Non-equilibrium stationary coherences in photosynthetic energy transfer under weak-field incoherent illumination

Frequency-Dependent Vibronic Effects in Steady State Energy Transport

The interplay between electronic and intramolecular high-frequency vibrational degrees of freedom is ubiquitous in natural light-harvesting systems. Recent studies have indicated that an intramolecular vibrational donor-acceptor frequency difference can enhance energy transport. Here, we analyze the extent to which different intramolecular donor-acceptor vibrational frequencies affect excitation energy transport in the natural nonequilibrium steady state configuration. Comments are included on the less physical equilibrium case for comparison with the literature. It is found that for constant Huang-Rhys factors, whereas the acceptor population increases in the equilibrium case when the intramolecular vibrational frequency of the acceptor exceeds that of the donor, this increase is negligible for the nonequilibrium steady state. Therefore, these changes in acceptor population do not significantly enhance energy transport in the nonequilibrium steady state for the natural scenario of incoherent light excitation with biologically relevant parameters of typical photosynthetic complexes. Insight about a potential mechanism to optimize energy transfer in the nonequilibrium steady state based on increasing the harvesting time at the reaction center is analyzed.

Memory effects in the efficiency control of energy transfer under incoherent light excitation in noisy environments

Fluctuations in energy gap and coupling constants between chromophores can play an important role in absorption and energy transfer across a collection of two-level systems. In photosynthesis, light-induced quantum coherence can affect the efficiency of energy transfer to the designated "trap" state. Theoretically, the interplay between fluctuations and coherence has been studied often, employing either a Markovian or a perturbative approximation. In this study, we depart from these approaches to incorporate memory effects by using Kubo's quantum stochastic Liouville equation. We introduce the effects of decay of the created excitation (to the ground state) on the desired propagation and trapping that provides a direction of flow of the excitation. In the presence of light-induced pumping, we establish a relation between the efficiency, the mean survival time, and the correlation decay time of the bath-induced fluctuations. A decrease in the steady-state coherence during the transition from the non-Markovian regime to the Markovian limit results in a decrease in efficiency. As in the well-known Haken-Strobl model, the ratio of the square of fluctuation strength to the rate plays a critical role in determining the mechanism of energy transfer and in shaping the characteristics of the efficiency profile. We recover a connection between the transfer flux and the imaginary part of coherences in both equilibrium and excited bath states, in both correlated and uncorrelated bath models. We uncover a non-monotonic dependence of efficiency on site energy heterogeneity for both correlated and uncorrelated bath models.

Light-Harvesting Efficiency Cannot Depend on Optical Coherence in the Absence of Orientational Order

The coherence of light has been proposed as a quantum-mechanical control for enhancing light-harvesting efficiency. In particular, optical coherence can be manipulated by changing either the polarization state or the spectral phase of the light. Here, we show that, in weak light, light-harvesting efficiency cannot be controlled using any form of optical coherence in molecular light-harvesting systems and, more broadly, those comprising orientationally disordered subunits and operating on longer-than-ultrafast time scales. Under those conditions, optical coherence does not affect the light-harvesting efficiency, meaning that it cannot be used for control. Specifically, polarization-state control is lost in disordered samples or when the molecules reorient on the time scales of light harvesting, and spectral-phase control is lost when the efficiency is time-averaged over a period longer than the optical coherence time. In practice, efficiency is always averaged over long times, meaning that coherent optical control is only possible through polarization and only in systems with orientational order.

