Coherent Energy Transfer under Incoherent Light Conditions

A quantum trajectory picture of single photon absorption and energy transport in photosystem II

We use quantum trajectory theory to study the dynamics of the first step in photosynthesis for a single photon interacting with photosystem II (PSII). By considering individual trajectories we are able to look beyond the ensemble average dynamics to compute the PSII system evolution conditioned upon individual photon counting measurements. Measurements of the transmitted photon beam strongly affects the system state, since detection of an outgoing photon confirms that the PSII must be in the electronic ground state, while a null measurement implies it is in an excited electronic state. We show that under ideal conditions, observing the null result transforms a state with a low excited state population to a state with nearly all population contained in the excited states. We study the PSII dynamics conditioned on such photon counting for both a pure excitonic model of PSII and a more realistic model with exciton-phonon coupling to a dissipative phononic environment. In the absence of such coupling, we show that the measured fluorescence rates show oscillations constituting a photon-counting witness of excitonic coherence. Excitonic coupling to the phonon environment has a strong effect on the observed rates of fluorescence, damping the oscillations. Addition of non-radiative decay and incoherent transitions to radical pair states in the reaction center to the phononic model allows extraction of a quantum efficiency of 92.5% from the long-time evolution, consistent with bulk experimental measurements.

Resonant vibrations produce quantum bridge over high-energy states in heterogeneous antenna

Photosynthetic light-harvesting complexes usually contain several pools of molecules with a big difference in transition energies, for example, chlorophylls a and b in plant antennas. Some pathways of the excitation energy transfer may include pigments from the low-energy pool separated by a site occupied by a high-energy molecule. We demonstrate that such pathways may be functional if high-frequency intramolecular vibrations fall in resonance with the energy gap between the neighboring molecules belonging to different pools. In this case, a vibration-assisted mixing of the excited states can produce delocalized vibronic states playing a role of 'quantum bridge' that facilitates a passage over high-energy barrier. We perform calculations of the excitation dynamics in the model three-state system with the parameters emerging from our previous studies of real antennas. Simulation of the dynamics in an explicit electron-vibrational basis demonstrates that the rate of transfer between the two chlorophylls a through the chlorophyll b intermediate is increased by a factor of 1.7-2 in the presence of resonant vibration. A possible influence of energetic disorder and other (non-resonant) vibrations on this effect is discussed.

Thermo-Field Dynamics Approach to Photo-induced Electronic Transitions Driven by Incoherent Thermal Radiation

The effects of thermal light-matter interaction on the dynamics of photo-induced electronic transitions in molecules are investigated using a novel first principles approach based on the thermo-field dynamics description of both the molecular vibrational modes and of the radiation field. The developed approach permits numerically accurate simulations of quantum dynamics of electronic/excitonic systems coupled to nuclear and photonic baths kept at different temperatures. The baths can be described by arbitrary spectral densities and can have any system-bath coupling strengths. In agreement with the results obtained previously by less rigorous methods, we show that the excitation process obtained by the continuous interaction with the suddenly turned-on thermal radiation field creates a mixed ensemble having a nonnegligible component consisting of a superposition of vibronic eigenstates which can sustain coherent oscillations for relatively long times. The results become especially relevant for the dynamics of electronic transitions upon sunlight excitation. Analytical results based on time-dependent perturbation theory support the numerical simulations and provide a simple interpretation of the time evolution of quantum observables.

Photon Energy-Dependent Ultrafast Exciton Transfer in Chlorosomes of Chlorobium tepidum and the Role of Supramolecular Dynamics

