We investigate the relevance of dynamic quantum coherence in the energy transfer efficiency of molecular aggregates. We contrast the dynamics after excitation of a quantum mechanical system with that of a classical system. We demonstrate how a classical description of an ensemble average can be satisfactorily interpreted either as a single system driven by a continuous force or as an ensemble of systems each driven by an impulsive force. We derive the time evolution of the density matrix for an open quantum system excited by light or by a neighboring antenna. We argue that unlike in the classical case, the quantum description does not allow for a formal decomposition of the dynamics into sudden jumps in the quantum mechanical state. Rather, there is a natural finite time-scale associated with the excitation process. We propose a simple experiment how to test the influence of this time scale on the yield of photosynthesis. Because photosynthesis is intrinsically an average process, the efficiency of photosynthesis can be assessed from the quantum mechanical expectation value calculated from the second-order response theory, which has the same validity as the perturbative description of ultrafast experiments. We demonstrate using typical parameters of the currently most studied photosynthetic antenna, the Fenna-Matthews-Olson (FMO) complex, and a typical energy transfer rate from the chlorosome baseplate, that dynamic coherences are averaged out in the complex despite excitation proceeding through a coherent superposition of its eigenstates. The dynamic coherence averages out even when the FMO model is completely free of all dissipation and dephasing. We conclude that under natural excitation conditions coherent dynamics cannot be responsible for the remarkable efficiency of the photosynthesis even when considering the dynamics at a single molecular level.
Equations of motion for weakly coupled excitonic complexes are derived. The description allows to treat the system in the basis of electronic states localized on individual chromophores, while at the same time accounting for experimentally observable delocalization effects in optical spectra. The equations are show to be related to the well-known Foerster type energy transfer rate equations, but unlike Foerster equations, they provide a description of the decoherence processes leading to suppression of the resonance coupling by bath fluctuations. Linear absorption and two-dimensional photon ec…
The theoretical and experimental study of energy transfer in photosynthesis has revealed an interesting transport regime, which lies at the borderline between classical transport dynamics and quantum-mechanical interference effects. Dissipation is caused by the coupling of electronic degrees of freedom to vibrational modes and leads to a directional energy transfer from the antenna complex to the target reaction-center. The dissipative driving is robust and does not rely on fine-tuning of specific vibrational modes. For the parameter regime encountered in the biological systems new theoretical…
We investigate the role of quantum coherence in modulating the energy transfer rate between two independent energy donors and a single acceptor participating in an excitonic energy transfer process. The energy transfer rate depends explicitly on the nature of the initial coherent superposition state of the two donors and we connect it to the observed absorption profile of the acceptor and the stimulated emission profile of the energy donors. We consider simple models with mesoscopic environments interacting with the donors and the acceptor and compare the expression we obtained for the energy …
We report two-dimensional electronic spectroscopy (2DES) experiments on the bacterial reaction center (BRC) from purple bacteria, revealing hidden excitonic and vibronic structure. Through analysis of the coherent dynamics of the BRC we resolve specific coherent signatures that allow us to definitively assign the upper exciton energy of the "special pair." This assignment is supported by simulations of coherent dynamics of a reduced excitonic model of the BRC. The simulations also identify nonsecular vibronic coherence transfer processes neglected in standard models of photosynthetic energy tr…
We present a study on the evolution of the Fenna-Matthews-Olson bacterial photosynthetic pigment-protein complex. This protein complex functions as an antenna. It transports absorbed photons - excitons - to a reaction center where photosynthetic reactions initiate. The efficiency of exciton transport is therefore fundamental for the photosynthetic bacterium's survival. We have reconstructed an ancestor of the complex to establish whether coherence in the exciton transport was selected for or optimized over time. We have also investigated on the role of optimizing free energy variation upon fol…
Experimental evidence shows that a variety of photosynthetic systems can preserve quantum beats in the process of electronic energy transfer, even at room temperature. However, whether this quantum coherence arises in vivo and whether it has any biological function have remained unclear. Here we present a theoretical model that suggests that the creation and recreation of coherence under natural conditions is ubiquitous. Our model allows us to theoretically demonstrate a mechanism for a ratchet effect enabled by quantum coherence, in a design inspired by an energy transfer pathway in the Fenna…
A vibronic exciton model is developed to investigate the origin of long lived coherences in light-harvesting complexes. Using experimentally determined parameters and uncorrelated site energy fluctuations, the model predicts oscillations in the nonlinear spectra of the Fenna-Matthews-Olson (FMO) complex with a dephasing time of 1.3 ps at 77 K. These oscillations correspond to the coherent superposition of vibronic exciton states with dominant contributions from vibrational excitations on the same pigment. Purely electronic coherences are found to decay on a 200 fs timescale.
