Finite temperature dynamics in a polarized sub-Ohmic heat bath: A hierarchical equations of motion-tensor train study

The dynamics of the sub-Ohmic spin-boson model under polarized initial conditions at finite temperatures is investigated by employing both analytical tools and the numerically accurate hierarchical equations of motion-tensor train method. By analyzing the features of nonequilibrium dynamics, we discovered a bifurcation phenomenon, which separates two regimes of the dynamics. It is found that before the bifurcation time, increasing temperature slows down the population dynamics, while the opposite effect occurs after the bifurcation time. The dynamics is highly sensitive to both initial preparation of the bath and thermal effects.

Theoretical model of femtosecond coherence spectroscopy of vibronic excitons in molecular aggregates

When used as pump pulses in transient absorption spectroscopy measurements, femtosecond laser pulses can produce oscillatory signals known as quantum beats. The quantum beats arise from coherent superpositions of the states of the sample and are best studied in the Fourier domain using Femtosecond Coherence Spectroscopy (FCS), which consists of one-dimensional amplitude and phase plots of a specified oscillation frequency as a function of the detection frequency. Prior works have shown ubiquitous amplitude nodes and π phase shifts in FCS from excited-state vibrational wavepackets in monomer samples. However, the FCS arising from vibronic-exciton states in molecular aggregates have not been studied theoretically. Here, we use a model of vibronic-exciton states in molecular dimers based on displaced harmonic oscillators to simulate FCS for dimers in two important cases. Simulations reveal distinct spectral signatures of excited-state vibronic-exciton coherences in molecular dimers that may be used to distinguish them from monomer vibrational coherences. A salient result is that, for certain relative orientations of the transition dipoles, the key resonance condition between the electronic coupling and the frequency of the vibrational mode may yield strong enhancement of the quantum-beat amplitude and, perhaps, also cause a significant decrease of the oscillation frequency to a value far lower than the vibrational frequency. Future studies using these results will lead to new insights into the excited-state coherences generated in photosynthetic pigment-protein complexes.

Dynamics of a Quantum System Interacting with White Non-Gaussian Baths: Poisson Noise Master Equation

Quantum systems are unavoidably open to their surrounding degrees of freedom. The theory of open quantum systems is thus crucial to understanding the fluctuations, dissipation, and decoherence of a quantum system of interest. Typically, the bath is modeled as an ensemble of harmonic oscillators, which yields Gaussian statistics of the bath influence on the quantum systems. However, there are also phenomena in which the bath consists of two-state systems, spins, or anharmonic oscillators; therefore, the non-Gaussian properties of the bath become important. Nevertheless, a theoretical framework to describe quantum systems under the influence of such non-Gaussian baths is not well established. Here, we develop a theory to describe quantum dissipative systems affected by Poisson noise properties of the bath, because the Lévi-Itô decomposition theorem asserts that Poisson noise is fundamental in describing arbitrary white noise beyond Gaussian properties. We introduce a quantum bath model that allows for the consistent description of dissipative quantum systems. The obtained master equation reveals non-Gaussian bath effects in the white noise regime, and provides an essential step toward describing open quantum dynamics under the influence of generic baths.

Exciton dynamics from the mapping approach to surface hopping: comparison with Förster and Redfield theories

We compare the recently introduced multi-state mapping approach to surface hopping (MASH) with the Förster and Redfield theories of excitation energy transfer. Whereas Förster theory relies on weak coupling between chromophores, and Redfield theory assumes the electronic excitations to be weakly coupled to fast chromophore vibrations, MASH is free from any perturbative or Markovian approximations. We illustrate this with an example application to the rate of energy transfer in a Frenkel-exciton dimer, showing that MASH interpolates correctly between the opposing regimes in which the Förster and Redfield results are reliable. We then compare the three methods for a realistic model of the Fenna-Matthews-Olson complex with a structured vibrational spectral density and static disorder in the excitation energies. In this case there are no exact results for comparison so we use MASH to assess the validity of Förster and Redfield theories. We find that Förster theory is the more accurate of the two on the picosecond timescale, as has been shown previously for a simpler model of this particular light-harvesting complex. We also explore various ways to sample the initial electronic state in MASH and find that they all give very similar results for exciton dynamics.

