Elucidation of the timescales and origins of quantum electronic coherence in LHCII

Energy transfer in N-component nanosystems enhanced by pulse-driven vibronic many-body entanglement

The processing of energy by transfer and redistribution, plays a key role in the evolution of dynamical systems. At the ultrasmall and ultrafast scale of nanosystems, quantum coherence could in principle also play a role and has been reported in many pulse-driven nanosystems (e.g. quantum dots and even the microscopic Light-Harvesting Complex II (LHC-II) aggregate). Typical theoretical analyses cannot easily be scaled to describe these general N-component nanosystems; they do not treat the pulse dynamically; and they approximate memory effects. Here our aim is to shed light on what new physics might arise beyond these approximations. We adopt a purposely minimal model such that the time-dependence of the pulse is included explicitly in the Hamiltonian. This simple model generates complex dynamics: specifically, pulses of intermediate duration generate highly entangled vibronic (i.e. electronic-vibrational) states that spread multiple excitons - and hence energy - maximally within the system. Subsequent pulses can then act on such entangled states to efficiently channel subsequent energy capture. The underlying pulse-generated vibronic entanglement increases in strength and robustness as N increases.

A quantum trajectory picture of single photon absorption and energy transport in photosystem II

We use quantum trajectory theory to study the dynamics of the first step in photosynthesis for a single photon interacting with photosystem II (PSII). By considering individual trajectories we are able to look beyond the ensemble average dynamics to compute the PSII system evolution conditioned upon individual photon counting measurements. Measurements of the transmitted photon beam strongly affects the system state, since detection of an outgoing photon confirms that the PSII must be in the electronic ground state, while a null measurement implies it is in an excited electronic state. We show that under ideal conditions, observing the null result transforms a state with a low excited state population to a state with nearly all population contained in the excited states. We study the PSII dynamics conditioned on such photon counting for both a pure excitonic model of PSII and a more realistic model with exciton-phonon coupling to a dissipative phononic environment. In the absence of such coupling, we show that the measured fluorescence rates show oscillations constituting a photon-counting witness of excitonic coherence. Excitonic coupling to the phonon environment has a strong effect on the observed rates of fluorescence, damping the oscillations. Addition of non-radiative decay and incoherent transitions to radical pair states in the reaction center to the phononic model allows extraction of a quantum efficiency of 92.5% from the long-time evolution, consistent with bulk experimental measurements.

Probing exciton dynamics with spectral selectivity through the use of quantum entangled photons

Quantum light is increasingly recognized as a promising resource for developing optical measurement techniques. Particular attention has been paid to enhancing the precision of the measurements beyond classical techniques by using nonclassical correlations between quantum entangled photons. Recent advances in the quantum optics technology have made it possible to manipulate spectral and temporal properties of entangled photons, and photon correlations can facilitate the extraction of matter information with relatively simple optical systems compared to conventional schemes. In these respects, the applications of entangled photons to time-resolved spectroscopy can open new avenues for unambiguously extracting information on dynamical processes in complex molecular and materials systems. Here, we propose time-resolved spectroscopy in which specific signal contributions are selectively enhanced by harnessing nonclassical correlations of entangled photons. The entanglement time characterizes the mutual delay between an entangled twin and determines the spectral distribution of photon correlations. The entanglement time plays a dual role as the knob for controlling the accessible time region of dynamical processes and the degrees of spectral selectivity. In this sense, the role of the entanglement time is substantially equivalent to the temporal width of the classical laser pulse. The results demonstrate that the application of quantum entangled photons to time-resolved spectroscopy leads to monitoring dynamical processes in complex molecular and materials systems by selectively extracting desired signal contributions from congested spectra. We anticipate that more elaborately engineered photon states would broaden the availability of quantum light spectroscopy.

Modeling of the entangled states transfer processes in microtubule tryptophan system

The paper simulates the process of the migration of a single energy excitation along a chain of tryptophans in cell microtubules connected by dipole-dipole interaction. The paper shows that the excited states propagation rate falls within the range of nerve impulse velocity. It was shown that such a process also causes a transfer of quantum entanglement between tryptophans, so that microtubules can be considered as signaling system, the basis for transmitting information via the quantum channel. The conditions under which the migration of entangled states in the microtubule is possible are obtained. In a certain sense, it allows us to argue that the signal function of tryptophans works as an analogue of a quantum repeater that transmits entangled states over microtubule by relaying through intermediate tryptophans. Thus, the paper shows that the tryptophan system can be considered as an environment that supports the existence of entangled states during the time comparable with the time of the processes in biosystems.

Spin selection in atomic-level chiral metal oxide for photocatalysis

The spin degree of freedom is an important and intrinsic parameter in boosting carrier dynamics and surface reaction kinetics of photocatalysis. Here we show that chiral structure in ZnO can induce spin selectivity effect to promote photocatalytic performance. The ZnO crystals synthesized using chiral methionine molecules as symmetry-breaking agents show hierarchical chirality. Magnetic circular dichroism spectroscopic and magnetic conductive-probe atomic force microscopic measurements demonstrate that chiral structure acts as spin filters and induces spin polarization in photoinduced carriers. The polarized carriers not only possess the prolonged carrier lifetime, but also increase the triplet species instead of singlet byproducts during reaction. Accordingly, the left- and right-hand chiral ZnO exhibit 2.0- and 1.9-times higher activity in photocatalytic O₂ production and 2.5- and 2.0-times higher activities in contaminant photodegradation, respectively, compared with achiral ZnO. This work provides a feasible strategy to manipulate the spin properties in metal oxides for electron spin-related redox catalysis.