The antenna complex of green sulfur bacteria, the chlorosome, is one of the most efficient supramolecular systems for efficient long-range exciton transfer in nature. Femtosecond transient absorption experiments provide new insight into how vibrationally induced quantum overlap between exciton states supports highly efficient long-range exciton transfer in the chlorosome of Chlorobium tepidum. Our work shows that excitation energy is delocalized over the chlorosome in <1 ps at room temperature. The following exciton transfer to the baseplate occurs in ∼3 to 5 ps, in line with earlier work also performed at room temperature, but significantly faster than at the cryogenic temperatures used in previous studies. This difference can be attributed to the increased vibrational motion at room temperature. We observe a so far unknown impact of the excitation photon energy on the efficiency of this process. This dependency can be assigned to distinct optical domains due to structural disorder, combined with an exciton trapping channel competing with exciton transfer toward the baseplate. An oscillatory transient signal damped in <1 ps has the highest intensity in the case of the most efficient exciton transfer to the baseplate. These results agree well with an earlier computational finding of exciton transfer driven by low-frequency rotational motion of molecules in the chlorosome. Such an exciton transfer process belongs to the quantum coherent regime, for which the Förster theory for intermolecular exciton transfer does not apply. Our work hence strongly indicates that structural flexibility is important for efficient long-range exciton transfer in chlorosomes.

Theoretical Description of Attosecond X-ray Absorption Spectroscopy of Frenkel Exciton Dynamics

Frenkel excitons are responsible for the transport of light energy in many molecular systems. Coherent electron dynamics govern the initial stage of Frenkel-exciton transfer. Capability to follow coherent exciton dynamics in real time will help to reveal their actual contribution to the efficiency of light-harvesting. Attosecond X-ray pulses are the tool with the necessary temporal resolution to resolve pure electronic processes with atomic sensitivity. We describe how attosecond X-ray pulses can probe coherent electronic processes during Frenkel-exciton transport in molecular aggregates. We analyze time-resolved absorption cross section taking broad spectral bandwidth of an attosecond pulse into account. We demonstrate that attosecond X-ray absorption spectra can reveal delocalization degree of coherent exciton transfer dynamics.

Efficient Many-Body Non-Markovian Dynamics of Organic Polaritons

We show how to simulate a model of many molecules with both strong coupling to many vibrational modes and collective coupling to a single photon mode. We do this by combining process tensor matrix product operator methods with a mean-field approximation which reduces the dimension of the problem. We analyze the steady state of the model under incoherent pumping to determine the dependence of the polariton lasing threshold on cavity detuning, light-matter coupling strength, and environmental temperature. Moreover, by measuring two-time correlations, we study quadratic fluctuations about the mean field to calculate the photoluminescence spectrum. Our method enables one to simulate many-body systems with strong coupling to multiple environments, and to extract both static and dynamical properties.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

Nonequilibrium steady-state picture of incoherent light-induced excitation harvesting

We formulate a comprehensive theoretical description of excitation harvesting in molecular aggregates photoexcited by weak incoherent radiation. An efficient numerical scheme that respects the continuity equation for excitation fluxes is developed to compute the nonequilibrium steady state (NESS) arising from the interplay between excitation generation, excitation relaxation, dephasing, trapping at the load, and recombination. The NESS is most conveniently described in the so-called preferred basis in which the steady-state excitonic density matrix is diagonal. The NESS properties are examined by relating the preferred-basis description to the descriptions in the site or excitonic bases. Focusing on a model photosynthetic dimer, we find that the NESS in the limit of long trapping time is quite similar to the excited-state equilibrium in which the stationary coherences originate from the excitation-environment entanglement. For shorter trapping times, we demonstrate how the properties of the NESS can be extracted from the time-dependent description of an incoherently driven but unloaded dimer. This relation between stationary and time-dependent pictures is valid, provided that the trapping time is longer than the decay time of dynamic coherences accessible in femtosecond spectroscopy experiments.

Exact description of excitonic dynamics in molecular aggregates weakly driven by light

We present a rigorous theoretical description of excitonic dynamics in molecular light-harvesting aggregates photoexcited by weak-intensity radiation of arbitrary properties. While the interaction with light is included up to the second order, the treatment of the excitation-environment coupling is exact and results in an exact expression for the reduced excitonic density matrix that is manifestly related to the spectroscopic picture of the photoexcitation process. This expression takes fully into account the environmental reorganization processes triggered by the two interactions with light. This is particularly important for slow environments and/or strong excitation-environment coupling. Within the exponential decomposition scheme, we demonstrate how our result can be recast as the hierarchy of equations of motion (HEOM) that explicitly and consistently includes the photoexcitation step. We analytically describe the environmental reorganization dynamics triggered by a delta-like excitation of a single chromophore and demonstrate how our HEOM, in appropriate limits, reduces to the Redfield equations comprising a pulsed photoexcitation and the nonequilibrium Förster theory. We also discuss the relation of our formalism to the combined Born-Markov-HEOM approaches in the case of excitation by thermal light.