Quantum Biology and the Potential Role of Entanglement and Tunneling in Non-Targeted Effects of Ionizing Radiation: A Review and Proposed Model

It is well established that cells, tissues, and organisms exposed to low doses of ionizing radiation can induce effects in non-irradiated neighbors (non-targeted effects or NTE), but the mechanisms remain unclear. This is especially true of the initial steps leading to the release of signaling molecules contained in exosomes. Voltage-gated ion channels, photon emissions, and calcium fluxes are all involved but the precise sequence of events is not yet known. We identified what may be a quantum entanglement type of effect and this prompted us to consider whether aspects of quantum biology such as tunneling and entanglement may underlie the initial events leading to NTE. We review the field where it may be relevant to ionizing radiation processes. These include NTE, low-dose hyper-radiosensitivity, hormesis, and the adaptive response. Finally, we present a possible quantum biological-based model for NTE.

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.

Vibrational response functions for multidimensional electronic spectroscopy in nonadiabatic models

The interplay of nuclear and electronic dynamics characterizes the multidimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response functions. Here, we report analytical expressions for the response functions corresponding to a class of model systems. These are characterized by coupling between the diabatic electronic states and the vibrational degrees of freedom, resulting in linear displacements of the corresponding harmonic oscillators, and by nonadiabatic couplings between pairs of diabatic states. In order to derive the linear response functions, we first perform the Dyson expansion of the relevant propagators with respect to the nonadiabatic component of the Hamiltonian, then derive and expand with respect to the displacements the propagators at given interaction times, and finally provide analytical expressions for the time integrals that lead to the different contributions to the linear response function. The approach is then applied to the derivation of third-order response functions describing different physical processes: ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence. Comparisons between the results obtained up to sixth order in the Dyson expansion and independent numerical calculation of the response functions provide evidence of the series convergence in a few representative cases.

Energy cascades in donor-acceptor exciton-polaritons observed by ultrafast two-dimensional white-light spectroscopy

Exciton-polaritons are hybrid states formed when molecular excitons are strongly coupled to photons trapped in an optical cavity. These systems exhibit many interesting, but not fully understood, phenomena. Here, we utilize ultrafast two-dimensional white-light spectroscopy to study donor-acceptor microcavities made from two different layers of semiconducting carbon nanotubes. We observe the delayed growth of a cross peak between the upper- and lower-polariton bands that is oftentimes obscured by Rabi contraction. We simulate the spectra and use Redfield theory to learn that energy cascades down a manifold of new electronic states created by intermolecular coupling and the two distinct bandgaps of the donor and acceptor. Energy most effectively enters the manifold when light-matter coupling is commensurate with the energy distribution of the manifold, contributing to long-range energy transfer. Our results broaden the understanding of energy transfer dynamics in exciton-polariton systems and provide evidence that long-range energy transfer benefits from moderately-coupled cavities.

Excitation energy transfer and vibronic coherence in intact phycobilisomes

The phycobilisome is an oligomeric chromoprotein complex that serves as the principal mid-visible light-harvesting system in cyanobacteria. Here we report the observation of excitation-energy-transfer pathways involving delocalized optical excitations of the bilin (linear tetrapyrrole) chromophores in intact phycobilisomes isolated from Fremyella diplosiphon. By using broadband multidimensional electronic spectroscopy with 6.7-fs laser pulses, we are able to follow the progress of excitation energy from the phycoerythrin disks at the ends of the phycobilisome's rods to the C-phycocyanin disks along their length in <600 fs. Oscillation maps show that coherent wavepacket motions prominently involving the hydrogen out-of-plane vibrations of the bilins mediate non-adiabatic relaxation of a manifold of vibronic exciton states. However, the charge-transfer character of the bilins in the allophycocyanin-containing segments localizes the excitations in the core of the phycobilisome, yielding a kinetic bottleneck that enables photoregulatory mechanisms to operate efficiently on the >10-ps timescale.