Revealing Intermolecular Electronic and Vibronic Coherence with Polarization-Dependent Two-Dimensional Beating Maps

Two-dimensional electronic spectroscopy (2DES) has been widely employed as an efficient tool to reveal the impact of intermolecular electronic and/or vibronic quantum coherence on excitation energy transfer in light-harvesting complexes. However, intramolecular vibrational coherence would also contribute to oscillating signals in 2D spectra, along with the intermolecular coherence signals that are directly related to energy transfer. In this work, the possibility of screening the vibrational coherence signals is explored through polarization-dependent 2DES. The all-parallel (AP) and double-crossed (DC) polarization-dependent two-dimensional rephasing spectra (2DRS) are simulated for a minimalist heterodimer model with vibrational coupling. By combining the DC-2DRS and the 2D beating maps, we demonstrate that the population and vibrational coherence signals can be largely suppressed, resulting in highlighted intermolecular electronic and vibronic coherence signals. Moreover, the AP- and DC-2DBMs show rather different patterns at the vibrational frequency, indicating a possible way to identify pure vibrational coherence.

Conformation of Light-Harvesting Complex II Trimer Depends upon Its Binding Site

The light-harvesting complex II (LHCII) trimer in plants functions as a major antenna complex and a quencher to protect it from photooxidative damage. Theoretical studies on the structure of an LHCII trimer have demonstrated that excitation energy transfer between chlorophylls (Chls) in LHCII can be modulated by its exquisite conformational fluctuation. However, conformational changes depending on its binding location have not yet been investigated, even though reorganization of protein complexes occurs by physiological regulations. In this study, we investigated conformational differences in LHCII by comparing published structures of an identical LHCII trimer in the three different photosystem supercomplexes from the green alga Chlamydomonas reinhardtii. Our results revealed distinct differences in Chl configurations as well as polypeptide conformations of the LHCII trimers depending on its binding location. We propose that these configurational differences readily modulate the function of LHCII and possibly lead to a change in excitation-energy flow over the photosynthetic supercomplex.

π-Stacking-Dependent Vibronic Couplings Drive Excited-State Dynamics in Perylenediimide Assemblies

Vibronic coupling, the interplay of electronic and nuclear vibrational motion, is considered a critical mechanism in photoinduced reactions such as energy transfer, charge transfer, and singlet fission. However, our understanding of how particular vibronic couplings impact excited-state dynamics is lacking due to the limited number of experimental studies of model molecular systems. Herein, we use two-dimensional electronic spectroscopy (2DES) to launch and interrogate a range of vibronic coherences in two distinct types of perylenediimide slip stacks─along the short and long molecular axes, which form either an excimer or a mixed state between the Frenkel exciton (FE) and charge transfer states. We explore the functionality of these vibronic coherences using quantum beatmaps, which display the Fourier amplitude signal oscillations as a function of pump and probe frequencies, along with knowledge of the characteristic signatures of the FE, ionic, and excimer species. We find that a low-frequency vibrational mode of the short-axis slip stack appears concomitantly with the formation of the excimer state, survives 2-fold longer than in the FE state in the reference monomer, and shows a phase shift compared to other modes. For the long-axis slip stacks, a pair of low-frequency modes coupled to a high-frequency coordinate of the FE state were found to play a critical role in mixed-state generation. Our findings thus experimentally reveal the complex and varying roles of vibronic couplings in tightly packed multimers undergoing a range of photoinduced processes.

Vibrational and vibronic coherences in the energy transfer process of light-harvesting complex II revealed by two-dimensional electronic spectroscopy

The presence of quantum coherence in light-harvesting complex II (LHCII) as a mechanism to understand the efficiency of the light-harvesting function in natural photosynthetic systems is still debated due to its structural complexity and weak-amplitude coherent oscillations. Here, we revisit the coherent dynamics and clarify different types of coherences in the energy transfer processes of LHCII using a joint method of the high-S/N transient grating and two-dimensional electronic spectroscopy. We find that the electronic coherence decays completely within 50 fs at room temperature. The vibrational coherences of chlorophyll a dominate over oscillations within 1 ps, whereas a low-frequency mode of 340 cm−1 with a vibronic mixing character may participate in vibrationally assisted energy transfer between chlorophylls a. Our results may suggest that vibronic mixing is relevant for rapid energy transfer processes among chlorophylls in LHCII.