Nonadiabatic sunlight harvesting

Experimental and theoretical evidence points out the crucial role of specific intramolecular vibrational modes resonant with excitonic splittings in the interpretation of long-lived coherences observed in the two-dimensional spectra of some natural and synthetic light harvesting complexes. For the natural situation of illumination by incoherent (sun)light, the relevance of these vibrations is analyzed here for light-harvesting vibronic prototype dimers. The detailed analysis of the density matrix dynamics reveals that the inclusion of intramolecular vibrational modes reinforces the exciton coherence up to one order of magnitude and may increase the populations of lowest energy single exciton states, as well as populations and coherences in the site basis. In sharp contrast to the case of initial-state preparation by coherent (laser)light-sources, the initial thermal state of the local vibrational modes, as well as that of the anticorrelated vibrational mode, evolves devoid of non-classical correlations as confirmed by the absence of negative values of its phase-space quasi-probability distribution at all times. Therefore, not only the long-lived coherences observed in the two-dimensional spectra are induced by the coherent character of pulsed laser sources, but it is unambiguously shown here that the non-classical character generally assigned to the anticorrelated vibrational mode also comes as the result of the preparation of the initial state by coherent pulsed laser sources.

Dynamic Disorder Drives Exciton Transfer in Tubular Chlorosomal Assemblies

Chlorosomes stand out for their highly efficient excitation energy transfer (EET) in extreme low light conditions. Yet, little is known about the EET when a chlorosome is excited to a pure state that is an eigenstate of the exciton Hamiltonian. In this work, we consider the dynamic disorder in the intermolecular electronic coupling explicitly by calculating the electronic coupling terms in the Hamiltonian using nuclear coordinates that are taken from molecular dynamics simulation trajectories. We show that this dynamic disorder is capable of driving the evolution of the exciton, being a stationary state of the initial Hamiltonian. In particular, long-distance excitation energy transfer between domains of high exciton population and oscillatory behavior of the population in the site basis are observed, in line with two-dimensional electronic spectroscopy studies. We also found that in the high exciton population domains, their population variation is correlated with their overall coupling strength. Analysis in a reference state basis shows that such dynamic disorder, originating from thermal energy, creates a fluctuating landscape for the exciton and promotes the EET process. We propose such dynamic disorder as an important microscopic origin for the high efficient EET widely observed in different types of chlorosomes, bioinspired tubular aggregates, or other light-harvesting complexes.

Classification of Coherent Enhancements of Light-Harvesting Processes

Several kinds of coherence have recently been shown to affect the performance of light-harvesting systems, in some cases significantly improving their efficiency. Here, we classify the possible mechanisms of coherent efficiency enhancements, based on the types of coherence that can characterize a light-harvesting system and the types of processes these coherences can affect. We show that enhancements are possible only when coherences and dissipative effects are best described in different bases of states. Our classification allows us to predict a previously unreported coherent enhancement mechanism, where coherence between delocalized eigenstates can be used to localize excitons away from dissipation, thus reducing the rate of recombination and increasing efficiency.

Limits of exciton delocalization in molecular aggregates

Exciton states of molecular aggregates, with a particular focus on delocalization length, are discussed. Despite the huge number of studies of molecular excitons, it is argued that there remain interesting open questions. It is hypothesized that limits for equilibrium delocalization length are generally in the range of tens of molecules, even at very low temperatures. Effects that limit delocalization include: phase disorder from wave-zone electronic coupling, polarization fluctuations, and the extreme sensitivity of perfect delocalization to disorder as the size of the molecular aggregate increases. To gain physical insight, the inverse participation ratio is compared to the order parameter for a classical system of coupled, and hence entrained, oscillators-the Kuramoto model. The main result of the paper is that the inverse participation ratio obtained from the quantum mechanical exciton model and the Kuramoto order parameter obtained from coupled classical oscillators estimate the same coherence length. Conclusions suggest discussion topics that touch on limits of delocalization, quantum-to-classical transitions in molecular exciton systems, and whether excitons are good prospects for exploring and exploiting quantum information resources from coherence.

