteins isolated from photosynthetic organisms to uncover the basic mechanisms at play. Intriguingly, recent work has documented that light-absorbing molecules in some photosynthetic proteins capture and transfer energy according to quantum-mechanical probability laws instead of classical laws at temperatures up to 180 K. This contrasts with the long-held view that long-range quantum coherence between molecules cannot be sustained in complex biological systems, even at low temperatures. Here we present two-dimensional photon echo spectroscopy measurements on two evolutionarily related light-harvesting proteins isolated from marine cryptophyte algae, which reveal exceptionally long-lasting excitation oscillations with distinct correlations and anti-correlations even at ambient temperature. These observations provide compelling evidence for quantum-coherent sharing of electronic excitation across the 5-nm-wide proteins under biologically relevant conditions, suggesting that distant molecules within the photosynthetic proteins are 'wired' together by quantum coherence for more efficient light-harvesting in cryptophyte marine algae.

Calculations of nonlinear wave-packet interferometry signals in the pump-probe limit as tests for vibrational control over electronic excitation transfer

The preceding paper [J. D. Biggs and J. A. Cina, J. Chem. Phys. 131, 224101 (2009)] (referred to here as Paper 1), describes a strategy for externally influencing the course of short-time electronic excitation transfer (EET) in molecular dimers and observing the process by nonlinear wave-packet interferometry (nl-WPI). External influence can, for example, be exerted by inducing coherent intramolecular vibration in one of the chromophores prior to short-pulse electronic excitation of the other. Within a sample of isotropically oriented dimers having a specified internal geometry, a vibrational mode internal to the acceptor chromophore can be preferentially driven by electronically nonresonant impulsive stimulated Raman (or resonant infrared) excitation with a short polarized "control" pulse. A subsequent electronically resonant polarized pump then preferentially excites the donor, and EET ensues. Paper 1 investigates control-pulse-influenced nl-WPI as a tool for the spectroscopic evaluation of the effect of coherent molecular vibration on excitation transfer, presenting general expressions for the nl-WPI difference signal from a dimer following the action of a control pulse of arbitrary polarization and shape. Electronic excitation is to be effected and its interchromophore transfer monitored by resonant pump and probe "pulses," respectively, each consisting of an optical-phase-controlled ultrashort pulse-pair having arbitrary polarization, duration, center frequency, and other characteristics. Here we test both the control strategy and its spectroscopic investigation-with some sacrifice of amplitude-level detail-by calculating the pump-probe difference signal. That signal is the limiting case of the control-influenced nl-WPI signal in which the two pulses in the pump pulse-pair coincide, as do the two pulses in the probe pulse-pair. We present calculated pump-probe difference signals for (1) a model excitation-transfer complex in which two equal-energy monomers each support one moderately Franck-Condon active intramolecular vibration; (2) a simplified model of the covalent dimer dithia-anthracenophane, representing its EET dynamics following selective impulsive excitation of the weakly Franck-Condon active nu(12) anthracene vibration at 385 cm(-1); and (3) a model complex featuring moderate electronic-vibrational coupling in which the site energy of the acceptor chromophore is lower than that of the donor.

Low light adaptation: energy transfer processes in different types of light harvesting complexes from Rhodopseudomonas palustris

Energy transfer processes in photosynthetic light harvesting 2 (LH2) complexes isolated from purple bacterium Rhodopseudomonas palustris grown at different light intensities were studied by ground state and transient absorption spectroscopy. The decomposition of ground state absorption spectra shows contributions from B800 and B850 bacteriochlorophyll (BChl) a rings, the latter component splitting into a low energy and a high energy band in samples grown under low light (LL) conditions. A spectral analysis reveals strong inhomogeneity of the B850 excitons in the LL samples that is well reproduced by an exponential-type distribution. Transient spectra show a bleach of both the low energy and high energy bands, together with the respective blue-shifted exciton-to-biexciton transitions. The different spectral evolutions were analyzed by a global fitting procedure. Energy transfer from B800 to B850 occurs in a mono-exponential process and the rate of this process is only slightly reduced in LL compared to high light samples. In LL samples, spectral relaxation of the B850 exciton follows strongly nonexponential kinetics that can be described by a reduction of the bleach of the high energy excitonic component and a red-shift of the low energetic one. We explain these spectral changes by picosecond exciton relaxation caused by a small coupling parameter of the excitonic splitting of the BChl a molecules to the surrounding bath. The splitting of exciton energy into two excitonic bands in LL complex is most probably caused by heterogenous composition of LH2 apoproteins that gives some of the BChls in the B850 ring B820-like site energies, and causes a disorder in LH2 structure.

Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing

Understanding the role of coherent electronic motion is expected to resolve general questions of importance in macromolecular energy transfer. We demonstrate a novel nonlinear optical method, angle-resolved coherent wave mixing, that separates out coherently coupled electronic transitions and energy transfers in an instantaneous two-dimensional mapping. Angular resolution of the signal is achieved by using millimeter laser beam waists at the sample and by signal relay to the far field; for this we use a high energy, ultrabroadband hollow fiber laser source. We reveal quantum electronic beating with a time-ordered selection of transition energies in a photosynthetic complex.