A polarization scheme that resolves cross-peaks with transient absorption and eliminates diagonal peaks in 2D spectroscopy

Two-dimensional (2D) optical spectroscopy contains cross-peaks that are helpful features for determining molecular structure and monitoring energy transfer, but they can be difficult to resolve from the much more intense diagonal peaks. Transient absorption (TA) spectra contain transitions similar to cross-peaks in 2D spectroscopy, but in most cases they are obscured by the bleach and stimulated emission peaks. We report a polarization scheme, <0°,0°,+θ₂(t₂),-θ₂(t₂)>, that can be easily implemented in the pump-probe beam geometry, used most frequently in 2D and TA spectroscopy. This scheme removes the diagonal peaks in 2D spectroscopies and the intense bleach/stimulated emission peaks in TA spectroscopies, thereby resolving the cross-peak features. At zero pump-probe delay, θ₂ = 60° destructively interferes two Feynman paths, eliminating all signals generated by field interactions with four parallel transition dipoles, and the intense diagonal and bleach/stimulated emission peaks. At later delay times, θ₂(t₂) is adjusted to compensate for anisotropy caused by rotational diffusion. When implemented with TA spectroscopy or microscopy, the pump-probe spectrum is dominated by the cross-peak features. The local oscillator is also attenuated, which enhances the signal two times. This overlooked polarization scheme reduces spectral congestion by eliminating diagonal peaks in 2D spectra and enables TA spectroscopy to measure similar information given by cross-peaks in 2D spectroscopy.

A partially linearized spin-mapping approach for simulating nonlinear optical spectra

We present a partially linearized method based on spin-mapping for computing both linear and nonlinear optical spectra. As observables are obtained from ensembles of classical trajectories, the approach can be applied to the large condensed-phase systems that undergo photosynthetic light-harvesting processes. In particular, the recently derived spin partially linearized density matrix method has been shown to exhibit superior accuracy in computing population dynamics compared to other related classical-trajectory methods. Such a method should also be ideally suited to describing the quantum coherences generated by interaction with light. We demonstrate that this is, indeed, the case by calculating the nonlinear optical response functions relevant for the pump-probe and 2D photon-echo spectra for a Frenkel biexciton model and the Fenna-Matthews-Olsen light-harvesting complex. One especially desirable feature of our approach is that the full spectrum can be decomposed into its constituent components associated with the various Liouville-space pathways, offering a greater insight beyond what can be directly obtained from experiments.

Multimode two-dimensional vibronic spectroscopy. II. Simulating and extracting vibronic coupling parameters from polarization-selective spectra

Experimental demonstrations of polarization-selection two-dimensional Vibrational-Electronic (2D VE) and 2D Electronic-Vibrational (2D EV) spectroscopies aim to map the magnitudes and spatial orientations of coupled electronic and vibrational coordinates in complex systems. The realization of that goal depends on our ability to connect spectroscopic observables with molecular structural parameters. In this paper, we use a model Hamiltonian consisting of two anharmonically coupled vibrational modes in electronic ground and excited states with linear and bilinear vibronic coupling terms to simulate polarization-selective 2D EV and 2D VE spectra. We discuss the relationships between the linear vibronic coupling and two-dimensional Huang-Rhys parameters and between the bilinear vibronic coupling term and Duschinsky mixing. We develop a description of the vibronic transition dipoles and explore how the Hamiltonian parameters and non-Condon effects impact their amplitudes and orientations. Using simulated polarization-selective 2D EV and 2D VE spectra, we show how 2D peak positions, amplitudes, and anisotropy can be used to measure parameters of the vibronic Hamiltonian and non-Condon effects. This paper, along with the first in the series, provides the reader with a detailed description of reading, simulating, and analyzing multimode, polarization-selective 2D EV and 2D VE spectra with an emphasis on extracting vibronic coupling parameters from complex spectra.

Multimode two-dimensional vibronic spectroscopy. I. Orientational response and polarization-selectivity

Two-dimensional Electronic-Vibrational (2D EV) spectroscopy and two-dimensional Vibrational-Electronic (2D VE) spectroscopy are among the newest additions to the coherent multidimensional spectroscopy toolbox, and they are directly sensitive to vibronic couplings. In this first of two papers, the complete orientational response functions are developed for a model system consisting of two coupled anharmonic oscillators and two electronic states in order to simulate polarization-selective 2D EV and 2D VE spectra with arbitrary combinations of linearly polarized electric fields. Here, we propose analytical methods to isolate desired signals within complicated spectra and to extract the relative orientation between vibrational and vibronic dipole moments of the model system using combinations of polarization-selective 2D EV and 2D VE spectral features. Time-dependent peak amplitudes of coherence peaks are also discussed as means for isolating desired signals within the time-domain. This paper serves as a field guide for using polarization-selective 2D EV and 2D VE spectroscopies to map coupled vibronic coordinates on the molecular frame.