Environmental Nonadditivity and Franck-Condon physics in Nonequilibrium Quantum Systems

We show that for a quantum system coupled to both vibrational and electromagnetic environments, enforcing additivity of their combined influences results in nonequilibrium dynamics that does not respect the Franck-Condon principle. We overcome this shortcoming by employing a collective coordinate representation of the vibrational environment, which permits the derivation of a nonadditive master equation. When applied to a two-level emitter our treatment predicts decreasing photon emission rates with increasing vibrational coupling, consistent with Franck-Condon physics. In contrast, the additive approximation predicts the emission rate to be completely insensitive to vibrations. We find that nonadditivity also plays a key role in the stationary nonequilibrium model behavior, enabling two-level population inversion under incoherent electromagnetic excitation.

Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices

Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.

Coherent electronic and nuclear dynamics in a rhodamine heterodimer-DNA supramolecular complex

Elucidating the role of quantum coherences in energy migration within biological and artificial multichromophoric antenna systems is the subject of an intense debate. It is also a practical matter because of the decisive implications for understanding the biological processes and engineering artificial materials for solar energy harvesting. A supramolecular rhodamine heterodimer on a DNA scaffold was suitably engineered to mimic the basic donor-acceptor unit of light-harvesting antennas. Ultrafast 2D electronic spectroscopic measurements allowed identifying clear features attributable to a coherent superposition of dimer electronic and vibrational states contributing to the coherent electronic charge beating between the donor and the acceptor. The frequency of electronic charge beating is found to be 970 cm^-1 (34 fs) and can be observed for 150 fs. Through the support of high level ab initio TD-DFT computations of the entire dimer, we established that the vibrational modes preferentially optically accessed do not drive subsequent coupling between the electronic states on the 600 fs of the experiment. It was thereby possible to characterize the time scales of the early time femtosecond dynamics of the electronic coherence built by the optical excitation in a large rigid supramolecular system at a room temperature in solution.

Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center

The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.

How exciton-vibrational coherences control charge separation in the photosystem II reaction center

In photosynthesis absorbed sun light produces collective excitations (excitons) that form a coherent superposition of electronic and vibrational states of the individual pigments. Two-dimensional (2D) electronic spectroscopy allows a visualization of how these coherences are involved in the primary processes of energy and charge transfer. Based on quantitative modeling we identify the exciton-vibrational coherences observed in 2D photon echo of the photosystem II reaction center (PSII-RC). We find that the vibrations resonant with the exciton splittings can modify the delocalization of the exciton states and produce additional states, thus promoting directed energy transfer and allowing a switch between the two charge separation pathways. We conclude that the coincidence of the frequencies of the most intense vibrations with the splittings within the manifold of exciton and charge-transfer states in the PSII-RC is not occurring by chance, but reflects a fundamental principle of how energy conversion in photosynthesis was optimized.

Proposal for probing energy transfer pathway by single-molecule pump-dump experiment

The structure of Fenna-Matthews-Olson (FMO) light-harvesting complex had long been recognized as containing seven bacteriochlorophyll (BChl) molecules. Recently, an additional BChl molecule was discovered in the crystal structure of the FMO complex, which may serve as a link between baseplate and the remaining seven molecules. Here, we investigate excitation energy transfer (EET) process by simulating single-molecule pump-dump experiment in the eight-molecules complex. We adopt the coherent modified Redfield theory and non-Markovian quantum jump method to simulate EET dynamics. This scheme provides a practical approach of detecting the realistic EET pathway in BChl complexes with currently available experimental technology. And it may assist optimizing design of artificial light-harvesting devices.