Hyperacceleration of quantum thermalization dynamics by bypassing long-lived coherences: An analytical treatment

We develop a perturbative technique for solving Markovian quantum dissipative dynamics, with the perturbation parameter being a small gap in the eigenspectrum. As an example, we apply the technique and straightforwardly obtain analytically the dynamics of a three-level system with quasidegenerate excited states, where quantum coherences persist for very long times, proportional to the inverse of the energy splitting squared. We then show how to bypass this long-lived coherent dynamics and accelerate the relaxation to thermal equilibration in a hyper-exponential manner, a Markovian quantum-assisted Mpemba-like effect. This hyperacceleration of the equilibration process manifests if the initial state is carefully prepared, such that its coherences precisely store the amount of population relaxing from the initial condition to the equilibrium state. Our analytical method for solving quantum dissipative dynamics readily provides equilibration timescales, and as such it reveals how coherent and incoherent effects interlace in the dynamics. It further advises on how to accelerate relaxation processes, which is desirable when long-lived quantum coherences stagnate dynamics.

Modification of ground-state chemical reactivity via light-matter coherence in infrared cavities

Reaction-rate modifications for chemical processes due to strong coupling between reactant molecular vibrations and the cavity vacuum have been reported; however, no currently accepted mechanisms explain these observations. In this work, reaction-rate constants were extracted from evolving cavity transmission spectra, revealing resonant suppression of the intracavity reaction rate for alcoholysis of phenyl isocyanate with cyclohexanol. We observed up to an 80% suppression of the rate by tuning cavity modes to be resonant with the reactant isocyanate (NCO) stretch, the product carbonyl (CO) stretch, and cooperative reactant-solvent modes (CH). These results were interpreted using an open quantum system model that predicted resonant modifications of the vibrational distribution of reactants from canonical statistics as a result of light-matter quantum coherences, suggesting links to explore between chemistry and quantum science.

Quantum Kinetic Rates within the Nonequilibrium Steady State

The nonequilibrium steady state (NESS) of a quantum network is central to a host of physical and biological scenarios. Examples include natural processes such as vision and photosynthesis as well as technical devices such as photocells, both activated by incoherent light (e.g., sunlight) and leading to quantum transport. Assessing time scales of the relevant chemical processes in the steady state is thus of utmost interest and is our goal in this paper. Here, a completely general approach to defining components of a quantum network in the NESS and obtaining rates of processes between these components is provided. Quantum effects are explicitly included throughout, both in (a) defining network components via projection operators and (b) determining the role of coherences in rate processes. As examples, the methodology is applied to model cases, two versions of the V-level system, and to the spin-boson model, wherein the roles of the environment and of internal system properties in determining the rates are examined. In addition, the role of Markovian vs non-Markovian contributions is quantified, exposing conditions under which NESS rates can be obtained by perturbing the nonequilibrium steady state.

Electronic-Vibrational Resonance Does Not Significantly Alter Steady-State Transport in Natural Light-Harvesting Systems

Oscillations in time-dependent two-dimensional electronic spectra appear as evidence of quantum coherence in light-harvesting systems related to electronic-vibrational resonant interactions. Nature, however, takes place in a non-equilibrium steady-state; therefore, the relevance of these arguments to the natural process is unclear. Here, we examine the role of intramolecular vibrations in the non-equilibrium steady-state of photosynthetic dimers in the natural scenario of incoherent light excitation. Specifically, we analyze the PEB dimer in the cryptophyte algae PE545 antenna protein. It is found that vibrations resonant with the energy difference between exciton states only marginally increase the quantum yield and the imaginary part of the intersite coherence that is relevant for transport compared to non-resonant vibrations in the natural non-equilibrium steady-state. That is, the electronic-vibrational resonance interaction does not significantly enhance energy transport under natural incoherent light excitation conditions.

Long-lived quantum coherent dynamics of a Λ-system driven by a thermal environment

