Quantum entanglement phenomena in photosynthetic light harvesting complexes
K. Birgitta Whaley, Mohan Sarovar, Akihito Ishizaki
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11 pages, 3 figures. Review article. To appear in the proceedings of the 22nd Solvay Conference in Chemistry on "Quantum Effects in Chemistry and Biology"
We review recent theoretical calculations of quantum entanglement in photosynthetic light harvesting complexes. These works establish, for the first time, a manifestation of this characteristically quantum mechanical phenomenon in biologically functional structures. We begin by summarizing calculations on model biomolecular systems that aim to reveal non-trivial characteristics of quantum entanglement in non-equilibrium biological environments. We then discuss and compare several calculations performed recently of excitonic dynamics in the Fenna-Matthews-Olson light harvesting complex and of the entanglement present in this widely studied pigment-protein structure. We point out the commonalities between the derived results and also identify and explain the differences. We also discuss recent work that examines entanglement in the structurally more intricate light harvesting complex II (LHCII). During this overview, we take the opportunity to clarify several subtle issues relating to entanglement in such biomolecular systems, including the role of entanglement in biological function, the complexity of dynamical modeling that is required to capture the salient features of entanglement in such biomolecular systems, and the relationship between entanglement and other quantum mechanical features that are observed and predicted in light harvesting complexes. Finally, we suggest possible extensions of the current work and also review the options for experimental confirmation of the predicted entanglement phenomena in light harvesting complexes.
We examine computational techniques and methodologies currently in use to explore electronic excitation energy transfer in the context of light-harvesting complexes in photosynthetic antenna systems, and comment on some new insights into the underlying physics. Advantages and pitfalls of these methodologies are discussed, as are some physical insights into the photosynthetic dynamics. By combining results from molecular modelling of the complexes (structural description) with an effective non-equilibrium statistical description (time evolution), we identify some general features, regardless of…
Several recent studies of energy transfer in photosynthetic light harvesting complexes have revealed a subtle interplay between coherent and decoherent dynamic contributions to the overall transfer efficiency in these open quantum systems. In this work we systematically investigate the impact of temporal and spatial correlations in environmental fluctuations on excitation transport in the Fenna-Matthews-Olson photosynthetic complex. We demonstrate that the exact nature of the correlations can have a large impact on the efficiency of light harvesting. In particular, we find that (i) spatial cor…
It has been suggested that excitation transport in photosynthetic light harvesting complexes features speedups analogous to those found in quantum algorithms. Here we compare the dynamics in these light harvesting systems to the dynamics of quantum walks, in order to elucidate the limits of such quantum speedups. For the Fenna-Matthews-Olson (FMO) complex of green sulfur bacteria, we show that while there is indeed speedup at short times, this is short lived (70 fs) despite longer lived (ps) quantum coherence. Remarkably, this time scale is independent of the details of the decoherence model. …
Non-Markovian and non-equilibrium phonon effects are believed to be key ingredients in the energy transfer in photosynthetic complexes, especially in complexes which exhibit a regime of intermediate exciton-phonon coupling. In this work, we utilize a recently-developed measure for non-Markovianity to elucidate the exciton-phonon dynamics in terms of the information flow between electronic and vibrational degrees of freedom. We study the measure in the hierarchical equation of motion approach which captures strong system-bath coupling effects and non-equilibrium molecular reorganization. We pro…
We provide a unified theoretical approach to the quantum dynamics of absorption of single photons and subsequent excitonic energy transfer in photosynthetic light-harvesting complexes. Our analysis combines a continuous mode <n>-photon quantum optical master equation for the chromophoric system with the hierarchy of equations of motion describing excitonic dynamics in presence of non-Markovian coupling to vibrations of the chromophores and surrounding protein. We apply the approach to simulation of absorption of single-photon coherent states by pigment-protein complexes containing between one …
Photosynthetic complexes improve the transfer of excitation energy from peripheral antennas to reaction centers in several ways. In particular, a downward energy funnel can direct excitons in the right direction, while coherent excitonic delocalization can enhance transfer rates through the cooperative phenomenon of supertransfer. However, isolating the role of purely coherent effects is difficult because any change to the delocalization also changes the energy landscape. Here, we show that the relative importance of the two processes can be determined by comparing the natural light-harvesting…
Transport phenomena in photosynthetic systems have attracted a great deal of attention due to their potential role in devising novel photovoltaic materials. In particular, energy transport in light-harvesting complexes is considered quite efficient due to the balance between coherent quantum evolution and decoherence, a phenomenon coined Environment-Assisted Quantum Transport (ENAQT). Although this effect has been extensively studied, its behavior is typically described in terms of the decoherence's strength, namely weak, moderate or strong. Here, we study the ENAQT in terms of quantum correla…
Research into the efficiency of photosynthetic light harvesting has focused on two factors: (1) entanglement of chromophores, and (2) environmental noise. While chromophores are conjugated $π$-bonding molecules with strongly correlated electrons, previous models have treated this correlation implicitly without a mathematical variable to gauge correlation-enhanced efficiency. Here we generalize the single-electron/exciton models to a multi-electron/exciton model that explicitly shows the effects of enhanced electron correlation within chromophores on the efficiency of energy transfer. The model…