An ICT-guided ratiometric naphthalene-benzothiazole-based probe for the detection of cyanide with real-time applications in human breast cancer cells

A methoxynaphthalene benzothiazole conjugate (MNBTZ) armed with CC vinylic double bonds was synthesized and utilized for the selective detection of CN^- ions. The probe showed yellow fluorescence due to ICT from the methoxynaphthalene moiety to benzothiazole, which instantly changed to light purple upon the nucleophilic addition of CN^- to the vinylic double bond, inhibiting ICT due to the break-in conjugation. The effectiveness of the probe was proved by this brilliant ratiometric fluorescence change, which was achieved selectively as observed by experiments with competing anions. ¹H NMR titrations and DFT calculations support this mechanism. A low detection limit of 2.1(±0.0022) × 10^-8 M along with good fluorescence color change on solid TLC plates and human breast cancer cells makes it amenable to CN^- sensing.

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.

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.

Synthetic Control of Exciton Dynamics in Bioinspired Cofacial Porphyrin Dimers

Understanding how the complex interplay among excitonic interactions, vibronic couplings, and reorganization energy determines coherence-enabled transport mechanisms is a grand challenge with both foundational implications and potential payoffs for energy science. We use a combined experimental and theoretical approach to show how a modest change in structure may be used to modify the exciton delocalization, tune electronic and vibrational coherences, and alter the mechanism of exciton transfer in covalently linked cofacial Zn-porphyrin dimers (meso-beta linked ABm-β and meso-meso linked AAm-m). While both ABm-β and AAm-m feature zinc porphyrins linked by a 1,2-phenylene bridge, differences in the interporphyrin connectivity set the lateral shift between macrocycles, reducing electronic coupling in ABm-β and resulting in a localized exciton. Pump-probe experiments show that the exciton dynamics is faster by almost an order of magnitude in the strongly coupled AAm-m dimer, and two-dimensional electronic spectroscopy (2DES) identifies a vibronic coherence that is absent in ABm-β. Theoretical studies indicate how the interchromophore interactions in these structures, and their system-bath couplings, influence excitonic delocalization and vibronic coherence-enabled rapid exciton transport dynamics. Real-time path integral calculations reproduce the exciton transfer kinetics observed experimentally and find that the linking-modulated exciton delocalization strongly enhances the contribution of vibronic coherences to the exciton transfer mechanism, and that this coherence accelerates the exciton transfer dynamics. These benchmark molecular design, 2DES, and theoretical studies provide a foundation for directed explorations of nonclassical effects on exciton dynamics in multiporphyrin assemblies.

Dynamics of Excitons in Conjugated Molecules and Organic Semiconductor Systems

The exciton, an excited electron-hole pair bound by Coulomb attraction, plays a key role in photophysics of organic molecules and drives practically important phenomena such as photoinduced mechanical motions of a molecule, photochemical conversions, energy transfer, generation of free charge carriers, etc. Its behavior in extended π-conjugated molecules and disordered organic films is very different and very rich compared with exciton behavior in inorganic semiconductor crystals. Due to the high degree of variability of organic systems themselves, the exciton not only exerts changes on molecules that carry it but undergoes its own changes during all phases of its lifetime, that is, birth, conversion and transport, and decay. The goal of this review is to give a systematic and comprehensive view on exciton behavior in π-conjugated molecules and molecular assemblies at all phases of exciton evolution with emphasis on rates typical for this dynamic picture and various consequences of the above dynamics. To uncover the rich variety of exciton behavior, details of exciton formation, exciton transport, exciton energy conversion, direct and reverse intersystem crossing, and radiative and nonradiative decay are considered in different systems, where these processes lead to or are influenced by static and dynamic disorder, charge distribution symmetry breaking, photoinduced reactions, electron and proton transfer, structural rearrangements, exciton coupling with vibrations and intermediate particles, and exciton dissociation and annihilation as well.