We present a theoretical study of quantum coherent dynamics of a three-level Λ-system driven by a thermal environment (such as blackbody radiation), which serves as an essential building block of photosynthetic light-harvesting models and quantum heat engines. By solving nonsecular Bloch-Redfield master equations, we obtain analytical results for the ground-state population and coherence dynamics and classify the dynamical regimes of the incoherently driven Λ-system as underdamped and overdamped depending on whether the ratio Δ/[rf(p)] is greater or less than one, where Δ is the ground-state energy splitting, r is the incoherent pumping rate, and f(p) is a function of the transition dipole alignment parameter p. In the underdamped regime, we observe long-lived coherent dynamics that lasts for τ_c ≃ 1/r, even though the initial state of the Λ-system contains no coherences in the energy basis. In the overdamped regime for p = 1, we observe the emergence of coherent quasi-steady states with the lifetime τ_c = 1.34(r/Δ²), which have a low von Neumann entropy compared to conventional thermal states. We propose an experimental scenario for observing noise-induced coherent dynamics in metastable He* atoms driven by x-polarized incoherent light. Our results suggest that thermal excitations can generate experimentally observable long-lived quantum coherent dynamics in the ground-state subspace of atomic and molecular Λ-systems in the absence of coherent driving.

Dynamics of photosynthetic light harvesting systems interacting with N-photon Fock states

We develop a method to simulate the excitonic dynamics of realistic photosynthetic light harvesting systems, including non-Markovian coupling to phonon degrees of freedom, under excitation by N-photon Fock state pulses. This method combines the input–output and the hierarchical equations of motion formalisms into a double hierarchy of density matrix equations. We show analytically that under weak field excitation relevant to natural photosynthesis conditions, an N-photon Fock state input and a corresponding coherent state input give rise to equal density matrices in the excited manifold. However, an N-photon Fock state input induces no off-diagonal coherence between the ground and excited subspaces, in contrast with the coherences created by a coherent state input. We derive expressions for the probability to absorb a single Fock state photon with or without the influence of phonons. For short pulses (or, equivalently, wide bandwidth pulses), we show that the absorption probability has a universal behavior that depends only upon a system-dependent effective energy spread parameter Δ and an exciton–light coupling constant Γ. This holds for a broad range of chromophore systems and for a variety of pulse shapes. We also analyze the absorption probability in the opposite long pulse (narrow bandwidth) regime. We then derive an expression for the long time emission rate in the presence of phonons and use it to study the difference between collective vs independent emission. Finally, we present a numerical simulation for the LHCII monomer (14-mer) system under single photon excitation that illustrates the use of the double hierarchy equations.

Computational elucidations on the role of vibrations in energy transfer processes of photosynthetic complexes

Coupling between pigment excitations and nuclear movements in photosynthetic complexes is known to modulate the excitation energy transfer (EET) efficiencies. Toward providing microscopic information, researchers often apply simulation techniques and investigate how vibrations are involved in EET processes. Here, reports on such roles of nuclear movements are discussed from a theory perspective. While vibrations naturally present random thermal fluctuations that can affect energy transferring characteristics, they can also be intertwined with exciton structures and create more specific non-adiabatic energy transfer pathways. For reliable simulations, a bath model that accurately mimics a given molecular system is required. Methods for obtaining such a model in combination with quantum chemical electronic structure calculations and molecular dynamics trajectory simulations are discussed. Various quantum dynamics simulation tools that can handle pigment-to-pigment energy transfers together with their vibrational characters are also touched on. Behaviors of molecular vibrations often deviate from ideality, especially when all-atom details are included, which practically forces us to treat them classically. We conclude this perspective by considering some recent reports that suggest that classical descriptions of bath effects with all-atom details may still produce valuable information for analyzing sophisticated contributions by vibrations to EET processes.

Funneling dynamics in a phenylacetylene trimer: Coherent excitation of donor excitonic states and their superposition