Dark States in the Light-Harvesting complex 2 Revealed by Two-dimensional Electronic Spectroscopy

Energy transfer and trapping in the light harvesting antennae of purple photosynthetic bacteria is an ultrafast process, which occurs with a quantum efficiency close to unity. However the mechanisms behind this process have not yet been fully understood. Recently it was proposed that low-lying energy dark states, such as charge transfer states and polaron pairs, play an important role in the dynamics and directionality of energy transfer. However, it is difficult to directly detect those states because of their small transition dipole moment and overlap with the B850/B870 exciton bands. Here we present a new experimental approach, which combines the selectivity of two-dimensional electronic spectroscopy with the availability of genetically modified light harvesting complexes, to reveal the presence of those dark states in both the genetically modified and the wild-type light harvesting 2 complexes of Rhodopseudomonas palustris. We suggest that Nature has used the unavoidable charge transfer processes that occur when LH pigments are concentrated to enhance and direct the flow of energy.

Optimal Energy Transfer in Light-Harvesting Systems

Photosynthesis is one of the most essential biological processes in which specialized pigment-protein complexes absorb solar photons, and with a remarkably high efficiency, guide the photo-induced excitation energy toward the reaction center to subsequently trigger its conversion to chemical energy. In this work, we review the principles of optimal energy transfer in various natural and artificial light harvesting systems. We begin by presenting the guiding principles for optimizing the energy transfer efficiency in systems connected to dissipative environments, with particular attention paid to the potential role of quantum coherence in light harvesting systems. We will comment briefly on photo-protective mechanisms in natural systems that ensure optimal functionality under varying ambient conditions. For completeness, we will also present an overview of the charge separation and electron transfer pathways in reaction centers. Finally, recent theoretical and experimental progress on excitation energy transfer, charge separation, and charge transport in artificial light harvesting systems is delineated, with organic solar cells taken as prime examples.

Simulation of two-dimensional electronic spectra of phycoerythrin 545 at ambient temperature

By using a hierarchical equations-of-motion approach, we reproduce the two-dimensional electronic spectra of phycoerythrin 545 from Rhodomonas CS24 at ambient temperature (294 K). The simulated spectra are in agreement with the experimental results reported in Wong et al. (Nat. Chem. 2012, 4, 396). The evolutions of cross peaks for rephasing spectra and diagonal peaks for nonrephasing spectra have also been plotted. The peaks oscillate with the population times, with frequencies, phases, and amplitudes of the oscillating curves also being qualitatively consistent with the experimental results.

Quantum Coherence in Photosynthesis for Efficient Solar Energy Conversion

The crucial step in the conversion of solar to chemical energy in Photosynthesis takes place in the reaction center where the absorbed excitation energy is converted into a stable charge separated state by ultrafast electron transfer events. However, the fundamental mechanism responsible for the near unity quantum efficiency of this process is unknown. Here we elucidate the role of coherence in determining the efficiency of charge separation in the plant photosystem II reaction centre (PSII RC) by comprehensively combining experiment (two-dimensional electronic spectroscopy) and theory (Redfield theory). We reveal the presence of electronic coherence between excitons as well as between exciton and charge transfer states which we argue to be maintained by vibrational modes. Furthermore, we present evidence for the strong correlation between the degree of electronic coherence and efficient and ultrafast charge separation. We propose that this coherent mechanism will inspire the development of new energy technologies.

Coherent multidimensional optical spectra measured using incoherent light

Four-wave mixing measurements can reveal spectral and dynamics information that is hidden in linear spectra by the interactions among light-absorbing molecules and with their environment. Coherent multidimensional optical spectroscopy is an important variant of four-wave mixing because it resolves a map of interactions and correlations between absorption bands. Previous coherent multidimensional optical spectroscopy measurements have used femtosecond pulses with great success, and it may seem that femtosecond pulses are necessary for such measurements. Here we present coherent two-dimensional electronic spectra measured using incoherent light. The spectra of model molecular systems using broadband spectrally incoherent light are similar but not identical to those expected from measurements using femtosecond pulses. Specifically, the spectra show particular sensitivity to long-lived intermediates such as photoisomers. The results will motivate the design of similar experiments in spectral ranges where femtosecond pulses are difficult to produce.