Light harvesting components of photosynthetic organisms are complex, coupled, many-body quantum systems, in which electronic coherence has recently been shown to survive for relatively long time scales despite the decohering effects of their environments. Within this context, we analyze entanglement in multi-chromophoric light harvesting complexes, and establish methods for quantification of entanglement by presenting necessary and sufficient conditions for entanglement and by deriving a measure of global entanglement. These methods are then applied to the Fenna-Matthews-Olson (FMO) protein to…
The Fenna-Matthews-Olson (FMO) antennae complex, responsible for light harvesting in green sulfur bacteria, consists of three monomers, each with seven chromophores. Here we show that multiple subsystems of the seven chromophores can transfer energy from either chromophore 1 or 6 to the reaction center with an efficiency matching or in many cases exceeding that of the full seven chromophore system. In the FMO complex these functional subsystems support multiple quantum pathways for efficient energy transfer that provide a built-in quantum redundancy. There are many instances of redundancy in n…
The functioning and efficiency of natural photosynthetic complexes is strongly influenced by their embedding in a noisy protein environment, which can even serve to enhance the transport efficiency. Interactions with the environment induce fluctuations of the transition energies of and interactions between the chlorophyll molecules, and due to the fact that different fluctuations will partially be caused by the same environmental factors, correlations between the various fluctuations will occur. We argue that fluctuations of the interactions should in general not be neglected, as these have a …
The prospect of coherent dynamics and excitonic delocalization across several light-harvesting structures in photosynthetic membranes is of considerable interest, but challenging to explore experimentally. Here we demonstrate theoretically that the excitonic delocalization across extended domains involving several light-harvesting complexes can lead to unambiguous signatures in the optical response, specifically, linear absorption spectra. We characterize, under experimentally established conditions of molecular assembly and protein-induced inhomogeneities, the optical absorption in these arra…
We propose a scheme to simulate the exciton energy transfer (EET) of photosynthetic complexes in a quantum superconducting circuit system. Our system is composed of two pairs of superconducting charge qubits coupled to two separated high-Q superconducting transmission line resonators (TLRs) connected by a capacitance. When the frequencies of the qubits are largely detuned with those of the TLRs, we simulate the process of the EET from the first qubit to the fourth qubit. By tuning the couplings between the qubits and the TLRs, and the coupling between the two TLRs, we can modify the effective …
Photosynthetic organisms use networks of chromophores to absorb sunlight and deliver the energy to reaction centres, where charge separation triggers a cascade of chemical steps to store the energy. We present a detailed model of the light-harvesting complexes in purple bacteria, including explicit interaction with sunlight; energy loss through radiative and non-radiative processes; and dephasing and thermalizing effects of coupling to a vibrational bath. An important feature of the model is that we capture the effect of slow vibrational modes by introducing time-dependent disorder. Our model …
We present a detailed theoretical study of the transfer of electronic excitation energy through the Fenna-Matthews-Olson (FMO) pigment-protein complex, using the new developed modified scaled hierarchical approach [Shi Q. et al, J Chem Phys 2009, 130, 084105]. We show that this approach is computationally more efficient than the original hierarchical approach. The modified approach reduces the truncation levels of the auxiliary density operators and the correlation function. We provide a systematic study of how the number of auxiliary density operators and the higher-order correlation function…
Near-unity energy transfer efficiency has been widely observed in natural photosynthetic complexes. This phenomenon has attracted broad interest from different fields, such as physics, biology, chemistry and material science, as it may offer valuable insights into efficient solar-energy harvesting. Recently, quantum coherent effects have been discovered in photosynthetic light harvesting, and their potential role on energy transfer has seen heated debate. Here, we perform an experimental quantum simulation of photosynthetic energy transfer using nuclear magnetic resonance (NMR). We show that a…
We develop a quantum scattering model to describe the exciton transport through the Fenna-Matthews-Olson(FMO) complex. It is found that the exciton transport involved the optimal quantum coherence is more efficient than that involved classical behavior alone. Furthermore, we also find that the quantum resonance condition is easier to be fulfilled in multiple pathways than that in one pathway. We then definitely demonstrate that the optimal distribution of the pigments, the multitude of energy delivery pathways and the quantum effects, are combined together to contribute to the perfect energy t…
The physical basis for observed long-lived electronic coherence in photosynthetic light-harvesting systems is identified using an analytically soluble model. Three physical features are found to be responsible for their long coherence lifetimes: i) the small energy gap between excitonic states, ii) the small ratio of the energy gap to the coupling between excitonic states, and iii) the fact that the molecular characteristics place the system in an effective low temperature regime, even at ambient conditions. Using this approach, we obtain decoherence times for a dimer model with FMO parameters…
The remarkable rotational symmetry of the photosynthetic antenna complexes of purple bacteria has long been thought to enhance their light harvesting and excitation energy transport. We study the role of symmetry by modeling hypothetical antennas whose symmetry is broken by altering the orientations of the bacteriochlorophyll pigments. We find that in both LH2 and LH1 complexes, symmetry increases energy transfer rates by enabling the cooperative, coherent process of supertransfer. The enhancement is particularly pronounced in the LH1 complex, whose natural geometry outperforms the average ran…
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.
