We show that the quantum decoherence of Forster resonant energy transfer between two optically active molecules can be described by a spin-boson model. This allows us to give quantitative criteria, in terms of experimentally measurable system parameters, that are necessary for coherent Bloch oscillations of excitons between the chromophores. Experimental tests of our results should be possible with Flourescent Resonant Energy Transfer (FRET) spectroscopy. Although we focus on the case of protein-pigment complexes our results are also relevant to quantum dots and organic molecules in a dielectric medium.
The interplay between exctions and vibrations is considered to be a key factor in determining the exciton transfer properties in light-harvesting exciton transfer complexes. Here we study this interplay theoretically in a model for exciton transport, composed of two chromophores coupled to an exciton source and sink in the presence of vibrations. We consider two cases, that show qualitatively distinct transport features. In the first, the vibrations are global and affect the two chromophores simultaneously. In the second case, the vibrations are localized on each chromophore. For global vibrat…
The non-classical spectral and temporal features of entangled photons offer new possibilities to investigate the interactions of excitons in photosynthetic complexes, and to target the excitation of specific states. Simulations of fluorescence in the bacterial reaction center induced by entangled light demonstrate a selectivity of double-exciton states which is not possible using classical stochastic light with the same power spectrum.
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…
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations at small length scales into dynamics over large length scales, without assumptions of time scale separation or specific forms of intra-module quantum dynamics. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic …
We study a large number of physically-plausible arrangements of chromophores, generated via a computational method involving stochastic real-space transformations of a naturally occurring `reference' structure, illustrating our methodology using the well-studied Fenna-Matthews-Olson complex (FMO). To explore the idea that the natural structure has been tuned for efficient energy transport we use an atomic transition charge method to calculate the excitonic couplings of each generated structure and a Lindblad master equation to study the quantum transport of an exciton from a `source' to a `dra…
We show that the quantum coherent transfer of excitations between biomolecular chromophores is strongly influenced by spatial correlations of the environmental fluctuations. The latter are due either to propagating environmental modes or to local fluctuations with a finite localization length. A simple toy model of a single donor-acceptor pair with spatially separated chromophore sites allows to investigate the influence of these spatial correlations on the quantum coherent excitation transfer. The sound velocity of the solvent determines the wave lengths of the environmental modes, which, in …
Photosynthetic light harvesting provides a natural blueprint for bioengineered and biomimetic solar energy and light detection technologies. Recent evidence suggests some individual light harvesting protein complexes (LHCs) and LHC subunits efficiently transfer excitons towards chemical reaction centers (RCs) via an interplay between excitonic quantum coherence, resonant protein vibrations, and thermal decoherence. The role of coherence in vivo is unclear however, where excitons are transferred through multi-LHC/RC aggregates over distances typically large compared with intra-LHC scales. Here …
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 …
We investigate the quantum dynamics of energy and charge transfer in a wheel-shaped artificial photosynthetic antenna-reaction center complex.This complex consists of six light-harvesting chromophores and an electron-acceptor fullerene. To describe quantum effects on a femtosecond time scale, we derive the set of exact non-Markovian equations for the Heisenberg operators of this photosynthetic complex in contact with a Gaussian heat bath. With these equations we can analyze the regime of strong system-bath interactions, where reorganization energies are of the order of the intersite exciton co…
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 …
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 …
Modeling linear absorption spectra of solvated chromophores is highly challenging as contributions are present both from coupling of the electronic states to nuclear vibrations and solute-solvent interactions. In systems where excited states intersect in the Condon region, significant non-adiabatic contributions to absorption lineshapes can also be observed. Here, we introduce a robust approach to model linear absorption spectra accounting for both environmental and non-adiabatic effects from first principles. This model parameterizes a linear vibronic coupling (LVC) Hamiltonian directly from …
Non-Markovian Quantum State Diffusion (NMQSD) has turned out to be an efficient method to calculate excitonic properties of aggregates composed of organic chromophores, taking into account the coupling of electronic transitions to vibrational modes of the chromophores. NMQSD is an open quantum system approach that incorporates environmental degrees of freedom (the vibrations in our case) in a stochastic way. We show in this paper that for linear optical spectra (absorption, circular dichroism) no stochastics is needed, even for finite temperatures. Thus, the spectra can be obtained by propagat…
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 show that quantum coherence of biomolecular excitons is maintained over exceedingly long times due to the constructive role of their non-Markovian protein-solvent environment. Using a numerically exact approach, we demonstrate that a slow quantum bath helps to sustain quantum entanglement of two pairs of Forster coupled excitons, in contrast to a Markovian environment. We consider the crossover from a fast to a slow bath and from weak to strong dissipation and show that a slow bath can generate robust entanglement. This persists to surprisingly high temperatures, even higher than the excito…