Anisotropy in fifth-order exciton-exciton-interaction two-dimensional spectroscopy

Exciton-exciton-interaction two-dimensional (EEI2D) spectroscopy is a fifth-order variant of 2D electronic spectroscopy. It can be used to probe biexciton dynamics in molecular systems and to observe exciton diffusion in extended systems such as polymers or light-harvesting complexes. The exciton transport strongly depends on the geometrical and energetic landscape and its perturbations. These can be of both local character, such as molecular orientation and energetic disorder, and long-range character, such as polymer kinks and structural domains. In the present theoretical work, we investigate the anisotropy in EEI2D spectroscopy. We introduce a general approach for how to calculate the anisotropy by using the response-function formalism in an efficient way. In numerical simulations, using a Frenkel exciton model with Redfield-theory dynamics, we demonstrate how the measurement of anisotropy in EEI2D spectroscopy can be used to identify various geometrical effects on exciton transport in dimers and polymers. Investigating a molecular heterodimer as an example, we demonstrate the utility of anisotropy in EEI2D spectroscopy for disentangling dynamic localization and annihilation. We further calculate the annihilation in extended systems such as conjugated polymers. In a polymer, a change in the anisotropy provides a unique signature for exciton transport between differently oriented sections. We analyze three types of geometry variations in polymers: a kink, varying geometric and energetic disorder, and different geometric domains. Our findings underline that employing anisotropy in EEI2D spectroscopy provides a way to distinguish between different geometries and can be used to obtain a better understanding of long-range exciton transport.

Model-Independent Simulation Complexity of Complex Quantum Dynamics

We present a model-independent measure of dynamical complexity based on simulation of complex quantum dynamics using stroboscopic Markovian dynamics. Tools from classical signal processing enable us to infer the Hilbert space dimension of the complex quantum system evolving under a time-independent Hamiltonian via pulsed interrogation. We illustrate this using simulated third-order pump-probe spectroscopy data for exciton transport in a toy model of a coupled dimer with vibrational levels, revealing the dimension of the singly excited manifold of the dimer. Finally, we probe the complexity of excitonic transport in light harvesting 2 (LH2) and Fenna-Matthews-Olson (FMO) complexes using data from two recent nonlinear ultrafast optical spectroscopy experiments. For the latter we make model-independent inferences that are commensurate with model-specific ones, including the estimation of the fewest number of parameters needed to fit the experimental data and identifying the spatial extent, i.e., delocalization size, of quantum states participating in this complex quantum dynamics.

Insights into Photosynthetic Energy Transfer Gained from Free-Energy Structure: Coherent Transport, Incoherent Hopping, and Vibrational Assistance Revisited

Giant strides in ultrashort laser pulse technology have enabled real-time observation of dynamical processes in complex molecular systems. Specifically, the discovery of oscillatory transients in the two-dimensional electronic spectra of photosynthetic systems stimulated a number of theoretical investigations exploring the possible physical mechanisms of the remarkable quantum efficiency of light harvesting processes. In this work, we revisit the elementary aspects of environment-induced fluctuations in the involved electronic energies and present a simple way to understand energy flow with the intuitive picture of relaxation in a funnel-type free-energy landscape. The presented free-energy description of energy transfer reveals that typical photosynthetic systems operate in an almost barrierless regime. The approach also provides insights into the distinction between coherent and incoherent energy transfer and the criteria by which the necessity of the vibrational assistance is considered.

The role of mixed vibronic Qy-Qx states in green light absorption of light-harvesting complex II

The importance of green light for driving natural photosynthesis has long been underappreciated, however, under the presence of strong illumination, green light actually drives photosynthesis more efficiently than red light. This green light is absorbed by mixed vibronic Q_y-Q_x states, arising from chlorophyll (Chl)-Chl interactions, although almost nothing is known about these states. Here, we employ polarization-dependent two-dimensional electronic-vibrational spectroscopy to study the origin and dynamics of the mixed vibronic Q_y-Q_x states of light-harvesting complex II. We show the states in this region dominantly arise from Chl b and demonstrate how it is possible to distinguish between the degree of vibronic Q_y versus Q_x character. We find that the dynamics for states of predominately Chl b Q_y versus Chl b Q_x character are markedly different, as excitation persists for significantly longer in the Q_x states and there is an oscillatory component to the Q_x dynamics, which is discussed. Our findings demonstrate the central role of electronic-nuclear mixing in efficient light-harvesting and the different functionalities of Chl a and Chl b.

The green component of the solar spectrum can efficiently drive natural photosynthesis, but the process has been little investigated due to the complexity of the excited states involved. Here the authors utilize polarization-dependent two-dimensional electronic-vibrational spectroscopy to define the origin and dynamics of these states in light-harvesting complex II.

Observation of Ultrafast Coherence Transfer and Degenerate States with Polarization-Controlled Two-Dimensional Electronic Spectroscopy

Optical spectroscopy is a powerful tool to interrogate quantum states of matter. We present simulation results for the cross-polarized two-dimensional electronic spectra of the light-harvesting system LH2 of purple bacteria. We identify a spectral feature on the diagonal, which we assign to ultrafast coherence transfer between degenerate states. The implication for the interpretation of previous experiments on different systems and the potential use of this feature are discussed. In particular, we foresee that this kind of feature will be useful for identifying mixed degenerate states and for identifying the origin of symmetry breaking disorder in systems like LH2. Furthermore, this may help identify both vibrational and electronic states in biological systems such as proteins and solid-state materials such as hybrid perovskites.