One of the important nonclassical effects in quantum optics is the anti-bunching, which has been observed in a large class of physical systems - including light-harvesting antennas with cyclic structures. The units of the ring couple with adjacent ones through dipole-dipole interactions. We show how this strong dipole-dipole interaction leads to photon-blockade resulting in the suppression of double excitation pathway and anti-bunching in photosynthesis systems. The robustness of the photon blockade is demonstrated against the disorder in the ring structures. We hypothesis that the effect may …
We investigate the role of long-lasting quantum coherence in the efficiency of energy transport at room temperature in Fenna-Matthews-Olson photosynthetic complexes. The excitation energy transfer due to the coupling of the light harvesting complex to the reaction center ("sink") is analyzed using an effective non-Hermitian Hamiltonian. We show that, as the coupling to the reaction center is varied, maximal efficiency in energy transport is achieved in the vicinity of the superradiance transition, characterized by a segregation of the imaginary parts of the eigenvalues of the effective non-Her…
In natural light harvesting systems, the sequential quantum events of photon absorption by specialized biological antenna complexes, charge separation, exciton formation and energy transfer to localized reaction centers culminates in the conversion of solar to chemical energy. A notable feature in these processes is the exceptionally high efficiencies ($>$ 95\%) at which excitation is transferred from the illuminated protein complex site to the reaction centers. The high speeds of excitation propagation within a system of interwoven biomolecular network structures, is yet to be replicated in a…
We study excitation energy transfer in a simple model of photosynthetic complex. The model, described by Lindblad equation, consists of pigments interacting via dipole-dipole interaction. Overlapping of pigments induces an on-site energy disorder, providing a mechanism for blocking the excitation transfer. Based on the average efficiency as well as robustness of random configurations of pigments, we calculate the optimal number of pigments that should be enclosed in a pigment-protein complex of a given size. The results suggest that a large fraction of pigment configurations are efficient as w…
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…
Primitive photosynthetic cells appear over three billion years prior to any other more complex life-forms, thus it is reasonable to assume that Nature has designed a photosynthetic mechanism using minimal resources but honed to perfection under the action of evolution. A number of different quantum models have been proposed to understand the high degree of efficient energy transport, most of them are limited to the scenario of single-exciton. Here we present a study on the dynamics in light-harvesting complexes beyond the single exciton limit, and show how this model describes the energy trans…
Open quantum system approaches are widely used in the description of physical, chemical and biological systems. A famous example is electronic excitation transfer in the initial stage of photosynthesis, where harvested energy is transferred with remarkably high efficiency to a reaction center. This transport is affected by the motion of a structured vibrational environment, which makes simulations on a classical computer very demanding. Here we propose an analog quantum simulator of complex open system dynamics with a precisely engineered quantum environment. Our setup is based on superconduct…
We consider the dependence of the electron transfer in photosynthetic complexes on correlation properties of random fluctuations of the protein environment. The electron subsystem is modeled by a finite network of connected electron (exciton) sites. The fluctuations of the protein environment are modeled by random telegraph processes, which act either collectively (correlated) or independently (uncorrelated) on the electron sites. We derived an exact closed system of first-order linear differential equations with constant coefficients, for the average density matrix elements and for their firs…
Recently, several works have analysed the efficiency of photosynthetic complexes in a transient scenario and how that efficiency is affected by environmental noise. Here, following a quantum master equation approach, we study the energy and excitation transport in fully connected networks both in general and in the particular case of the Fenna-Matthew-Olson complex. The analysis is carried out for the steady state of the system where the excitation energy is constantly "flowing" through the system. Steady state transport scenarios are particularly relevant if the evolution of the quantum syste…
We investigate the evolution of entanglement in the Fenna-Matthew-Olson (FMO) complex based on simulations using the scaled hierarchy equation of motion (HEOM) approach. We examine the role of multipartite entanglement in the FMO complex by direct computation of the convex roof optimization for a number of measures, including some that have not been previously evaluated. We also consider the role of monogamy of entanglement in these simulations. We utilize the fact that the monogamy bounds are saturated in the single exciton subspace. This enables us to compute more measures of entanglement ex…
Artificially reproducing the biological light reactions responsible for the remarkably efficient photon-to-charge conversion in photosynthetic complexes represents a new direction for the future development of photovoltaic devices. Here, we develop such a paradigm and present a model photocell based on the nanoscale architecture of photosynthetic reaction centres that explicitly harnesses the quantum mechanical effects recently discovered in photosynthetic complexes. Quantum interference of photon absorption/emission induced by the dipole-dipole interaction between molecular excited states gua…