Photosynthetic light harvesting: excitons and coherence

Photosynthesis begins with light harvesting, where specialized pigment-protein complexes transform sunlight into electronic excitations delivered to reaction centres to initiate charge separation. There is evidence that quantum coherence between electronic excited states plays a role in energy transfer. In this review, we discuss how quantum coherence manifests in photosynthetic light harvesting and its implications. We begin by examining the concept of an exciton, an excited electronic state delocalized over several spatially separated molecules, which is the most widely available signature of quantum coherence in light harvesting. We then discuss recent results concerning the possibility that quantum coherence between electronically excited states of donors and acceptors may give rise to a quantum coherent evolution of excitations, modifying the traditional incoherent picture of energy transfer. Key to this (partially) coherent energy transfer appears to be the structure of the environment, in particular the participation of non-equilibrium vibrational modes. We discuss the open questions and controversies regarding quantum coherent energy transfer and how these can be addressed using new experimental techniques.

Non-classicality of the molecular vibrations assisting exciton energy transfer at room temperature

Advancing the debate on quantum effects in light-initiated reactions in biology requires clear identification of non-classical features that these processes can exhibit and utilize. Here we show that in prototype dimers present in a variety of photosynthetic antennae, efficient vibration-assisted energy transfer in the sub-picosecond timescale and at room temperature can manifest and benefit from non-classical fluctuations of collective pigment motions. Non-classicality of initially thermalized vibrations is induced via coherent exciton-vibration interactions and is unambiguously indicated by negativities in the phase-space quasi-probability distribution of the effective collective mode coupled to the electronic dynamics. These quantum effects can be prompted upon incoherent input of excitation. Our results therefore suggest that investigation of the non-classical properties of vibrational motions assisting excitation and charge transport, photoreception and chemical sensing processes could be a touchstone for revealing a role for non-trivial quantum phenomena in biology.

Quantum Coherence and its Impact on Biomimetic Light-Harvesting

The survival of all photosynthetic organisms relies on the initial light harvesting step, and thus, after ~3 billion years of evolution energy capture and transfer has become a highly efficient and effective process. Here we examine the latest developments on understanding light harvesting, particularly in systems that exhibit an ultrafast energy transfer mechanism known as quantum coherence. With increasing knowledge of the structural and function parameters that produce quantum coherence in photosynthetic organisms, we can begin to replicate this process through biomimetic systems providing a faster and more efficient approach to harvesting and storing solar power for the worlds energy needs. Importantly, synthetic systems that display signs of quantum coherence have also been created and the first design principles for synthetic systems utilising quantum coherence are beginning to emerge. Recent claims that quantum coherence also plays a key role in ultrafast charge-separation highlights the importance for chemists, biologists, and material scientists to work more closely together to uncover the role of quantum coherence in photosynthesis and solar energy research.

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.

Excitation energy transfer in a classical analogue of photosynthetic antennae

We formulate a classical pure dephasing system-bath interaction model in a full correspondence to the well-studied quantum model of natural light-harvesting antennae. The equations of motion of our classical model not only represent the correct classical analogy to the quantum description of excitonic systems, but they also have exactly the same functional form. We demonstrate derivation of classical dissipation and relaxation tensor in second order perturbation theory. We find that the only difference between the classical and quantum descriptions is in the interpretation of the state and in certain limitations imposed on the parameters of the model by classical physics. The effects of delocalization, transfer pathway interference, and the transition from coherent to diffusive transfer can be found already in the classical realm. The only qualitatively new effect occurring in quantum systems is the preference for a downhill energy transfer and the resulting possibility of trapping the energy in the lowest energy state.

Does Coherence Enhance Transport in Photosynthesis?

Recent observations of coherence in photosynthetic complexes have led to the question of whether quantum effects can occur in vivo, not under femtosecond laser pulses but in incoherent sunlight and at steady state, and, if so, whether the coherence explains the high exciton transfer efficiency. We introduce the distinction between state coherence and process coherence and show that although some photosynthetic pathways are partially coherent processes, photosynthesis in nature proceeds through stationary states. This distinction allows us to rule out several mechanisms of transport enhancement in sunlight. In particular, although they are crucial for understanding exciton transport, neither wavelike motion nor microscopic coherence, on their own, enhance the efficiency. By contrast, two partially coherent mechanisms-ENAQT and supertransfer-can enhance transport even in sunlight and thus constitute motifs for the optimization of artificial sunlight harvesting. Finally, we clarify the importance of ultrafast spectroscopy in understanding incoherent processes.

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.