Two distinct approaches, the Frenkel-Dirac time-dependent variation and the Haken-Strobl model, are adopted to study energy transfer dynamics in single-ring and double-ring light-harvesting systems in purple bacteria. It is found that inclusion of long-range dipolar interactions in the two methods results in significant increases in intra- or inter-ring exciton transfer efficiency. The dependence of exciton transfer efficiency on trapping positions on single rings of LH2 (B850) and LH1 is similar to that in toy models with nearest-neighbor coupling only. However, owing to the symmetry breaking…
The observed prevalence of oscillatory signals in the spectroscopy of biological light-harvesting complexes at ambient temperatures has led to a search for mechanisms supporting coherent transport through larger molecules in noisy environments. We demonstrate a generic mechanism supporting long-lasting electronic coherence up to 0.3 ps at a temperature of 277 K. The mechanism relies on two properties of the spectral density: (i) a large dissipative coupling to a continuum of higher-frequency vibrations required for efficient transport and (ii) a small slope of the spectral density at zero freq…
Dependence of energy relaxation and vibrational coherence on the location of light-harvesting chromoproteins in photosynthetic antenna protein complexes
We demonstrate that the coupling of excitonic and vibrational motion in biological complexes can provide mechanisms to explain the long-lived oscillations that have been obtained in non linear spectroscopic signals of different photosynthetic pigment protein complexes and we discuss the contributions of excitonic versus purely vibrational components to these oscillatory features. Considering a dimer model coupled to a structured spectral density we exemplify the fundamental aspects of the electron-phonon dynamics, and by analyzing separately the different contributions to the non linear signal…
We theoretically investigate exciton relaxation dynamics in molecular aggregates based on model photosynthetic complexes under various conditions of incoherent excitation. We show that noise-induced quantum coherence is generated between spatially-separated exciton states which belong to the same or different energy transfer pathways, coupled via real and virtual transfer processes. Such quantum coherence effects may be used to improve light-harvesting efficiency and to reveal quantum phenomena in biology.
Photosynthetic antenna complexes capture and concentrate solar radiation by transferring the excitation to the reaction center which stores energy from the photon in chemical bonds. This process occurs with near-perfect quantum efficiency. Recent experiments at cryogenic temperatures have revealed that coherent energy transfer - a wavelike transfer mechanism - occurs in many photosynthetic pigment-protein complexes (1-4). Using the Fenna-Matthews-Olson antenna complex (FMO) as a model system, theoretical studies incorporating both incoherent and coherent transfer as well as thermal dephasing p…
This paper investigates the dynamics of excitonic transport in photocomplex LHCII, the primary component of the photosynthetic apparatus in green plants. The dynamics exhibits a strong interplay between coherent processes mediated by the excitonic Hamiltonian, and incoherent processes due to interactions with the environment. The spreading of the exciton over a single monomer is well described by a proper measure of delocalization that allows one to identify two relevant time scales. An exciton initially localized in one chromophore first spreads coherently to neighboring chromophores. During …
Answering the titular question has become a central motivation in the field of quantum biology, ever since the idea was raised following a series of experiments demonstrating wave-like behavior in photosynthetic complexes. Here, we report a direct evaluation of the effect of quantum coherence on the efficiency of three natural complexes. An open quantum systems approach allows us to simultaneously identify their level of "quantumness" and efficiency, under natural physiological conditions. We show that these systems reside in a mixed quantum-classical regime, characterized by dephasing-assiste…
In this paper we consider 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 to asses effects of different light properties on the photo-induced dynamics of a molecular system. We show that once the properties of light are known in terms of certain two-point correlation function, the only information needed to reconstruct the system dynamics is the reduced evolution superoperator. The later quantity is in principle accessible through ultrafast non-linear spectroscopy. Consi…
During the first steps of photosynthesis, the energy of impinging solar photons is transformed into electronic excitation energy of the light-harvesting biomolecular complexes. The subsequent energy transfer to the reaction center is understood in terms of exciton quasiparticles which move on a grid of biomolecular sites on typical time scales less than 100 femtoseconds (fs). Since the early days of quantum mechanics, this energy transfer is described as an incoherent Forster hopping with classical site occupation probabilities, but with quantum mechanically determined rate constants. This ort…
Until recently it was believed that photosynthesis, a fundamental process for life on earth, could be fully understood with semi-classical models. However, puzzling quantum phenomena have been observed in several photosynthetic pigment-protein complexes, prompting questions regarding the nature and role of these effects. Recent attention has focused on discrete vibrational modes that are resonant or quasi-resonant with excitonic energy splittings and strongly coupled to these excitonic states. Here we unambiguously identify excited state coherent superpositions in photosynthetic light-harvesti…
We expose a new excitation transport channel in FMO, consisting of the 7 intramonomeric pigments and their 2nd nearest intermonomeric counterpart. Such a channel outcompetes the standard alternative, where intramonomeric pigments partner with their closest intermonomeric pigment. The efficient performance of the new channel lies at the interplay between incoherent energy transfer and the capacity of quantum coherence to build optimal acceptor levels. Finally, the differential fitness and peculiarity of the new over the alternative channel highlights its possible role within natural selection.