Triphenylamine-based small-molecule fluorescent probes

Ammonia with the three hydrogens substituted by phenyls is known as triphenylamine (TPA), and is one of the most useful compounds because of its vast practical applications. Chemists have produced thousands of TPA derivatives to date. Because of its biocompatibility and structural features, it has been widely used in the fields of molecular recognition, molecular imaging, materials chemistry, and also in biology and medical science. Its strong electron-donating ability encourages scientists to produce different types of probes for molecular recognition. This review is based on recent developments and advances in TPA-based small molecular fluorescent probes within the time period 2010-2021. This extensive review may expedite improvements in more advanced fluorescent probes for vast and stimulating applications in the future.

Observation of robust energy transfer in the photosynthetic protein allophycocyanin using single-molecule pump-probe spectroscopy

Photosynthetic organisms convert sunlight to electricity with near unity quantum efficiency. Absorbed photoenergy transfers through a network of chromophores positioned within protein scaffolds, which fluctuate due to thermal motion. The resultant variation in the individual energy transfer steps has not yet been measured, and so how the efficiency is robust to this variation has not been determined. Here, we describe single-molecule pump-probe spectroscopy with facile spectral tuning and its application to the ultrafast dynamics of single allophycocyanin, a light-harvesting protein from cyanobacteria. We disentangled the energy transfer and energetic relaxation from nuclear motion using the spectral dependence of the dynamics. We observed an asymmetric distribution of timescales for energy transfer and a slower and more heterogeneous distribution of timescales for energetic relaxation, which was due to the impact of the protein environment. Collectively, these results suggest that energy transfer is robust to protein fluctuations, a prerequisite for efficient light harvesting.

Detecting initial correlations via correlated spectroscopy in hybrid quantum systems

Generic mesoscopic quantum systems that interact with their environment tend to display appreciable correlations with environment that often play an important role in the physical properties of the system. However, the experimental methods needed to characterize such systems either ignore the role of initial correlations or scale unfavourably with system dimensions. Here, we present a technique that is agnostic to system-environment correlations and can be potentially implemented experimentally. Under a specific set of constraints, we demonstrate the ability to detect and measure specific correlations. We apply the technique to two cases related to Nitrogen Vacancy Centers (NV). Firstly, we use the technique on an NV coupled to a P1 defect centre in the environment to demonstrate the ability to detect dark spins. Secondly, we implement the technique on a hybrid quantum system of NV coupled to an optical cavity with initial correlations. We extract the interaction strength and effective number of interacting NVs from the initial correlations using our technique.

Ultrafast energy transfer between lipid-linked chromophores and plant light-harvesting complex II

Light-Harvesting Complex II (LHCII) is a membrane protein found in plant chloroplasts that has the crucial role of absorbing solar energy and subsequently performing excitation energy transfer to the reaction centre subunits of Photosystem II. LHCII provides strong absorption of blue and red light, however, it has minimal absorption in the green spectral region where solar irradiance is maximal. In a recent proof-of-principle study, we enhanced the absorption in this spectral range by developing a biohybrid system where LHCII proteins together with lipid-linked Texas Red (TR) chromophores were assembled into lipid membrane vesicles. The utility of these systems was limited by significant LHCII quenching due to protein-protein interactions and heterogeneous lipid structures. Here, we organise TR and LHCII into a lipid nanodisc, which provides a homogeneous, well-controlled platform to study the interactions between TR molecules and single LHCII complexes. Fluorescence spectroscopy determined that TR-to-LHCII energy transfer has an efficiency of at least 60%, resulting in a 262% enhancement of LHCII fluorescence in the 525-625 nm range, two-fold greater than in the previous system. Ultrafast transient absorption spectroscopy revealed two time constants of 3.7 and 128 ps for TR-to-LHCII energy transfer. Structural modelling and theoretical calculations indicate that these timescales correspond to TR-lipids that are loosely- or tightly-associated with the protein, respectively, with estimated TR-to-LHCII separations of ∼3.5 nm and ∼1 nm. Overall, we demonstrate that a nanodisc-based biohybrid system provides an idealised platform to explore the photophysical interactions between extrinsic chromophores and membrane proteins with potential applications in understanding more complex natural or artificial photosynthetic systems.

