Excitonic Dimer Research Articles

Simulating Non-Markovian Dynamics in Multidimensional Electronic Spectroscopy via Quantum Algorithm.

Including the effect of the molecular environment in the numerical modeling of time-resolved electronic spectroscopy remains an important challenge in computational spectroscopy. In this contribution, we present a general approach for the simulation of the optical response of multichromophore systems in a structured environment and its implementation as a quantum algorithm. A key step of the procedure is the pseudomode embedding of the system-environment problem resulting in a finite set of quantum states evolving according to a Markovian quantum master equation. This formulation is then solved by a collision model integrated into a quantum algorithm designed to simulate linear and nonlinear response functions. The workflow is validated by simulating spectra for the prototypical excitonic dimer interacting with fast (memoryless) and finite-memory environments. The results demonstrate, on the one hand, the potential of the pseudomode embedding for simulating the dynamical features of nonlinear spectroscopy, including lineshape, spectral diffusion, and relaxations along delay times. On the other hand, the explicit synthesis of quantum circuits provides a fully quantum simulation protocol of nonlinear spectroscopy harnessing the efficient quantum simulation of many-body dynamics promised by the future generation of fault-tolerant quantum computers.

Incoherent ultrafast energy transfer in phycocyanin 620 from Thermosynechococcus vulcanus revealed by polarization-controlled two dimensional electronic spectroscopy.

Phycocyanin 620 (PC620) is the outermost light-harvesting complex in phycobilisome of cyanobacteria, engaged in light collection and energy transfer to the core antenna, allophycocyanin. Recently, long-lived exciton-vibrational coherences have been observed in allophycocyanin, accounting for the coherent energy transfer [Zhu et al., Nat. Commun. 15, 3171 (2024)]. PC620 has a nearly identical spatial location of three α84-β84 phycocyanobilin pigment pairs to those in allophycocyanin, inferring an existence of possible coherent energy transfer pathways. However, whether PC620 undergoes coherent or incoherent energy transfer remains debated. Furthermore, accurate determination of energy transfer rates in PC620 is still necessary owing to the spectral overlap and broadening in conventional time-resolved spectroscopic measurements. In this work, the energy transfer process within PC620 was directly resolved by polarization-controlled two dimensional electronic spectroscopy (2DES) and global analysis. The results show that the energy transfer from α84 to the adjacent β84 has a lifetime constant of 400fs, from β155 to β84 of 6-8ps, and from β155 to α84 of 66ps, fully conforming to the Förster resonance energy transfer mechanism. The circular dichroism spectrum also reveals that the α84-β84 pigment pair does not form excitonic dimer, and the observed oscillatory signals are confirmed to be vibrational coherence, excluding the exciton-vibrational coupling. Nodal line slope analysis of 2DES further reveals that all the vibrational modes participate in the energy dissipation of the excited states. Our results consolidate that the ultrafast energy transfer process in PC620 is incoherent, where the twisted conformation of α84 is suggested as the main cause for preventing the formation of α84-β84 excitonic dimer in contrast to allophycocyanin.

Nonzero current due to coherent dynamic electron transport through a dimer with no external bias

We have proposed a mechanism of the interplay of injected coherence and decoherence dynamics of the system in electron transport through an excitonic dimer when it is simultaneously connected to thermocoherent electron source and a thermal electron sink. Due to such an interplay, the variation of current with the energy gap between two excitonic states which is the internal bias of the system, is largely affected and it markedly bears the signature of the decoherence dynamics. We have also shown an extension in the modification of Landauer conductance formula for electron transport through excitonic dimer. The current has the property of an asymmetry in spectral width which can be understood in terms of sum of two Lorentzian profiles. More remarkably we have shown that current due to electron transport through the dimer can also arise at zero external bias which is a purely quantum coherent effect of the source fermionic reservoir having zero thermal occupation number.