DNA scaffold supports long-lived vibronic coherence in an indodicarbocyanine (Cy5) dimer

Vibronic coupling between pigment molecules is believed to prolong coherences in photosynthetic pigment–protein complexes. Reproducing long-lived coherences using vibronically coupled chromophores in synthetic DNA constructs presents a biomimetic route to efficient artificial light harvesting. Here, we present two-dimensional (2D) electronic spectra of one monomeric Cy5 construct and two dimeric Cy5 constructs (0 bp and 1 bp between dyes) on a DNA scaffold and perform beating frequency analysis to interpret observed coherences. Power spectra of quantum beating signals of the dimers reveal high frequency oscillations that correspond to coherences between vibronic exciton states. Beating frequency maps confirm that these oscillations, 1270 cm⁻¹ and 1545 cm⁻¹ for the 0-bp dimer and 1100 cm⁻¹ for the 1-bp dimer, are coherences between vibronic exciton states and that these coherences persist for ∼300 fs. Our observations are well described by a vibronic exciton model, which predicts the excitonic coupling strength in the dimers and the resulting molecular exciton states. The energy spacing between those states closely corresponds to the observed beat frequencies. MD simulations indicate that the dyes in our constructs lie largely internal to the DNA base stacking region, similar to the native design of biological light harvesting complexes. Observed coherences persist on the timescale of photosynthetic energy transfer yielding further parallels to observed biological coherences, establishing DNA as an attractive scaffold for synthetic light harvesting applications.

Dyes coupled to DNA display distance-dependent vibronic couplings that prolongs quantum coherences detected with 2D spectroscopy.

Exciton properties and optical spectra of light harvesting complex II from a fully atomistic description

We present a fully atomistic simulation of linear optical spectra (absorption, fluorescence and circular dichroism) of the Light Harvesting Complex II (LHCII) trimer using a hybrid approach, which couples a quantum chemical description of the chlorophylls with a classical model for the protein and the external environment (membrane and water). The classical model uses a polarizable Molecular Mechanics force field, thus allowing mutual polarization effects in the calculations of the excitonic properties. The investigation is performed both on the crystal structure and on structures generated by a μs long classical molecular dynamics simulation of the complex within a solvated membrane. The results show that this integrated approach not only provides a good description of the excitonic properties and optical spectra without the need for additional refinements of the excitonic parameters, but it also allows an atomistic investigation of the relative importance of electronic, structural and environment effects in determining the optical spectra.

Monitoring the evolution of intersite and interexciton coherence in electronic excitation transfer via wave-packet interferometry

We detail an experimental strategy for tracking the generation and time-development of electronic coherence within the singly excited manifold of an energy-transfer dimer. The technique requires that the two monomers have nonparallel electronic transition-dipole moments and that these possess fixed orientations in space. It makes use of two-dimensional wave-packet interferometry (WPI or whoopee) measurements in which the A, B, C, and D pulses have respective polarizations e, e, e, and e'. In the case of energy-transfer coupling that is weak or strong compared to electronic-nuclear interactions, it is convenient to follow the evolution of intersite or interexciton coherence, respectively. Under weak coupling, e could be perpendicular to the acceptor chromophore's transition dipole moment and the unit vector e' would be perpendicular to the donor's transition dipole. Under strong coupling, e could be perpendicular to the ground-to-excited transition dipole to the lower exciton level and e' would be perpendicular to the ground-to-excited transition dipole to the upper exciton level. If the required spatial orientation can be realized for an entire ensemble, experiments of the kind proposed could be performed by either conventional four-wave-mixing or fluorescence-detected WPI methods. Alternatively, fluorescence-detected whoopee experiments of this kind could be carried out on a single energy-transfer dimer of fixed orientation. We exhibit detailed theoretical expressions for the desired WPI signal, explain the physical origin of electronic coherence detection, and show calculated observed-coherence signals for model dimers with one, two, or three internal vibrational modes per monomer and both weak and strong energy-transfer coupling.

Effect of disorder and polarization sequences on two-dimensional spectra of light-harvesting complexes

Two-dimensional electronic spectra (2DES) provide unique ways to track the energy transfer dynamics in light-harvesting complexes. The interpretation of the peaks and structures found in experimentally recorded 2DES is often not straightforward, since several processes are imaged simultaneously. The choice of specific pulse polarization sequences helps to disentangle the sometimes convoluted spectra, but brings along other disturbances. We show by detailed theoretical calculations how 2DES of the Fenna-Matthews-Olson complex are affected by rotational and conformational disorder of the chromophores.

Quantum biology revisited

Photosynthesis is a highly optimized process from which valuable lessons can be learned about the operating principles in nature. Its primary steps involve energy transport operating near theoretical quantum limits in efficiency. Recently, extensive research was motivated by the hypothesis that nature used quantum coherences to direct energy transfer. This body of work, a cornerstone for the field of quantum biology, rests on the interpretation of small-amplitude oscillations in two-dimensional electronic spectra of photosynthetic complexes. This Review discusses recent work reexamining these claims and demonstrates that interexciton coherences are too short lived to have any functional significance in photosynthetic energy transfer. Instead, the observed long-lived coherences originate from impulsively excited vibrations, generally observed in femtosecond spectroscopy. These efforts, collectively, lead to a more detailed understanding of the quantum aspects of dissipation. Nature, rather than trying to avoid dissipation, exploits it via engineering of exciton-bath interaction to create efficient energy flow.

