Two-dimensional electronic spectroscopy of molecular aggregates

Intramolecular charge transfer and the function of vibronic excitons in photosynthetic light harvesting

A widely discussed explanation for the prevalence of pairs or clusters of closely spaced electronic chromophores in photosynthetic light-harvesting proteins is the presence of ultrafast and highly directional excitation energy transfer pathways mediated by vibronic excitons, the delocalized optical excitations derived from mixing of the electronic and vibrational states of the chromophores. We discuss herein the hypothesis that internal conversion processes between exciton states on the <100 fs timescale are possible when the excitonic potential energy surfaces are controlled by the vibrational modes that induce charge transfer character in a strongly coupled system of chromophores. We discuss two examples, the peridinin-chlorophyll protein from marine dinoflagellates and the intact phycobilisome from cyanobacteria, in which the intramolecular charge-transfer (ICT) character arising from out-of-plane distortion of the conjugation of carotenoid or bilin chromophores also results in localization of the initially delocalized optical excitation on the vibrational timescale. Tuning of the ground state conformations of the chromophores to manipulate their ICT character provides a natural photoregulatory mechanism, which would control the overall quantum yield of excitation energy transfer by turning on and off the delocalized character of the optical excitations.

Full visible range two-dimensional electronic spectroscopy with high time resolution

Two-dimensional electronic spectroscopy (2DES) is a powerful method to study coherent and incoherent interactions and dynamics in complex quantum systems by correlating excitation and detection energies in a nonlinear spectroscopy experiment. Such dynamics can be probed with a time resolution limited only by the duration of the employed laser pulses and in a spectral range defined by the pulse spectrum. In the blue spectral range (<500 nm), the generation of sufficiently broadband ultrashort pulses with pulse durations of 10 fs or less has been challenging so far. Here, we present a 2DES setup based on a hollow-core fiber supercontinuum covering the full visible range (400-700 nm). Pulse compression via custom-made chirped mirrors yields a time resolution of <10 fs. The broad spectral coverage, in particular the extension of the pulse spectra into the blue spectral range, unlocks new possibilities for coherent investigations of blue-light absorbing and multichromophoric compounds, as demonstrated by a 2DES measurement of chlorophyll a.

Experimental Access to Mode-Specific Coupling between Quantum Molecular Vibrations and Classical Bath Modes

The interaction of quantum-mechanical systems with a fluctuating thermal environment (bath) is fundamental to molecular mechanics and energy transport/dissipation. Its complete picture requires mode-specific measurements of this interaction and an understanding of its nature. Here, we present a combined experimental and theoretical study providing detailed insights into the coupling between a high-frequency vibrational two-level system and thermally excited terahertz modes. Experimentally, two-dimensional terahertz-infrared-visible spectroscopy reports directly on the coupling between quantum oscillators represented by CH3 streching vibrations in liquid dimethyl sulfoxide and distinct low-frequency modes. Theoretically, we present a mixed quantum-classical formalism of the sample response to enable the simultaneous quantum description of high-frequency oscillators and a classical description of the bath. We derive the strength and nature of interaction and find different coupling between CH3 stretch and low-frequency modes. This general approach enables quantitative and mode-specific analysis of coupled quantum and classical dynamics in complex chemical systems.

Ultrafast Anisotropy Decay Reveals Structure and Energy Transfer in Supramolecular Aggregates

Chlorosomes from green bacteria perform the most efficient light capture and energy transfer, as observed among natural light-harvesting antennae. Hence, their unique functional properties inspire developments in artificial light-harvesting and molecular optoelectronics. We examine two distinct organizations of the molecular building blocks as proposed in the literature, demonstrating how these organizations alter light capture and energy transfer, which can serve as a mechanism that the bacteria utilize to adapt to changes in light conditions. Spectral simulations of polarization-resolved two-dimensional electronic spectra unravel how changes in the helicity of chlorosomal aggregates alter energy transfer. We show that ultrafast anisotropy decay presents a spectral signature that reveals contrasting energy pathways in different chlorosomes.

Development of Two-Dimensional Electronic-Vibrational Sum Frequency Generation (2D-EVSFG) for Vibronic and Solvent Couplings of Molecules at Interfaces and Surfaces