Unraveling Electronic and Vibrational Coherences Following a Charge Transfer Process in a Photosystem II Reaction Center

A reaction center is a unique biological system that performs the initial charge separation within a Photosystem II (PSII) multiunit enzyme, which eventually drives the catalytic water-splitting in plants and algae. The possible role of quantum coherences coinciding with the energy and charge transfer processes in PSII reaction center is one of the active areas of research. Here, we study these quantum coherences by using a numerically exact method on an excitonic dimer model, including linear vibronic coupling and employing optimal parameters from experimental two-dimensional coherent spectroscopic measurements. This enables us to precisely capture the excitonic interaction between pigments and the dissipation of the energy from electronic and charge-transfer (CT) states to the protein environment. We employ the time nonlocal (TNL) quantum master equation to calculate the population dynamics, which yields numerically reliable results. The calculated results show that, due to the strong dissipation, the lifetime of electronic coherence is too short to have direct participation in the charge transfer processes. However, there are long-lived vibrational coherences present in the system at frequencies close to the excitionic energy gap. These are strongly coupled with the electronic coherences, which makes the detection of the electronic coherences with conventional techniques very challenging. Additionally, we unravel the strong excitonic interaction of radical pair (PD1 and PD2) in the reaction center, which results in a long-lived electronic coherence of >100 fs, even at room temperature. Our work provide important physical insight to the charge separation process in PSII reaction center, which may be helpful for better understanding of photophysical processes in other natural and artificial light-harvesting systems.

Quantum phase synchronization via exciton-vibrational energy dissipation sustains long-lived coherence in photosynthetic antennas

The lifetime of electronic coherences found in photosynthetic antennas is known to be too short to match the energy transfer time, rendering the coherent energy transfer mechanism inactive. Exciton-vibrational coherence time in excitonic dimers which consist of two chromophores coupled by excitation transfer interaction, can however be much longer. Uncovering the mechanism for sustained coherences in a noisy biological environment is challenging, requiring the use of simpler model systems as proxies. Here, via two-dimensional electronic spectroscopy experiments, we present compelling evidence for longer exciton-vibrational coherence time in the allophycocyanin trimer, containing excitonic dimers, compared to isolated pigments. This is attributed to the quantum phase synchronization of the resonant vibrational collective modes of the dimer, where the anti-symmetric modes, coupled to excitonic states with fast dephasing, are dissipated. The decoupled symmetric counterparts are subject to slower energy dissipation. The resonant modes have a predicted nearly 50% reduction in the vibrational amplitudes, and almost zero amplitude in the corresponding dynamical Stokes shift spectrum compared to the isolated pigments. Our findings provide insights into the mechanisms for protecting coherences against the noisy environment.

Spectroscopic response theory with classical mapping Hamiltonians.

Exact quantum dynamics with a time-independent Hamiltonian in a discrete state space can be computed using classical mechanics through the classical Meyer-Miller-Stock-Thoss mapping Hamiltonian. In order to compute quantum response functions from classical dynamics, we extend this mapping to a quantum Hamiltonian with time-dependence arising from a classical field. This generalization requires attention to time-ordering in quantum and classical propagators. Quantum response theory with the original quantum Hamiltonian is equivalent to classical response theory with the classical mapping Hamiltonian. We elucidate the structure of classical response theory with the mapping Hamiltonian, thereby generating classical versions of the two-sided quantum density operator diagrams conventionally used to describe spectroscopic processes. This formal development can provide a foundation for new semiclassical approximations to spectroscopic observables for models in which classical nuclear degrees of freedom are introduced into a mapping Hamiltonian describing electronic states. Calculations of the temperature-dependence of two-dimensional electronic spectra for an exciton dimer using two semiclassical approaches are compared with benchmark calculations using the hierarchical equations of motion method.

Exciton transfer using rates extracted from the "hierarchical equations of motion".