Vibronic mixing enables ultrafast energy flow in light-harvesting complex II

Since the discovery of quantum beats in the two-dimensional electronic spectra of photosynthetic pigment-protein complexes over a decade ago, the origin and mechanistic function of these beats in photosynthetic light-harvesting has been extensively debated. The current consensus is that these long-lived oscillatory features likely result from electronic-vibrational mixing, however, it remains uncertain if such mixing significantly influences energy transport. Here, we examine the interplay between the electronic and nuclear degrees of freedom (DoF) during the excitation energy transfer (EET) dynamics of light-harvesting complex II (LHCII) with two-dimensional electronic-vibrational spectroscopy. Particularly, we show the involvement of the nuclear DoF during EET through the participation of higher-lying vibronic chlorophyll states and assign observed oscillatory features to specific EET pathways, demonstrating a significant step in mapping evolution from energy to physical space. These frequencies correspond to known vibrational modes of chlorophyll, suggesting that electronic-vibrational mixing facilitates rapid EET over moderately size energy gaps.

Does electronic coherence enhance anticorrelated pigment vibrations under realistic conditions?

The light-harvesting efficiency of a photoactive molecular complex is largely determined by the properties of its electronic quantum states. Those, in turn, are influenced by molecular vibrational states of the nuclear degrees of freedom. Here, we reexamine two recently formulated concepts that a coherent vibronic coupling between molecular states would either extend the electronic coherence lifetime or enhance the amplitude of the anticorrelated vibrational mode at longer times. For this, we study a vibronically coupled dimer and calculate the nonlinear two-dimensional (2D) electronic spectra that directly reveal electronic coherence. The time scale of electronic coherence is initially extracted by measuring the antidiagonal bandwidth of the central peak in the 2D spectrum at zero waiting time. Based on the residual analysis, we identify small-amplitude long-lived oscillations in the cross-peaks, which, however, are solely due to groundstate vibrational coherence, regardless of having resonant or off-resonant conditions. Our studies neither show an enhancement of the electronic quantum coherence nor an enhancement of the anticorrelated vibrational mode by the vibronic coupling under ambient conditions.

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.

Modification of excitation and charge transfer in cavity quantum-electrodynamical chemistry

Excitation and charge transfer are fundamental processes in nature, and controlling these processes is a major goal of quantum chemistry. While these processes are well understood for the usual free-space case, when the electromagnetic vacuum is changed due to, e.g., a cavity, these processes can be dramatically different. We consider these changes in transfer processes with real-space donor–acceptor models, where we put an emphasis on the impact of electron–electron correlations. We find results in line with recent experiments, where strong light–matter interaction leads to enhanced transfer reactions, even when in the corresponding free-space situation no transfer should be possible. We highlight that the processes depend crucially on the Coulomb and self-polarization interactions.

Energy transfer in terms of excitation or charge is one of the most basic processes in nature, and understanding and controlling them is one of the major challenges of modern quantum chemistry. In this work, we highlight that these processes as well as other chemical properties can be drastically altered by modifying the vacuum fluctuations of the electromagnetic field in a cavity. By using a real-space formulation from first principles that keeps all of the electronic degrees of freedom in the model explicit and simulates changes in the environment by an effective photon mode, we can easily connect to well-known quantum-chemical results such as Dexter charge-transfer and Förster excitation-transfer reactions, taking into account the often-disregarded Coulomb and self-polarization interaction. We find that the photonic degrees of freedom introduce extra electron–electron correlations over large distances and that the coupling to the cavity can drastically alter the characteristic charge-transfer behavior and even selectively improve the efficiency. For excitation transfer, we find that the cavity renders the transfer more efficient, essentially distance-independent, and further different configurations of highest efficiency depending on the coherence times. For strong decoherence (short coherence times), the cavity frequency should be in between the isolated excitations of the donor and acceptor, while for weak decoherence (long coherence times), the cavity should enhance a mode that is close to resonance with either donor or acceptor. Our results highlight that changing the photonic environment can redefine chemical processes, rendering polaritonic chemistry a promising approach toward the control of chemical reactions.

Double-crossed polarization transient grating for distinction and characterization of coherences

Coherent phenomena have been widely suggested to play a role in efficient photosynthetic light harvesting and charge separation processes. To substantiate these ideas, separation of intramolecular vibrational coherences from purely electronic or mixed vibronic coherences is essential. To this end, polarization-controlled two-dimensional electronic spectroscopy has been shown to provide an effective selectivity. We show that analogous discrimination can be achieved in a transient grating experiment by employing the double-crossed polarization scheme. This is demonstrated in a study of bacterial reaction centers. Significantly faster acquisition times of these experiments make longer population time scans feasible, thereby achieving improved frequency resolution and allowing for accurate extraction of coherence frequencies and dephasing times. These parameters are crucial for the discussion on relevance of the measured coherences to energy or electron transfer phenomena.

