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-assisted transport. Yet, we find that the change in efficiency at this regime is minute at best, implying that the presence of quantum coherence does not play a significant role in enhancing efficiency. However, in this regime efficiency is independent of any structural parameters, suggesting that evolution may have driven natural complexes to their parameter regime in order to "design" their structure for other uses.
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…
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.
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…
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…
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 …
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…
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…
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…
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…
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). …
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…
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…
We demonstrate numerically that superradiance could play a significant role in nonphotochemical quenching (NPQ) in light-harvesting complexes. Our model consists of a network of five interconnected sites (discrete excitonic states) that are responsible for the NPQ mechanism. Damaging and charge transfer states are linked to their sinks (independent continuum electron spectra), in which the chemical reactions occur. The superradiance transition in the charge transfer (or in the damaging) channel, occurs at particular electron transfer rates from the discrete to the continuum electron spectra, a…
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…
Photosynthesis transfers energy efficiently through a series of antenna complexes to the reaction center where charge separation occurs. Energy transfer in vivo is primarily monitored by measuring fluorescence signals from the small fraction of excitations that fail to result in charge separation. Here, we use two-dimensional electronic spectroscopy to follow the entire energy transfer process in a thriving culture of the purple bacteria, Rhodobacter sphaeroides. By removing contributions from scattered light, we extract the dynamics of energy transfer through the dense network of antenna comp…
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…
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…
We address the role of topology in the energy transport process that occurs in networks of photosynthetic complexes. We take inspiration from light harvesting networks present in purple bacteria and simulate an incoherent dissipative energy transport process on more general and abstract networks, considering both regular structures (Cayley trees and hyperbranched fractals) and randomly-generated ones. We focus on the the two primary light harvesting complexes of purple bacteria, i.e., the LH1 and LH2, and we use network-theoretical centrality measures in order to select different LH1 arrangeme…
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. …
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 …
Dependence of energy relaxation and vibrational coherence on the location of light-harvesting chromoproteins in photosynthetic antenna protein complexes
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…
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…
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…
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…
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…
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…
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…
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 …
Charge separation in light-harvesting complexes occurs in a pair of tightly coupled chlorophylls at the heart of photosynthetic reaction centers of both plants and bacteria. Recently it has been shown that quantum coherence can, in principle, enhance the efficiency of a solar cell, working like a quantum heat engine (QHE). Here, we propose a biological quantum heat engine (BQHE) motivated by Photosystem {\rm II} reaction center (PS{\rm II} RC) to describe the charge separation. Our model mainly considers two charge-separation pathways more than that in the published literature. The two pathway…
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 (…
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…
Natural organisms such as photosynthetic bacteria, algae, and plants employ complex molecular machinery to convert solar energy into biochemical fuel. An important common feature shared by most of these photosynthetic organisms is that they capture photons in the form of excitons typically delocalized over a few to tens of pigment molecules embedded in protein environments of light harvesting complexes (LHCs). Delocalized excitons created in such LHCs remain well protected despite being swayed by environmental fluctuations, and are delivered successfully to their destinations over hundred nano…
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 …
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…
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…
A variety of open quantum networks are currently under intense examination to model energy transport in photosynthetic systems. Here we study the coherent transfer of a quantum excitation over a network incoherently coupled with a structured and small environment that effectively models the photosynthetic reaction center. Our goal is to distill a few basic, possibly universal, mechanisms or "effects" that are featured in simple energy-transfer models. In particular, we identify three different phenomena: the congestion effect, the asymptotic unitarity and the staircase effects. We begin with f…
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 distinguish several types of 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, alth…
The fundamental physical mechanisms of energy transfer in photosynthetic complexes is not yet fully understood. In particular, the degree of efficiency or sensitivity of these systems for energy transfer is not known given their non-perturbative and non-Markovian interactions with proteins backbone and surrounding photonic and phononic environments. One major problem in studying light-harvesting complexes has been the lack of an efficient method for simulation of their dynamics in biological environments. To this end, here we revisit the second-order time-convolution (TC2) master equation and …
The dynamics of pigment-pigment and pigment-protein interactions in light-harvesting complexes is studied with a novel approach which combines molecular dynamics (MD) simulations with quantum chemistry (QC) calculations. The MD simulations of an LH-II complex, solvated and embedded in a lipid bilayer at physiological conditions (with total system size of 87,055 atoms) revealed a pathway of a water molecule into the B800 binding site, as well as increased dimerization within the B850 BChl ring, as compared to the dimerization found for the crystal structure. The fluctuations of pigment (B850 BC…
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…
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…
Excitation transfer through interacting systems plays an important role in many areas of physics, chemistry, and biology. The uncontrollable interaction of the transmission network with a noisy environment is usually assumed to deteriorate its transport capacity, especially so when the system is fundamentally quantum mechanical. Here we identify key mechanisms through which noise such as dephasing, perhaps counter intuitively, may actually aid transport through a dissipative network by opening up additional pathways for excitation transfer. We show that these are processes that lead to the inh…
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…
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…
It was once purported that biological systems were far too warm and wet to support quantum phenomena mainly due to thermal effects disrupting quantum coherence. However recent experimental results and theoretical analyses have shown that thermal energy may assist, rather than disrupt, quantum coherence, especially in the dry hydrophobic interiors of biomolecules. Specifically, evidence has been accumulating for the necessary involvement of quantum coherence and entanglement between uniquely arranged chromophores in light harvesting photosynthetic complexes. Amazingly, the tubulin subunit prote…
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 classi…
The quantum dynamics of transport networks in the presence of noisy environments have recently received renewed attention with the discovery of long-lived coherences in different photosynthetic complexes. This experimental evidence has raised two fundamental questions: Firstly, what are the mechanisms supporting long-lived coherences and secondly, how can we assess the possible functional role that the interplay of noise and quantum coherence might play in the seemingly optimal operation of biological systems under natural conditions? Here we review recent results, illuminate them at the hand …
Long lasting coherence in photosynthetic pigment-protein complexes has been observed even at physiological temperatures. Experiments have demonstrated quantum coherent behaviour in the long-time operation of the D-Wave quantum computer as well. Quantum coherence is the common feature between the two phenomena. An explanations for eight orders of magnitude discrepancy between the single flux qubit coherence time and the long-time quantum behaviour of an array of thousand flux qubits in the quantum computer was suggested within a theory where the flux qubits are coupled to an environment of part…