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…
The pseudomode approach is discussed with an emphasis to Gorini-Kossakowski-Sudarshan-Lindblad form of this approach. The connection of the pseudomode approach with solutions of both the Friedrichs model and Jaynes-Cummings model with dissipation at zero temperature is shown. The obtained results are applied to non-Markovian phenomena description in the Fenna-Matthews-Olson complexes, estimations based on experimental data are done. A deformation approach to generalization of the pseudomode approach to the finite-temperature case is discussed.
The quantum network model with real variables is usually used to describe the excitation energy transfer (EET) in the Fenna-Matthews-Olson(FMO) complexes. In this paper we add the quantum phase factors to the hopping terms and find that the quantum phase factors play an important role in the EET. The quantum phase factors allow us to consider the space structure of the pigments. It is found that phase coherence within the complexes would allow quantum interference to affect the dynamics of the EET. There exist some optimal phase regions where the transfer efficiency takes its maxima, which ind…
Despite several different measures of efficiency that are applicable to the photosynthetic systems, a precise degree of efficiency of these systems is not completely determined. Introducing an efficient model for the dynamics of light-harvesting complexes in biological environments is a major purpose in investigating such systems. Here, we investigate the effect of macroscopic quantum behavior of a system of two pigments on the transport phenomena in this system model which interacts with an oscillating environment. We use the second-order perturbation theory to calculate the time-dependent po…
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…
Chlorosomes are likely the largest and most efficient natural light-harvesting photosynthetic antenna systems. They are composed of large numbers of bacteriochlorophylls organized into supramolecular aggregates. We explore the microscopic origin of the fast excitation energy transfer in the chlorosome using the recently-resolved structure and atomistic-detail simulations. Despite the dynamical disorder effects on the electronic transitions of the bacteriochlorophylls, our simulations show that the exciton delocalizes over the entire aggregate in about 200 fs. The memory effects associated to t…
Underlying physical principles for the high efficiency of excitation energy transfer in light-harvesting complexes are not fully understood. Notably, the degree of robustness of these systems for transporting energy is not known considering their realistic interactions with vibrational and radiative environments within the surrounding solvent and scaffold proteins. In this work, we employ an efficient technique to estimate energy transfer efficiency of such complex excitonic systems. We observe that the dynamics of the Fenna-Matthews-Olson (FMO) complex leads to optimal and robust energy trans…
We investigate the influence of static disorder and thermal excitations on excitonic energy transport in the light-harvesting apparatus of photosynthetic systems by solving the Schrödinger equation and taking into account the coherent hoppings of excitons, the rates of exciton creation and annihilation in antennas and reaction centers, and the coupling to thermally excited phonons. The antennas and reaction centers are modeled, respectively, as the sources and drains which provide the channels for creation and annihilation of excitons. Phonon modes below a maximum frequency are coupled to the …
Transport phenomena in organic, self-assembled molecular J-aggregates have long attracted a great deal of attention due to its potential role in designing novel organic photovoltaic devices. A large number of theoretical and experimental studies have been carried out describing excitonic energy transfer in J-aggregates under the assumption that excitons are induced by a coherent laser-light source or initialized by a localized excitation on a particular chromophore. However, these assumptions may not provide an accurate description to assess the efficiency of J-aggregates, particularly as buil…
This work asks how light harvesting in photosynthetic systems can be optimised for economically scalable, sustainable energy production. Hierarchy theory is introduced as a system-analysis and optimisation tool better able to handle multiscale, multiprocess complexities in photosynthetic energetics compared with standard linear-process analysis. Within this framework, new insights are given into relationships between composition, structure and energetics at the scale of the thylakoid membrane, and also into how components at different scales cooperate under functional objectives of the whole p…
We have evaluated excitation energy transfer rates in photosyntetic complexes using the exact HEOM method and various approximate methods frequently used in the literature, namely, the Förster method, the Redfield method, the modified Redfield method and the variational master equation. The rates are evaluated for the case of a simple dimer and a trimer photosynthetic complex, with vibrational environment characterized by the Drude-Lorentz spectral density. Comparing approximate rates to the exact ones, we have confirmed the validity of approximate methods within appropriate limits, however th…
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.