Many photoinduced excited states' relaxation processes and chemical reactions occur at interfaces and surfaces, including charge transfer, energy transfer, proton transfer, proton-coupled electron transfer, configurational dynamics, conical intersections, etc. Of them, interactions of electronic and vibrational motions, namely, vibronic couplings, are the main determining factors for the relaxation processes or reaction pathways. However, time-resolved electronic-vibrational spectroscopy for interfaces and surfaces is lacking. Here we develop interface/surface-specific two-dimensional electronic-vibrational sum frequency generation spectroscopy (2D-EVSFG) for time-dependent vibronic coupling of excited states at interfaces and surfaces. We further demonstrate the fourth-order technique by investigating vibronic coupling, solvent correlation, and time evolution of the coupling for photoexcited interface-active molecules, crystal violet (CV), at the air/water interface as an example. The two vibronic absorption peaks for CV molecules at the interface from the 2D-EVSFG experiments were found to be more prominent than their counterparts in bulk from 2D-EV. Quantitative analysis of the vibronic peaks in 2D-EVSFG suggested that a non-Condon process participates in the photoexcitation of CV at the interface. We further reveal vibrational solvent coupling for the zeroth level on the electronic state with respect to that on the ground state, which is directly related to the magnitude of its change in solvent reorganization energy. The change in the solvent reorganization energy at the interface is much smaller than that in bulk methanol. Time-dependent center line slopes (CLSs) of 2D-EVSFG also showed that kinetic behaviors of CV at the air/water interface are significantly different from those in bulk methanol. Our ultrafast 2D-EVSFG experiments not only offer vibrational information on both excited states and the ground state as compared with the traditional doubly resonant sum frequency generation and electronic-vibrational coupling but also provide vibronic coupling, dynamical solvent effects, and time evolution of vibronic coupling at interfaces.

An accurate and efficient Ehrenfest dynamics approach for calculating linear and nonlinear electronic spectra

Linear and nonlinear electronic spectra provide an important tool to probe the absorption and transfer of electronic energy. Here, we introduce a pure state Ehrenfest approach to obtain accurate linear and nonlinear spectra that is applicable to systems with large numbers of excited states and complex chemical environments. We achieve this by representing the initial conditions as sums of pure states and unfolding multi-time correlation functions into the Schrödinger picture. By doing this, we show that one can obtain significant improvements in accuracy over the previously used projected Ehrenfest approach and that these benefits are particularly pronounced in cases where the initial condition is a coherence between excited states. While such initial conditions do not arise when calculating linear electronic spectra, they play a vital role in capturing multidimensional spectroscopies. We demonstrate the performance of our method by showing that it is able to quantitatively capture the exact linear, 2D electronic spectroscopy, and pump-probe spectra for a Frenkel exciton model in slow bath regimes and is even able to reproduce the main spectral features in fast bath regimes.

Measuring the Ultrafast Spectral Diffusion and Vibronic Coupling Dynamics in CdSe Colloidal Quantum Wells using Two-Dimensional Electronic Spectroscopy

We measure the ultrafast spectral diffusion, vibronic dynamics, and energy relaxation of a CdSe colloidal quantum wells (CQWs) system at room temperature using two-dimensional electronic spectroscopy (2DES). The energy relaxation of light-hole (LH) excitons and hot carriers to heavy-hole (HH) excitons is resolved with a time scale of ∼210 fs. We observe the equilibration dynamics between the spectroscopically accessible HH excitonic state and a dark state with a time scale of ∼160 fs. We use the center line slope analysis to quantify the spectral diffusion dynamics in HH excitons, which contains an apparent sub-200 fs decay together with oscillatory features resolved at 4 and 25 meV. These observations can be explained by the coupling to various lattice phonon modes. We further perform quantum calculations that can replicate and explain the observed dynamics. The 4 meV mode is observed to be in the near-critically damped regime and may be mediating the transition between the bright and dark HH excitons. These findings show that 2DES can provide a comprehensive and detailed characterization of the ultrafast spectral properties in CQWs and similar nanomaterials.

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.

Gaussian process regression for absorption spectra analysis of molecular dimers

A common task is the determination of system parameters from spectroscopy, where one compares the experimental spectrum with calculated spectra, that depend on the desired parameters. Here we discuss an approach based on a machine learning technique, where the parameters for the numerical calculations are chosen from Gaussian Process Regression (GPR). This approach does not only quickly converge to an optimal parameter set, but in addition provides information about the complete parameter space, which allows for example to identify extended parameter regions where numerical spectra are consistent with the experimental one. We consider as example dimers of organic molecules and aim at extracting in particular the interaction between the monomers, and their mutual orientation. We find that indeed the GPR gives reliable results which are in agreement with direct calculations of these parameters using quantum chemical methods.

Plasmon-Enhanced Exciton Delocalization in Squaraine-Type Molecular Aggregates

Enlarging exciton coherence lengths in molecular aggregates is critical for enhancing the collective optical and transport properties of molecular thin film nanostructures or devices. We demonstrate that the exciton coherence length of squaraine aggregates can be increased from 10 to 24 molecular units at room temperature when preparing the aggregated thin film on a metallic rather than a dielectric substrate. Two-dimensional electronic spectroscopy measurements reveal a much lower degree of inhomogeneous line broadening for aggregates on a gold film, pointing to a reduced disorder. The result is corroborated by simulations based on a Frenkel exciton model including exciton-plasmon coupling effects. The simulation shows that localized, energetically nearly resonant excitons on spatially well separated segments can be radiatively coupled via delocalized surface plasmon polariton modes at a planar molecule-gold interface. Such plasmon-enhanced delocalization of the exciton wave function is of high importance for improving the coherent transport properties of molecular aggregates on the nanoscale. Additionally, it may help tailor the collective optical response of organic materials for quantum optical applications.