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.

Designing excitonic circuits for the Deutsch-Jozsa algorithm: mitigating fidelity loss by merging gate operations

In this manuscript, we examine design strategies for the development of excitonic circuits that are capable of performing simple 2-qubit multi-step quantum algorithms. Specifically, we compare two different strategies for designing dye-based systems that prescribe exciton evolution encoding a particular quantum algorithm. A serial strategy implements the computation as a step-by-step series of circuits, with each carrying out a single operation of the quantum algorithm, and a combined strategy implements the entire computation in a single circuit. We apply these two approaches to the well-studied Deutsch-Jozsa algorithm and evaluate circuit fidelity in an idealized system under a model harmonic bath, and also for a bath that is parameterized to reflect the thermal fluctuations of an explicit molecular environment. We find that the combined strategy tends to yield higher fidelity and that the harmonic bath approximation leads to lower fidelity than a model molecular bath. These results imply that the programming of excitonic circuits for quantum computation should favor hard-coded modules that incorporate multiple algorithmic steps and should represent the molecular nature of the circuit environment.

The avian compass can be sensitive even without sustained electron spin coherence

Theoretical studies indicating the presence of long-lived coherence in the radical pair system have engendered questions about its utilitarian role in the avian compass. In this paper, we investigate the role of electron spin coherence in a multinuclear radical pair system including its impact on compass sensitivity. We find that sustenance of long-lived electron spin coherence is unlikely in a multinuclear hyperfine environment. After probing the role of the hyperfine interactions in the compass, we affirm the hyperfine anisotropy to be an essential parameter for the necessary sensitivity required for the compass action. Thereby, we identify a parameter regime where the compass would exhibit good sensitivity even without sustained electron spin coherence.

Turn-on fluorescent naphthalimide-benzothiazole probe for cyanide detection and its two-mode aggregation-induced emission behavior

Naphthalimide-benzothiazole conjugate (NBTZ) linked by cinnamonitrile was designed, synthesized, and fully characterized by NMR (¹H, ¹³C, DEPT, HSQC) and high-resolution mass spectrometry. NBTZ exhibited unique turn-on fluorescence in the presence of CN^- with relatively high selectivity compared to other anions such as SCN^-, HSO₄^-, ClO₄^-, NO₃^-, Cl^-, Br^-, I^-, and PO₄^-3 in tetrahydrofuran (THF). The detection limit for CN^- was found to be 3.35 × 10^-8 M in THF. The sensing mechanism was analyzed through ¹H, ¹³C, DEPT, and mass spectroscopy. NBTZ also showed two-mode aggregation-induced emission (AIE) in THF-H₂O mixtures. In a 30:70 THF-H₂O (v/v) mixture, the maximum AIE was observed at 430 nm (blue) because of the rotation of the CC bond between the naphthalimide ring and the phenyl ring was restricted. In 10:90 THF-H₂O (v/v), a new red-shifted AIE appeared at 490 nm (cyan), due to the extended π-conjugation induced by restriction of rotation of the CC bond between the benzothiazole and naphthalimide rings.

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.