We explore various design principles for efficient excitation energy transport in complex quantum systems. We investigate energy transfer efficiency in randomly disordered geometries consisting of up to 20 chromophores to explore spatial and spectral properties of small natural/artificial Light-Harvesting Complexes (LHC). We find significant statistical correlations among highly efficient random structures with respect to ground state properties, excitonic energy gaps, multichromophoric spatial connectivity, and path strengths. These correlations can even exist beyond the optimal regime of env…
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…
Excitonic transport in photosynthesis exhibits a wide range of time scales. Absorption and initial relaxation takes place over tens of femtoseconds. Excitonic lifetimes are on the order of a nanosecond. Hopping rates, energy differences between chromophores, reorganization energies, and decoherence rates correspond to time scales on the order of picoseconds. The functional nature of the divergence of time scales is easily understood: strong coupling to the electromagnetic field over a broad band of frequencies yields rapid absorption, while long excitonic lifetimes increase the amount of energ…
We study the interplay between two environmental influences on excited state energy transfer in photosynthetic light harvesting complexes, namely, vibrationally assisted energy transfer (VAET) and environment-assisted quantum transport (ENAQT), considering a dimeric chromophore donor-acceptor model as a prototype for larger systems. We demonstrate how the basic features of the excitonic energy transfer are influenced by these two environments, both separately and together, with the environment being fully quantum in the case of VAET and treated in the Haken-Strobl-Reineker classical limit in t…
We study theoretically the noise-assisted quantum exciton (electron) transfer (ET) in bio-complexes consisting of a single-level electron donor and an acceptor which has a complicated internal structure, and is modeled by many electron energy levels. Interactions are included between the donor and the acceptor energy levels and with the protein-solvent noisy environment. Different regions of parameters are considered, which characterize (i) the number of the acceptor levels, (ii) the acceptor \band-width", and (iii) the amplitude of noise and its correlation time. Under some conditions, we der…
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…
We present a theoretical analysis of exciton transfer and decoherence effects in a photosynthetic dimer interacting with collective (correlated) and local (uncorrelated) protein-solvent environments. Our approach is based on the framework of the spin-boson model. We derive explicitly the thermal relaxation and decoherence rates of the exciton transfer process, valid for arbitrary temperatures and for arbitrary (in particular, large) interaction constants between the dimer and the environments. We establish a generalization of the Marcus formula, giving reaction rates for dimer levels possibly …
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 how collective behaviors of vibrations such as cooperativity and interference can enhance energy transfer in a nontrivial way, focusing on an example of a donor-bridge-acceptor trimeric chromophore system coupled to two vibrational degrees of freedom. Employing parameters selected to provide an overall uphill energy transfer from donor to acceptor, we use numerical calculations of dynamics in a coupled exciton-vibration basis, together with perturbation-based analytics and calculation of vibronic spectra, we identify clear spectral features of single- and multi-phonon vibrationa…
We show that an ensemble of organic dye molecules with permanent electric dipole moments embedded in a microcavity can lead to strong optical nonlinearities at the single photon level. The strong long-range electrostatic interaction between chromophores due to their permanent dipoles introduces the desired nonlinearity of the light-matter coupling in the microcavity. We obtain the absorption spectra of a weak probe field under the influence of strong exciton-photon coupling with the cavity field. Using realistic parameters, we demonstrate that a single cavity photon can significantly modify th…
The description of excited state dynamics in multichromophoric systems constitutes both a theoretical and experimental challenge in modern physical chemistry. An experimental protocol which can systematically characterize both coherent and dissipative processes at the level of the evolving quantum state of the chromophores is desired. In this article, we show that a carefully chosen set of polarization controlled two-color heterodyned photon-echo experiments can be used to reconstruct the time-evolving density matrix of the one-exciton manifold of a heterodimer. This possibility in turn allows…
For more than 50 years we have known that photosynthetic systems harvest solar energy with almost unit {\it quantum efficiency}. However, recent experimental evidence of {\it quantum coherence} during the excitonic energy transport in photosynthetic organisms challenges our understanding of this fundamental biological function. Currently, and despite numerous efforts, the causal connection between coherence and efficiency is still a matter of debate. We show, through the study of extensive simulations of quantum coherent transport on networks, that three dimensional structures characterized by…
We model and simulate the performance of charge-transfer in nonphotochemical quenching (NPQ) in the CP29 light-harvesting antenna-complex associated with photosystem II (PSII). The model consists of five discrete excitonic energy states and two sinks, responsible for the potentially damaging processes and charge-transfer channels, respectively. We demonstrate that by varying (i) the parameters of the chlorophyll-based dimer, (ii) the resonant properties of the protein-solvent environment interaction, and (iii) the energy transfer rates to the sinks, one can significantly improve the performanc…
A remarkable amount of theoretical research has been carried out to elucidate the physical origins of the recently observed long-lived quantum coherence in the electronic energy transfer process in biological photosynthetic systems. Although successful in many respects, several widely used descriptions only include an effective treatment of the protein-chromophore interactions. In this work, by combining an all-atom molecular dynamics simulation, time-dependent density functional theory, and open quantum system approaches, we successfully simulate the dynamics of the electronic energy transfer…