Excitonic couplings between (bacterio)chlorophyll molecules are necessary for simulating energy transport in photosynthetic complexes. Many techniques for calculating the couplings are in use, from the simple (but inaccurate) point-dipole approximation to fully quantum-chemical methods. We compared several approximations to determine their range of applicability, noting that the propagation of experimental uncertainties poses a fundamental limit on the achievable accuracy. In particular, the uncertainty in crystallographic coordinates yields an uncertainty of about 20% in the calculated coupli…
Recent evidence of electronic coherence during energy transfer in photosynthetic antenna complexes has reinvigorated the discussion of whether coherence and/or entanglement has any practical functionality for these molecular systems. Here we investigate quantitative relationships between the quantum yield of a light-harvesting complex and the distribution of entanglement among its components. Our study focusses on the entanglement yield or average entanglement surviving a time scale comparable to the average excitation trapping time. As a prototype system we consider the Fenna-Matthews-Olson (…
Photosynthesis powers life on our planet. The basic photosynthetic architecture comprises antenna complexes to harvest solar energy and reaction centers to convert the energy into a stable charge separated state. In oxygenic photosynthesis, the initial charge separation event occurs in the photosystem II reaction center; the only known natural enzyme that uses solar energy to split water. Energy transfer and charge separation in photosynthesis are rapid and have high quantum efficiencies. Recently, nonlinear spectroscopic experiments have suggested that electronic coherence may play a role in …
We describe a simple and consistent quantum mathematical model that simulates the possible role of quantum interference and sink effects in the nonphotochemical quenching (NPQ) in light-harvesting complexes (LHCs). Our model consists of a network of five interconnected sites (excitonic states) responsible for the NPQ mechanism: (i) Two excited states of chlorophyll molecules, $ChlA^*$ and $ChlB^*$, forming an LHC dimer, which is initially populated; (ii) A "damaging" site which is responsible for production of singlet oxygen and other destructive outcomes; (iii) The $(ChlA-Zea)^*$ heterodimer …
The striking efficiency of energy transfer in natural photosynthetic systems and the recent evidence of long-lived quantum coherence in biological light harvesting complexes has triggered much excitement, due to the evocative possibility that these systems - essential to practically all life on earth -- use quantum mechanical effects to achieve optimal functionality. A large body of theoretical work has addressed the role of local environments in determining the transport properties of excitons in photosynthetic networks and the survival of quantum coherence in a classical environment. Nonethe…
We study the evolution of quantum entanglement during exciton energy transfer (EET) in a network model of the Fenna-Matthews-Olson (FMO) complex, a biological pigment-protein complex involved in the early steps of photosynthesis in sulphur bacteria. The influence of Markovian, as well as spatially and temporally correlated (non-Markovian) noise on the generation of entanglement across distinct chromophores (site entanglement) and different excitonic eigenstates (mode entanglement) is studied for different injection mechanisms, including thermal and coherent laser excitation. Additionally, we s…
Photosynthetic antenna complexes are responsible for absorbing energy from sunlight and transmitting it to remote locations where it can be stored. Recent experiments have found that this process involves long-lived quantum coherence between pigment molecules, called chromophores, which make up these complexes. Expected to decay within 100 fs at room temperature, these coherences were instead found to persist for picosecond time scales, despite having no apparent isolation from the thermal environment of the cell. This paper derives a quantum master equation which describes the coherent evolut…
It is shown that quantum sustainability is a universal phenomenon which emerges during environment-assisted electronic excitation energy transfer (EET) in photobiological complexes (PBCs), such as photosynthetic reaction centers and centers of melanogenesis. We demonstrate that quantum photobiological systems must be sustainable for them to simultaneously endure continuous energy transfer and keep their internal structure from destruction or critical instability. These quantum effects occur due to the interaction of PBCs with their environment which can be described by means of the reduced den…
Transport of excitons through transfer networks is a unique example where the interplay between quantum coherence and environment-induced dephasing leads to non-trivial effects. One exciting example is the "environment-assisted quantum transport", (ENAQT), where, counter intuitively, the environment interrupts quantum transport in a way that enhances the transfer efficiency. Here we show that the interplay between dephasing and quantum coherence can lead to an additional function in exciton transport - photo-protection, that is the reduction of current upon increased excitation. We start by de…