Effect of logarithmic perturbations in ohmic like spectral densities in dynamics of electronic excitation using variational polaron transformation approach

Electronic excitation energy transfer is a ubiquitous process that has generated prime research interest since its discovery. Recently developed variational polaron transformation-based second-order master equation is capable of interpolating between Förster and Redfield limits with exceptional accuracy. Forms of spectral density functions studied so far through the variational approach provide theoretical support for various experiments. Recently introduced ohmic like spectral density function that can account for logarithmic perturbations provides generality and exposition to a unique and practical set of environments. In this paper, we exploit the energy transfer dynamics of a two-level system attached to an ohmic like spectral density function with logarithmic perturbations using a variational polaron transformed master equation. Our results demonstrate that even for a relatively large bath coupling strength, quantum coherence effects can be increased by introducing logarithmic perturbations of the order of one and two in super-ohmic environments. Moreover, for particular values of the ohmicity parameter, the effect of logarithmic perturbations is observed to be insignificant for the overall dynamics. In regard to ohmic environments, as logarithmic perturbations increase, damping characteristics of the coherent transient dynamics also increase in general. It is also shown that, having logarithmic perturbations of the order of one in an ohmic environment can result in a less efficient energy transfer for relatively larger system bath coupling strengths.

Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)

An open quantum system refers to a system that is further coupled to a bath system consisting of surrounding radiation fields, atoms, molecules, or proteins. The bath system is typically modeled by an infinite number of harmonic oscillators. This system-bath model can describe the time-irreversible dynamics through which the system evolves toward a thermal equilibrium state at finite temperature. In nuclear magnetic resonance and atomic spectroscopy, dynamics can be studied easily by using simple quantum master equations under the assumption that the system-bath interaction is weak (perturbative approximation) and the bath fluctuations are very fast (Markovian approximation). However, such approximations cannot be applied in chemical physics and biochemical physics problems, where environmental materials are complex and strongly coupled with environments. The hierarchical equations of motion (HEOM) can describe the numerically "exact" dynamics of a reduced system under nonperturbative and non-Markovian system-bath interactions, which has been verified on the basis of exact analytical solutions (non-Markovian tests) with any desired numerical accuracy. The HEOM theory has been used to treat systems of practical interest, in particular, to account for various linear and nonlinear spectra in molecular and solid state materials, to evaluate charge and exciton transfer rates in biological systems, to simulate resonant tunneling and quantum ratchet processes in nanodevices, and to explore quantum entanglement states in quantum information theories. This article presents an overview of the HEOM theory, focusing on its theoretical background and applications, to help further the development of the study of open quantum dynamics.

Frenkel excitons in heat-stressed supramolecular nanocomposites enabled by tunable cage-like scaffolding

Delocalized Frenkel excitons-coherently shared excitations among chromophores-are responsible for the remarkable efficiency of supramolecular light-harvesting assemblies within photosynthetic organisms. The translation of nature's design principles to applications in optoelectronic devices has been limited by the fragility of the supramolecular structures used and the delicate nature of Frenkel excitons, particularly under mildly changing solvent conditions and elevated temperatures and upon deposition onto solid substrates. Here, we overcome those functionalization barriers through composition of stable supramolecular light-harvesting nanotubes enabled by tunable (~4.3-4.9 nm), uniform (±0.3 nm) cage-like scaffolds. High-resolution cryogenic electron microscopy, combined with scanning electron microscopy, broadband femtosecond transient absorption spectroscopy and near-field scanning optical microscopy revealed that excitons within the cage-like scaffolds are robust, even under extreme heat stress, and control over nanocomposite dimensions is maintained on solid substrates. Our bio-inspired nanocomposites provide a general framework for the development of next-generation organic devices made from stable supramolecular materials.