Frenkel exciton population dynamics of an excitonic dimer is studied by comparing the results from a quantum master equation involving rates from second-order perturbative treatment with respect to the excitonic coupling with the non-perturbative results from "Hierarchical Equations of Motion" (HEOM). By formulating generic Liouville-space expressions for the rates, we can choose to evaluate them either via HEOM propagations or by applying the cumulant expansion. The coupling of electronic transitions to bath modes is modeled either as overdamped oscillators for the description of thermal bath components or as underdamped oscillators to account for intramolecular vibrations. Cases of initial nonequilibrium and equilibrium vibrations are discussed. In the case of HEOM, initial equilibration enters via a polaron transformation. Pointing out the differences between the nonequilibrium and equilibrium approach in the context of the projection operator formalism, we identify a further description, where the transfer dynamics is driven only by fluctuations without involvement of dissipation. Despite this approximation, this approach can also yield meaningful results in certain parameter regimes. While for the chosen model, HEOM has no technical advantage for evaluation of the rate expressions compared to cumulant expansion, there are situations where only evaluation with HEOM is applicable. For instance, a separation of reference and interaction Hamiltonian via a polaron transformation to account for the interplay between Coulomb coupling and vibrational oscillations of the bath at the level of a second-order treatment can be adjusted for a treatment with HEOM.

One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories.

We extend the semiclassical optimized mean trajectory (OMT) procedure to calculate electronic spectra for a dimer with excitonic and vibronic interactions. The electronic part of the quantum Hamiltonian is expressed in the Miller-Meyer-Stock-Thoss form with one fictitious harmonic oscillator per electronic state, and the classical limit is taken, transforming a quantum Hamiltonian governing discrete states to an equivalent classical form. The ad hoc addition of classical nuclear degrees of freedom and electron-nuclear coupling yields a classical Hamiltonian with one degree of freedom per each electronic state and also per each nuclear motion. Semiclassical quantization is applied to this Hamiltonian through the OMT, originally developed to describe nuclear dynamics on a single potential surface and subsequently generalized to include electronic transitions. The accuracy and practicality of this trajectory-based method is assessed for an excitonically coupled dimer. The semiclassical one- and two-dimensional spectra are shown to compare well with quantum dynamical calculations performed with the hierarchical equations of motion method.

An Oligonucleotide Delivery Platform to Enable Assessment of Intracellular Transcripts in Live Cells by Flow Cytometry.

The measurement of mRNA transcripts in live cells has been limited by inefficient delivery vehicles for oligonucleotides. Using a delivery platform which utilizes fluorophores capable of forming intramolecular H-type excitonic dimers, we show that antisense oligonucleotides (ASOs) can be delivered across the plasma membrane directly into the cytosol without receptor mediation. With HIV infection of CD4+ lymphocytes as a model system, we quantitate the level of viral infection present in live single cells with flow cytometry by measuring the hybridization of ASOs to viral sequences; we then compare this measurement with a standard HIV analysis, that is, binding of an antibody against the HIV cell surface protein gp120. The nucleic acids delivery platform described herein also enables inhibition of HIV infection by addition of ASO constructs targeting sequences in the virus' highly conserved 5'-untranslated region. Our analysis quantitates the level of inhibition by comparing both the MFI values and the mean fluorescence intensity as calculated by integration under each curve. Thus, a means for measuring intracellular transcripts at the live single cell level and the potential for delivery of a new class of antiviral agents is described. © 2020 International Society for Advancement of Cytometry.

Effect of Time-Delayed Feedback on the Interaction of a Dimer System with its Environment

In this work, we report modeling of non-Markovian open quantum systems, consisting of an excitonic dimer that displays memory effect due to time delayed interaction with its environment. We, indeed investigate the effect of these time delays on quantum coherence and excitation dynamical behavior in the time domain generally considered for photosynthetic experiments (few hundred femtoseconds). In particular, we show that the coherence is maintained for periods proportional to time delays. Additionally, if delay is taken into account, coupling to the environment can be tuned to lower values, unlike in previous studies. This kind of intriguing effect can, therefore, when generalized to complete systems, permit more control on the experimental parameters, which may lead to more accurate description of the photosynthetic energy transfer functioning and subsequent applications in artificial photovoltaic research.

How Markovian is exciton dynamics in purple bacteria?