Funneling dynamics in conjugated dendrimers has raised great interest in the context of artificial light-harvesting processes. Photoinduced relaxation has been explored by time-resolved spectroscopy and simulations, mainly by semiclassical approaches or referring to open quantum systems methods, within the Redfield approximation. Here, we take the benefit of an ab initio investigation of a phenylacetylene trimer, and in the spirit of a divide-and-conquer approach, we focus on the early dynamics of the hierarchy of interactions. We build a simplified but realistic model by retaining only bright electronic states and selecting the vibrational domain expected to play the dominant role for timescales shorter than 500 fs. We specifically analyze the role of the in-plane high-frequency skeletal vibrational modes involving the triple bonds. Open quantum system non-adiabatic dynamics involving conical intersections is conducted by separating the electronic subsystem from the high-frequency tuning and coupling vibrational baths. This partition is implemented within a robust non-perturbative and non-Markovian method, here the hierarchical equations of motion. We will more precisely analyze the coherent preparation of donor states or of their superposition by short laser pulses with different polarizations. In particular, we extend the π-pulse strategy for the creation of a superposition to a V-type system. We study the relaxation induced by the high-frequency vibrational collective modes and the transitory dissymmetry, which results from the creation of a superposition of electronic donor states.

Environmentally Improved Coherent Light Harvesting

Coherence-enhanced light harvesting has not been directly observed experimentally, despite theoretical evidence that coherence can significantly enhance light-harvesting performance. The main experimental obstacle has been the difficulty in isolating the effect of coherence in the presence of confounding variables. Recent proposals for externally controlling coherence by manipulating the light's degree of polarization showed that coherent efficiency enhancements would be possible, but they were restricted to light-harvesting systems weakly coupled to their environment. Here, we show that increases in system-bath coupling strength can amplify coherent efficiency enhancements, rather than suppress them. This result dramatically broadens the range of systems that could be used to conclusively demonstrate coherence-enhanced light harvesting or to engineer coherent effects into artificial light-harvesting devices.

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

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

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

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

Energy transfer under natural incoherent light: Effects of asymmetry on efficiency

The non-equilibrium stationary coherences that form in donor-acceptor systems are investigated to determine their relationship to the efficiency of energy transfer to a neighboring reaction center. It is found that the effects of asymmetry in the dimer are generally detrimental to the transfer of energy. Four types of systems are examined, arising from combinations of localized trapping, delocalized (Forster) trapping, eigenstate dephasing, and site basis dephasing. In the cases of site basis dephasing, the interplay between the energy gap of the excited dimer states and the environment is shown to give rise to a turnover effect in the efficiency under weak dimer coupling conditions. Furthermore, the nature of the coherences and associated flux is interpreted in terms of pathway interference effects. In addition, regardless of the cases considered, the ratio of the real part and the imaginary part of the coherences in the energy-eigenbasis tends to a constant value in the steady state limit.

Steady-State Analysis of Light-Harvesting Energy Transfer Driven by Incoherent Light: From Dimers to Networks

The question of how quantum coherence facilitates energy transfer has been intensively debated in the scientific community. Since natural and artificial light-harvesting units operate under the stationary condition, we address this question via a nonequilibrium steady-state analysis of a molecular dimer irradiated by incoherent sunlight and then generalize the key predictions to arbitrarily complex exciton networks. The central result of the steady-state analysis is the coherence-flux-efficiency relation: η = c∑_i≠jF_ijκ_j = 2c∑_i≠jJ_ijIm[ρ_ij]κ_j, where c is the normalization constant. In this relation, the first equality indicates that the energy transfer efficiency, η, is uniquely determined by the trapping flux, which is the product of the flux, F, and branching ratio, κ, for trapping at the reaction centers, and the second equality indicates that the energy transfer flux, F, is equivalent to the quantum coherence measured by the imaginary part of the off-diagonal density matrix, that is, F_ij = 2J_ijIm[ρ_ij]. Consequently, maximal steady-state coherence gives rise to optimal efficiency. The coherence-flux-efficiency relation holds rigorously and generally for any exciton network of arbitrary connectivity under the stationary condition and is not limited to incoherent radiation or incoherent pumping. For light-harvesting systems under incoherent light, the nonequilibrium energy transfer flux (i.e., steady-state coherence) is driven by the breakdown of detailed balance and by the quantum interference of light excitations and leads to the optimization of energy transfer efficiency. It should be noted that the steady-state coherence or, equivalently, efficiency is the combined result of light-induced transient coherence, inhomogeneous depletion, and the system-bath correlation and is thus not necessarily correlated with quantum beatings. These findings are generally applicable to quantum networks and have implications for quantum optics and devices.