Coherent phenomena in photosynthetic light harvesting: part two-observations in biological systems

Considerable debate surrounds the question of whether or not quantum mechanics plays a significant, non-trivial role in photosynthetic light harvesting. Many have proposed that quantum superpositions and/or quantum transport phenomena may be responsible for the efficiency and robustness of energy transport present in biological systems. The critical experimental observations comprise the observation of coherent oscillations or "quantum beats" via femtosecond laser spectroscopy, which have been observed in many different light harvesting systems. Part Two of this review aims to provide an overview of experimental observations of energy transfer in the most studied light harvesting systems. Length scales, derived from crystallographic studies, are combined with energy and time scales of the beats observed via spectroscopy. A consensus is emerging that most long-lived (hundreds of femtoseconds) coherent phenomena are of vibrational or vibronic origin, where the latter may result in coherent excitation transport within a protein complex. In contrast, energy transport between proteins is likely to be incoherent in nature. The question of whether evolution has selected for these non-trivial quantum phenomena may be an unanswerable question, as dense packings of chromophores will lead to strong coupling and hence non-trivial quantum phenomena. As such, one cannot discern whether evolution has optimised light harvesting systems for high chromophore density or for the ensuing quantum effects as these are inextricably linked and cannot be switched off.

Identification and characterization of diverse coherences in the Fenna-Matthews-Olson complex

The idea that excitonic (electronic) coherences are of fundamental importance to natural photosynthesis gained popularity when slowly dephasing quantum beats (QBs) were observed in the two-dimensional electronic spectra of the Fenna-Matthews-Olson (FMO) complex at 77 K. These were assigned to superpositions of excitonic states, a controversial interpretation, as the strong chromophore-environment interactions in the complex suggest fast dephasing. Although it has been pointed out that vibrational motion produces similar spectral signatures, a concrete assignment of these oscillatory signals to distinct physical processes is still lacking. Here we revisit the coherence dynamics of the FMO complex using polarization-controlled two-dimensional electronic spectroscopy, supported by theoretical modelling. We show that the long-lived QBs are exclusively vibrational in origin, whereas the dephasing of the electronic coherences is completed within 240 fs even at 77 K. We further find that specific vibrational coherences are produced via vibronically coupled excited states. The presence of such states suggests that vibronic coupling is relevant for photosynthetic energy transfer.

Vibronic Coherence in the Charge Separation Process of the Rhodobacter sphaeroides Reaction Center

Two-dimensional electronic spectroscopy was applied to a variant of the reaction center (RC) of purple bacterium Rhodobacter sphaeroides lacking the primary acceptor ubiquinone in order to understand the ultrafast separation and transfer of charge between the bacteriochlorin cofactors. For the first time, characteristic 2D spectra were obtained for the participating excited and charge-transfer states, and the electron-transfer cascade (including two different channels, the P* and B* channels) was fully mapped. By analyzing quantum beats using 2D frequency maps, excited-state vibrational modes at 153 and 33 cm-1 were identified. We speculate that these modes couple to the charge separation (CS) process and collectively optimize the CS and are responsible for the superhigh efficiency.

Control of Excitation Energy Transfer in Condensed Phase Molecular Systems by Floquet Engineering

Excitation energy transfer (EET) is one of the most important processes in both natural and artificial chemical systems including, for example, photosynthetic complexes and organic solar cells. The EET rate, however, is strongly suppressed when there is a large difference in the excitation energy between the donor and acceptor molecules. Here, we demonstrate both analytically and numerically that the EET rate can be greatly enhanced by periodically modulating the excitation energy difference. The enhancement of EET by using this Floquet engineering, in which the system's Hamiltonian is made periodically time-dependent, turns out to be efficient even in the presence of strong fluctuations and dissipations induced by the coupling with a huge number of dynamic degrees of freedom in the surrounding molecular environments. As an effect of the environment on the Floquet engineering of EET, the optimal driving frequency is found to depend on the relative magnitudes of the system and environment's characteristic time scales with an observed frequency shift when moving from the limit of slow environmental fluctuations (inhomogeneous broadening limit) to that of fast fluctuations (homogeneous broadening limit).

Two-dimensional electronic-Raman spectroscopy

We present a new technique, two-dimensional electronic-Raman spectroscopy (2DER), which combines femtosecond stimulated Raman spectroscopy and a pulse-shaper-assisted 2D spectroscopic scheme for the actinic pump. The 2DER spectrum presents the initial actinic excitation wavelength with nanometer spectral resolution in the first axis and the detected stimulated Raman spectra in the second axis. We measured the correlation of the electronic and vibrational states in the photosynthetic accessory pigment β-carotene and reveal its photoexcited state manifold.

Evidence for coherent mixing of excited and charge-transfer states in the major plant light-harvesting antenna, LHCII

LHCII, the major light harvesting antenna from plants, plays a dual role in photosynthesis. In low light it is a light-harvester, while in high light it is a quencher that protects the organism from photodamage. The switching mechanism between these two orthogonal conditions is mediated by protein dynamic disorder and photoprotective energy dissipation. The latter in particular is thought to occur in part via spectroscopically 'dark' states. We searched for such states in LHCII trimers from spinach, at both room temperature and at 77 K. Using 2D electronic spectroscopy, we explored coherent interactions between chlorophylls absorbing on the low-energy side of LHCII, which is the region that is responsible for both light-harvesting and photoprotection. 2D beating frequency maps allow us to identify four frequencies with strong excitonic character. In particular, our results show the presence of a low-lying state that is coupled to a low-energy excitonic state. We assign this to a mixed excitonic-charge transfer state involving the state with charge separation within the Chl a603-b609 heterodimer, borrowing some dipole strength from the Chl a602-a603 excited states. Such a state may play a role in photoprotection, in conjunction with specific and environmentally controlled realizations of protein dynamic disorder. Our identification and assignment of the coherences observed in the 2D frequency maps suggests that the structure of exciton states as well as a mixing of the excited and charge-transfer states is affected by coupling of these states to resonant vibrations in LHCII.