We investigate the extent to which the dynamics of excitons in the light-harvesting complex LH2 of purple bacteria can be described using a Markovian approximation. To analyse the degree of non-Markovianity in these systems, we introduce a measure based on fitting Lindblad dynamics, as well as employing a recently introduced trace-distance measure. We apply these measures to a chromophore-dimer model of exciton dynamics and use the hierarchical equation-of-motion method to take into account the broad, low-frequency phonon bath. With a smooth phonon bath, small amounts of non-Markovianity are present according to the trace-distance measure, but the dynamics is poorly described by a Lindblad master equation unless the excitonic dimer coupling strength is modified. Inclusion of underdamped, high-frequency modes leads to significant deviations from Markovian evolution in both measures. In particular, we find that modes that are nearly resonant with gaps in the excitonic spectrum produce dynamics that deviate most strongly from the Lindblad approximation, despite the trace distance measuring larger amounts of non-Markovianity for higher frequency modes. Overall we find that the detailed structure in the high-frequency region of the spectral density has a significant impact on the nature of the dynamics of excitons.

Two-dimensional photon echoes reveal non-Markovian energy transfer in an excitonic dimer.

We show that strong non-Markovian effects can be revealed by the steady-state two-dimensional (2D) photon echo spectra at asymptotic waiting times. For this, we use a simple dimer toy model that is strongly coupled to a harmonic bath with parameters typical for photoactive biomolecules. We calculate the 2D photon echo spectra employing both the numerically exact hierarchy equation of motion and the quasiadiabatic path integral approach and compare these results with approximate results from a time-nonlocal quantum master equation approach. While the latter correctly reproduces the exact population dynamics at long times, it fails at the same time to correctly describe the 2D photon echo spectra at long waiting times. The differences show that non-Markovian effects are much more important for the steady-state 2D photon echoes than for the equilibrium populations. Thus, accurate theoretical descriptions of the energy transfer dynamics in biomolecular complexes have to be based on numerically exact simulations of the environmental fluctuations when nonlinear response functions are analyzed.

Biphasic aggregation of a perylene bisimide dye identified by exciton-vibrational spectra.

The quantum efficiency of light emission is a crucial parameter of supramolecular aggregates that can be tuned by the molecular design of the monomeric species. Here, we report on a strong variation of the fluorescence quantum yield due to different phases of aggregation for the case of a perylene bisimide dye. In particular, a change of the dominant aggregation character from H- to J-type within the first aggregation steps is found, explaining the observed dramatic change in quantum yield. This behaviour is rationalised by means of a systematic study of the intermolecular potential energy surfaces using the time-dependent density functional based tight-binding (TD-DFTB) method. This provides a correlation between structural changes and a coupling strength and supports the notion of H-type stacked dimers and J-type stack-slipped dimers. The exciton-vibrational level structure is modelled by means of an excitonic dimer model including two effective vibrational modes per monomer. Calculated absorption and fluorescence spectra are found to be in reasonable agreement with experimental ones, thus supporting the conclusion on the aggregation behaviour.

Exact stochastic unraveling of an optical coherence dynamics by cumulant expansion.

A numerically exact Monte Carlo scheme for calculation of open quantum system dynamics is proposed and implemented. The method consists of a Monte Carlo summation of a perturbation expansion in terms of trajectories in Liouville phase-space with respect to the coupling between the excited states of the molecule. The trajectories are weighted by a complex decoherence factor based on the second-order cumulant expansion of the environmental evolution. The method can be used with an arbitrary environment characterized by a general correlation function and arbitrary coupling strength. It is formally exact for harmonic environments, and it can be used with arbitrary temperature. Time evolution of an optically excited Frenkel exciton dimer representing a molecular exciton interacting with a charge transfer state is calculated by the proposed method. We calculate the evolution of the optical coherence elements of the density matrix and linear absorption spectrum, and compare them with the predictions of standard simulation methods.

Exciton coupling induces vibronic hyperchromism in light-harvesting complexes

The recently suggested possibility that weak vibronic transitions can be excitonically enhanced in light-harvesting complexes is studied in detail. A vibronic exciton dimer model that includes ground-state vibrations is investigated using the multi-configuration time-dependent Hartree method with a parameter set typical to photosynthetic light-harvesting complexes. The absorption spectra are discussed based on the Coulomb coupling, the detuning of the site energies, and the number of vibrational modes. Fluorescence spectra calculations show that the spectral densities obtained from the low-temperature fluorescence line-narrowing measurements of light-harvesting systems need to be corrected for the effects of excitons. For the J-aggregate configuration, as in most light-harvesting complexes, the true spectral density has a larger amplitude than that obtained from the measurement.