Nonadiabatic sunlight harvesting

Experimental and theoretical evidence points out the crucial role of specific intramolecular vibrational modes resonant with excitonic splittings in the interpretation of long-lived coherences observed in the two-dimensional spectra of some natural and synthetic light harvesting complexes. For the natural situation of illumination by incoherent (sun)light, the relevance of these vibrations is analyzed here for light-harvesting vibronic prototype dimers. The detailed analysis of the density matrix dynamics reveals that the inclusion of intramolecular vibrational modes reinforces the exciton coherence up to one order of magnitude and may increase the populations of lowest energy single exciton states, as well as populations and coherences in the site basis. In sharp contrast to the case of initial-state preparation by coherent (laser)light-sources, the initial thermal state of the local vibrational modes, as well as that of the anticorrelated vibrational mode, evolves devoid of non-classical correlations as confirmed by the absence of negative values of its phase-space quasi-probability distribution at all times. Therefore, not only the long-lived coherences observed in the two-dimensional spectra are induced by the coherent character of pulsed laser sources, but it is unambiguously shown here that the non-classical character generally assigned to the anticorrelated vibrational mode also comes as the result of the preparation of the initial state by coherent pulsed laser sources.

Observation of dissipative chlorophyll-to-carotenoid energy transfer in light-harvesting complex II in membrane nanodiscs

Plants prevent photodamage under high light by dissipating excess energy as heat. Conformational changes of the photosynthetic antenna complexes activate dissipation by leveraging the sensitivity of the photophysics to the protein structure. The mechanisms of dissipation remain debated, largely due to two challenges. First, because of the ultrafast timescales and large energy gaps involved, measurements lacked the temporal or spectral requirements. Second, experiments have been performed in detergent, which can induce non-native conformations, or in vivo, where contributions from homologous antenna complexes cannot be disentangled. Here, we overcome both challenges by applying ultrabroadband two-dimensional electronic spectroscopy to the principal antenna complex, LHCII, in a near-native membrane. Our data provide evidence that the membrane enhances two dissipative pathways, one of which is a previously uncharacterized chlorophyll-to-carotenoid energy transfer. Our results highlight the sensitivity of the photophysics to local environment, which may control the balance between light harvesting and dissipation in vivo.

Light polarization dependency existing in the biological photosystem and possible implications for artificial antenna systems

The processes of biological photosynthesis provide inspiration and valuable lessons for artificial energy collection, transfer, and conversion systems. The extraordinary efficiency of each sequential process of light to biomass conversion originates from the unique architecture and mechanism of photosynthetic proteins. Near 100% quantum efficiency of energy transfer in biological photosystems is achieved by the chlorophyll assemblies in antenna complexes, which also exhibit a significant degree of light polarization. The three-dimensional chiral assembly of chlorophylls is an optimized biological architecture that enables maximum energy transfer efficiency with precisely designed coupling between chlorophylls. In this review, we summarize the key lessons from the photosynthetic processes in biological photosystems, and move our focus to energy transfer mechanisms and the chiral structure of the chlorophyll assembly. Then, we introduce recent approaches and possible implications to realize the biological energy transfer processes on bioinspired scaffold-based artificial antenna systems.

Improved population operators for multi-state nonadiabatic dynamics with the mixed quantum-classical mapping approach

Application to the 7-state Frenkel-exciton Hamiltonian for the Fenna–Matthews–Olson complex shows that using a different representation of the electronic population operators can drastically improve the accuracy of the quasiclassical mapping approach without increasing the computational effort.

Satisfying fermionic statistics in the modeling of non-Markovian dynamics with one-electron reduced density matrices

Treatment of Markovian, many-electron dynamics from the solution of the Lindblad equation for the 1-electron reduced density matrix requires additional constraints on the bath operators to maintain fermion statistics. Recently, we generalized Lindblad's formalism to non-Markovian dynamics through an ensemble of Lindbladian trajectories. Here we show that the fermion statistics of non-Markovian dynamics can be enforced through analogous constraints on the bath operators of each Lindbladian trajectory in the ensemble. To illustrate, we apply the non-Markovian method to three distinct systems of two fermions in three levels. While the electrons violate the fermion statistics without the constraints, correct fermion behavior is recovered with the constraints.