Photon Correlation Spectroscopy as a Witness for Quantum Coherence

The development of spectroscopic techniques able to detect and verify quantum coherence is a goal of increasing importance given the rapid progress of new quantum technologies, the advances in the field of quantum thermodynamics, and the emergence of new questions in chemistry and biology regarding the possible relevance of quantum coherence in biochemical processes. Ideally, these tools should be able to detect and verify the presence of quantum coherence in both the transient dynamics and the steady state of driven-dissipative systems, such as light-harvesting complexes driven by thermal photons in natural conditions. This requirement poses a challenge for standard laser spectroscopy methods. Here, we propose photon correlation measurements as a new tool to analyze quantum dynamics in molecular aggregates in driven-dissipative situations. We show that the photon correlation statistics of the light emitted in several models of molecular aggregates can signal the presence of coherent dynamics. Deviations from the counting statistics of independent emitters constitute a direct fingerprint of quantum coherence in the steady state. Furthermore, the analysis of frequency resolved photon correlations can signal the presence of coherent dynamics even in the absence of steady state coherence, providing direct spectroscopic access to the much sought-after site energies in molecular aggregates.

LH1-RC light-harvesting photocycle under realistic light-matter conditions

Quantum master equations are used to simulate the photocycle of the light-harvesting complex 1 (LH1) and the associated reaction center (RC) in purple bacteria excited with natural incoherent light. The influence of the radiation and protein environments and the full photocycle of the complexes, including the charge separation and RC recovery processes, are taken into account. Particular emphasis is placed on the steady state excitation energy transfer rate between the LH1 and the RC and the steady state dependence on the light intensity. The transfer rate is shown to scale linearly with light intensity near the value in the natural habitat and at higher light intensities is found to be bounded by the rate-determining step of the photocycle, the RC recovery rate. Transient (e.g., pulsed laser induced) dynamics, however, shows rates higher than the steady state value and continues to scale linearly with the intensity. The results show a correlation between the transfer rate and the manner in which the donor state is prepared. In addition, the transition from the transient to the steady state results can be understood as a cascade of ever slower rate-determining steps and quasi-stationary states inherent in multi-scale sequential processes. This type of transition of rates is relevant in most light-induced biological machinery.

Classification of Coherent Enhancements of Light-Harvesting Processes

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

Photochemical dynamics under incoherent illumination: Light harvesting in self-assembled molecular J-aggregates

Transport phenomena in organic, self-assembled molecular J-aggregates have long attracted a great deal of attention due to their 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 building blocks of organic solar cells. Under natural conditions, J-aggregates would be subjected to an incoherent source of light (as is sunlight), which would illuminate the whole photosynthetic complex rather than a single molecule. In this work, we present the first study of the efficiency of photosynthetic energy transport in self-assembled molecular aggregates under incoherent sunlight illumination. By making use of a minimalistic model of a cyanine dye J-aggregate, we demonstrate that long-range transport efficiency is enhanced when exciting the aggregate with incoherent light. Our results thus support the conclusion that J-aggregates are, indeed, excellent candidates for devices where efficient long-range incoherently induced exciton transport is desired, such as in highly efficient organic solar cells.

Shedding (Incoherent) Light on Quantum Effects in Light-Induced Biological Processes

Light-induced processes that occur in nature, such as photosynthesis and photoisomerization in the first steps in vision, are often studied in the laboratory using coherent pulsed laser sources, which induce time-dependent coherent wavepacket molecule dynamics. Nature, however, uses stationary incoherent thermal radiation, such as sunlight, leading to a totally different molecular response, the time-independent steady state. It is vital to appreciate this difference in order to assess the role of quantum coherence effects in biological systems. Developments in this area are discussed in detail.