Exciton-vibrational coupling in molecular aggregates: Electronic versus vibronic dimer

The influence of exciton-vibrational coupling on the energy level structure, oscillator strength, and relaxation dynamics is investigated for two different excitonic dimer models. As compared with a purely electronic dimer, the inclusion of local vibrational modes within a vibronic dimer gives rise to a complex energy level structure including avoided crossings and changes of the nature of the exciton states from electronic to vibrational character. Besides these static properties, the dissipative dynamics of the two models is systematically investigated using Redfield relaxation theory. In case of the vibronic dimer this allows to treat selected vibrational degrees of freedom beyond the limits of perturbation theory and Markov approximation. It is demonstrated that the vibronic dimer gives rise to transient vibrational population trapping in the one-exciton manifold.

Optimized hierarchical equations of motion theory for Drude dissipation and efficient implementation to nonlinear spectroscopies

Hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on the basis of a Padé spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the a priori convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system. We combine the present theory with several advanced techniques such as the block hierarchical dynamics in mixed Heisenberg-Schrödinger picture and the on-the-fly filtering algorithm for the efficient evaluation of third-order optical response functions.

Quantum state and process tomography of energy transfer systems via ultrafast spectroscopy

The description of excited state dynamics in energy transfer systems constitutes a theoretical and experimental challenge in modern chemical physics. A spectroscopic protocol that systematically characterizes both coherent and dissipative processes of the probed chromophores is desired. Here, we show that a set of two-color photon-echo experiments performs quantum state tomography (QST) of the one-exciton manifold of a dimer by reconstructing its density matrix in real time. This possibility in turn allows for a complete description of excited state dynamics via quantum process tomography (QPT). Simulations of a noisy QPT experiment for an inhomogeneously broadened ensemble of model excitonic dimers show that the protocol distills rich information about dissipative excitonic dynamics, which appears nontrivially hidden in the signal monitored in single realizations of four-wave mixing experiments.

Advancing Hierarchical Equations of Motion for Efficient Evaluation of Coherent Two-dimensional Spectroscopy

To advance hierarchical equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg-Schrödinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. The new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focusing on the effects of intermolecular transfer coupling and bi-exciton interaction.

Quantum process tomography of excitonic dimers from two-dimensional electronic spectroscopy. I. General theory and application to homodimers

Is it possible to infer the time evolving quantum state of a multichromophoric system from a sequence of two-dimensional electronic spectra (2D-ES) as a function of waiting time? Here we provide a positive answer for a tractable model system: a coupled dimer. After exhaustively enumerating the Liouville pathways associated to each peak in the 2D-ES, we argue that by judiciously combining the information from a series of experiments varying the polarization and frequency components of the pulses, detailed information at the amplitude level about the input and output quantum states at the waiting time can be obtained. This possibility yields a quantum process tomography (QPT) of the single-exciton manifold, which completely characterizes the open quantum system dynamics through the reconstruction of the process matrix. In this manuscript, we present the general theory as well as specific and numerical results for a homodimer, for which we prove that signals stemming from coherence to population transfer and vice versa vanish upon isotropic averaging, therefore, only allowing for a partial QPT in such case. However, this fact simplifies the spectra, and it follows that only two polarization controlled experiments (and no pulse-shaping requirements) suffice to yield the elements of the process matrix, which survive under isotropic averaging. Redundancies in the 2D-ES amplitudes allow for the angle between the two site transition dipole moments to be self-consistently obtained, hence simultaneously yielding structural and dynamical information of the dimer. Model calculations are presented, as well as an error analysis in terms of the angle between the dipoles and peak amplitude extraction. In the second article accompanying this study, we numerically exemplify the theory for heterodimers and carry out a detailed error analysis for such case. This investigation reveals an exciting quantum information processing (QIP) approach to spectroscopic experiments of excitonic systems, and hence, bridges an important gap between theoretical studies on excitation energy transfer from the QIP standpoint and experimental methods to study such systems in the chemical physics community.