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.

Chebyshev hierarchical equations of motion for systems with arbitrary spectral densities and temperatures

The time evolution in open quantum systems, such as a molecular aggregate in contact with a thermal bath, still poses a complex and challenging problem. The influence of the thermal noise can be treated using a plethora of schemes, several of which decompose the corresponding correlation functions in terms of weighted sums of exponential functions. One such scheme is based on the hierarchical equations of motion (HEOM), which is built using only certain forms of bath correlation functions. In the case where the environment is described by a complex spectral density or is at a very low temperature, approaches utilizing the exponential decomposition become very inefficient. Here, we utilize an alternative decomposition scheme for the bath correlation function based on Chebyshev polynomials and Bessel functions to derive a HEOM approach up to an arbitrary order in the environmental coupling. These hierarchical equations are similar in structure to the popular exponential HEOM scheme, but are formulated using the derivatives of the Bessel functions. The proposed scheme is tested up to the fourth order in perturbation theory for a two-level system and compared to benchmark calculations for the case of zero-temperature quantum Ohmic and super-Ohmic noise. Furthermore, the benefits and shortcomings of the present Chebyshev-based hierarchical equations are discussed.

Room temperature quantum coherence vs. electron transfer in a rhodanine derivative chromophore

Understanding electron transfer in organic molecules is of great interest in quantum materials for light harvesting, energy conversion and integration of molecules into solar cells. This, however, poses the challenge of designing specific optimal molecular structure for which the processes of ultrafast quantum coherence and electron transport are not so well understood. In this work, we investigate subpicosecond time scale quantum dynamics and electron transfer in an efficient electron acceptor rhodanine chromophoric complex. We consider an open quantum system approach to model the complex-solvent interaction, and compute the crossover from weak to strong dissipation on the reduced system dynamics for both a polar (methanol) and a non polar solvent (toluene). We show that the electron transfer rates are enhanced in the strong chromophore-solvent coupling regime, being the highest transfer rates those found at room temperature. Even though the computed dynamics are highly non-Markovian, and they may exhibit a quantum character up to hundreds of femtoseconds, we show that quantum coherence does not necessarily optimise the electron transfer in the chromophore.

Density matrix dynamics in twin-formulation: An efficient methodology based on tensor-train representation of reduced equations of motion

The twin-formulation of quantum statistical mechanics is employed to describe a new methodology for the solution of the equations of motion of the reduced density matrix in their hierarchical formulation. It is shown that the introduction of tilde operators and of their algebra in the dual space greatly simplifies the application of numerical techniques for the propagation of the density matrix. The application of tensor-train representation of a vector to solve complex quantum dynamical problems within the framework of the twin-formulation is discussed. Next, applications of the hierarchical equations of motion to a dissipative polaron model are presented showing the validity and accuracy of the new approach.

High-dimensional exciton-vibrational wave-packet dynamics in the FMO complex. influence of site-specific spectral densities

The correlated exciton-vibrational dynamics of the Fenna-Matthews-Olson (FMO) complex is studied using Multi-layer Multi-configuration Time-dependent Hartree (ML-MCTDH) wavepacket propagation. Exciton populations and coherences are shown to be sensitive to the details of the spectral density.

Synthesis and Spectral Characteristics of BODIPY Dyes with Two or Three Dipyrrin Domains

Several boron-dipyrrin (BODIPY) based fluorophores with two and three dipyrrin cores were synthesized and investigated in solvents under the concentration variation. Comparative analysis of spectral and photophysical changes under increasing the number of the cores in the dye molecule was made. Mutual influence of dipyrrin cores was detected leading to the increasing of the compounds rigidity and, thus, the absence of fluorescent molecular rotor effects under the viscosity variation. Aggregation induced quenching, which was observed for many mono-domain BODIPY dyes is reduced in case of investigated poly-domain compounds.