Nodeless vibrational amplitudes and quantum nonadiabatic dynamics in the nested funnel for a pseudo Jahn-Teller molecule or homodimer

The nonadiabatic states and dynamics are investigated for a linear vibronic coupling Hamiltonian with a static electronic splitting and weak off-diagonal Jahn-Teller coupling through a single vibration with a vibrational-electronic resonance. With a transformation of the electronic basis, this Hamiltonian is also applicable to the anti-correlated vibration in a symmetric homodimer with marginally strong constant off-diagonal coupling, where the non-adiabatic states and dynamics model electronic excitation energy transfer or self-exchange electron transfer. For parameters modeling a free-base naphthalocyanine, the nonadiabatic couplings are deeply quantum mechanical and depend on wavepacket width; scalar couplings are as important as the derivative couplings that are usually interpreted to depend on vibrational velocity in semiclassical curve crossing or surface hopping theories. A colored visualization scheme that fully characterizes the non-adiabatic states using the exact factorization is developed. The nonadiabatic states in this nested funnel have nodeless vibrational factors with strongly avoided zeroes in their vibrational probability densities. Vibronic dynamics are visualized through the vibrational coordinate dependent density of the time-dependent dipole moment in free induction decay. Vibrational motion is amplified by the nonadiabatic couplings, with asymmetric and anisotropic motions that depend upon the excitation polarization in the molecular frame and can be reversed by a change in polarization. This generates a vibrational quantum beat anisotropy in excess of 2/5. The amplitude of vibrational motion can be larger than that on the uncoupled potentials, and the electronic population transfer is maximized within one vibrational period. Most of these dynamics are missed by the adiabatic approximation, and some electronic and vibrational motions are completely suppressed by the Condon approximation of a coordinate-independent transition dipole between adiabatic states. For all initial conditions investigated, the initial nonadiabatic electronic motion is driven towards the lower adiabatic state, and criteria for this directed motion are discussed.

Photoelectrochemical Complexes of Fucoxanthin-Chlorophyll Protein for Bio-Photovoltaic Conversion with a High Open-Circuit Photovoltage

Open-circuit photovoltage (V_oc ) is among the critical parameters for achieving an efficient light-to-charge conversion in existing solar photovoltaic devices. Natural photosynthesis exploits light-harvesting chlorophyll (Chl) protein complexes to transfer sunlight energy efficiently. We describe the exploitation of photosynthetic fucoxanthin-chlorophyll protein (FCP) complexes for realizing photoelectrochemical cells with a high V_oc . An antenna-dependent photocurrent response and a V_oc up to 0.72 V are observed and demonstrated in the bio-photovoltaic devices fabricated with photosynthetic FCP complexes and TiO₂ nanostructures. Such high V_oc is determined by fucoxanthin in FCP complexes, and is rarely found in photoelectrochemical cells with other natural light-harvesting antenna. We think that the FCP-based bio-photovoltaic conversion will provide an opportunity to fabricate environmental benign photoelectrochemical cells with high V_oc , and also help improve the understanding of the essential physics behind the light-to-charge conversion in photosynthetic complexes.

Quantum coherence as a witness of vibronically hot energy transfer in bacterial reaction center

Photosynthetic proteins have evolved over billions of years so as to undergo optimal energy transfer to the sites of charge separation. On the basis of spectroscopically detected quantum coherences, it has been suggested that this energy transfer is partially wavelike. This conclusion depends critically on the assignment of the coherences to the evolution of excitonic superpositions. We demonstrate that, for a bacterial reaction center protein, long-lived coherent spectroscopic oscillations, which bear canonical signatures of excitonic superpositions, are essentially vibrational excited-state coherences shifted to the ground state of the chromophores. We show that the appearance of these coherences arises from a release of electronic energy during energy transfer. Our results establish how energy migrates on vibrationally hot chromophores in the reaction center, and they call for a reexamination of claims of quantum energy transfer in photosynthesis.

Quantum design of photosynthesis for bio-inspired solar-energy conversion

Photosynthesis is the natural process that converts solar photons into energy-rich products that are needed to drive the biochemistry of life. Two ultrafast processes form the basis of photosynthesis: excitation energy transfer and charge separation. Under optimal conditions, every photon that is absorbed is used by the photosynthetic organism. Fundamental quantum mechanics phenomena, including delocalization, underlie the speed, efficiency and directionality of the charge-separation process. At least four design principles are active in natural photosynthesis, and these can be applied practically to stimulate the development of bio-inspired, human-made energy conversion systems.