The long-standing problem of nearly perfect photosynthetic yield in some types of bacteria and nearly all kinds of plants despite the interaction with a hot and noisy environment has witnessed quantum optical explanations in the last decade or so. Typically in these explanations, photosynthetic reaction centers are modeled as five-level quantum heat engines where the generation of Fano-type interference due to the coupling of discrete state transitions with a common Markovian reservoir is held responsible for the enhancement of the photosynthetic efficiency. In this work, we go beyond the Born…
The process of photosynthesis, the main source of energy in the animate world, converts sunlight into chemical energy. The surprisingly high efficiency of this process is believed to be enabled by an intricate interplay between the quantum nature of molecular structures in photosynthetic complexes and their interaction with the environment. Investigating these effects in biological samples is challenging due to their complex and disordered structure. Here we experimentally demonstrate a new approach for studying photosynthetic models based on superconducting quantum circuits. In particular, we…
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…
A vibronic-exciton model is applied to investigate the mechanism of enhancement of coherent oscillations due to mixing of electronic and nuclear degrees of freedom recently proposed as the origin of the long-lived oscillations in 2D spectra of the FMO complex [Christensson et al. J. Phys. Chem. B 116 (2012) 7449]. We reduce the problem to a model BChl dimer to elucidate the role of resonance coupling, site energies, nuclear mode and energy disorder in the enhancement of vibronic-exciton and ground-state vibrational coherences, and to identify regimes where this enhancement is significant. For …
We model the quantum electron transfer (ET) in the photosynthetic reaction center (RC), using a non-Hermitian Hamiltonian approach. Our model includes (i) two protein cofactors, donor and acceptor, with discrete energy levels and (ii) a third protein pigment (sink) which has a continuous energy spectrum. Interactions are introduced between the donor and acceptor, and between the acceptor and the sink, with noise acting between the donor and acceptor. The noise is considered classically (as an external random force), and it is described by an ensemble of two-level systems (random fluctuators). …
Understanding how the effectiveness of natural photosynthetic energy harvesting systems arises from the interplay between quantum coherence and environmental noise represents a significant challenge for quantum theory. Recently it has begun to be appreciated that discrete molecular vibrational modes may play an important role in the dynamics of such systems. As an alternative to computationally demanding numerical approaches, we present a microscopic mechanism by which intramolecular vibrations contribute to the efficiency and directionality of energy transfer. Excited vibrational states creat…
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…
Long-lived electronic coherences in various photosynthetic complexes at cryogenic and room temperature have generated vigorous efforts both in theory and experiment to understand their origins and explore their potential role to biological function. The ultrafast signals resulting from the experiments that show evidence for these coherences result from many contributions to the molecular polarization. Quantum process tomography (QPT) was conceived in the context of quantum information processing to characterize and understand general quantum evolution of controllable quantum systems, for examp…
We model energy transfer between two coupled four-level chromophores with arbitrarily spaced energy levels. Our analysis takes into account the crucial---yet often ignored---process of initial excitation by light that is incident on the chromophores. We show that the amount of entanglement generated between the chromophores is strongly dependent on the degree of initial excitation as well as the inclusion of higher energy levels. We apply our model to the specific example of chlorophyll. Our results suggest that an excitation-dependent approach should be employed for entanglement studies on mu…
Electron transfer (ET) between primary electron donors and acceptors is modeled in the photosystem II reaction center (RC). Our model includes (i) two discrete energy levels associated with donor and acceptor, interacting through a dipole-type matrix element and (ii) two continuum manifolds of electron energy levels ("sinks"), which interact directly with the donor and acceptor. Namely, two discrete energy levels of the donor and acceptor are embedded in their independent sinks through the corresponding interaction matrix elements. We also introduce classical (external) noise which acts simult…