The influence of a Hamiltonian vibration vs a bath vibration on the 2D electronic spectra of a homodimer

We elucidate the influence of the system–bath boundary placement within an open quantum system, with emphasis on the two-dimensional electronic spectra, through the application of the hierarchical equations of motion formalism for an exciton system. We apply two different models, the Hamiltonian vibration model (HVM) and bath vibration model (BVM), to a monomer and a homodimer. In the HVM, we specifically include the vibronic states in the Hamiltonian capturing vibronic quenching, whereas in the BVM, all vibrational details are contained within the bath and described by an underdamped spectral density. The resultant spectra are analyzed in terms of energetic peak position and thermodynamic broadening precision in order to evaluate the efficacy of the two models. The HVM produces 2D spectra with accurate peak positional information, while the BVM is well suited to modeling dynamic peak broadening. For the monomer, both models produce equivalent spectra in the limit where additional damping associated with the underdamped vibration in the BVM approaches zero. This is supported by analytical results. However, for the homodimer, the BVM spectra are redshifted with respect to the HVM due to an absence of vibronic quenching in the BVM. The computational efficiency of the two models is also discussed in order to inform us of the most appropriate use of each method.

Hybridized Exciton-Photon-Phonon States in a Transition Metal Dichalcogenide van der Waals Heterostructure Microcavity

Excitons in atomically thin transition-metal dichalcogenides (TMDs) have been established as an attractive platform to explore polaritonic physics, owing to their enormous binding energies and giant oscillator strength. Basic spectral features of exciton polaritons in TMD microcavities, thus far, were conventionally explained via two-coupled-oscillator models. This ignores, however, the impact of phonons on the polariton energy structure. Here we establish and quantify the threefold coupling between excitons, cavity photons, and phonons. For this purpose, we employ energy-momentum-resolved photoluminescence and spatially resolved coherent two-dimensional spectroscopy to investigate the spectral properties of a high-quality-factor microcavity with an embedded WSe_{2} van der Waals heterostructure at room temperature. Our approach reveals a rich multibranch structure which thus far has not been captured in previous experiments. Simulation of the data reveals hybridized exciton-photon-phonon states, providing new physical insight into the exciton polariton system based on layered TMDs.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

Signatures of coherent vibronic exciton dynamics and conformational control in two-dimensional electronic spectroscopy of conjugated polymers

Two-dimensional electronic spectroscopy (2DES) signals for homo-oligomer J-aggregates are computed, with a focus on the role of structural change induced by low-frequency torsional modes along with quasi-stationary trapping effects induced...

Aggregation induced by the synergy of sodium chloride and high-pressure improves chlorophyll stability

The development of green vegetable processing is still limited by the imperfect green protection now. Chlorophyll (Chl), the main pigment presented in green vegetables, was studied that the effects of NaCl on the stability of it, and the synergy of NaCl and high-pressure on Chl protection. Compared to the control, the retention of Chl was increased by 80.14% and the activation energy was 62.7% higher in 7.8% NaCl solution. When the pressure was 600 MPa with 7.8% NaCl, the synergy of NaCl and high-pressure increased the Chl retention by 100%. The restriction of NaCl to H₂O provided Chl with a lower polarity environment and increased the contact between Chl molecules. And the fluorescence quenching confirmed the aggregation of Chls induced by high-pressure. This study explains the mechanism of green protection by NaCl and high-pressure, broadening the horizon for the development of color protection in vegetable processing.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

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.

Quantum Dynamics of Exciton Transport and Dissociation in Multichromophoric Systems

Due to the subtle interplay of site-to-site electronic couplings, exciton delocalization, nonadiabatic effects, and vibronic couplings, quantum dynamical studies are needed to elucidate the details of ultrafast photoinduced energy and charge transfer events in organic multichromophoric systems. In this vein, we review an approach that combines first-principles parameterized lattice Hamiltonians with accurate quantum dynamical simulations using advanced multiconfigurational methods. Focusing on the elementary transfer steps in organic functional materials, we address coherent exciton migration and creation of charge transfer excitons in homopolymers, notably representative of the poly(3-hexylthiophene) material, as well as exciton dissociation at polymer:fullerene heterojunctions. We emphasize the role of coherent transfer, trapping effects due to high-frequency phonon modes, and thermal activation due to low-frequency soft modes that drive a diffusive dynamics.

Exciton-phonon coupling strength in single-layer MoSe2 at room temperature

Single-layer transition metal dichalcogenides are at the center of an ever increasing research effort both in terms of fundamental physics and applications. Exciton–phonon coupling plays a key role in determining the (opto)electronic properties of these materials. However, the exciton–phonon coupling strength has not been measured at room temperature. Here, we use two-dimensional micro-spectroscopy to determine exciton–phonon coupling of single-layer MoSe₂. We detect beating signals as a function of waiting time induced by the coupling between A excitons and A′₁ optical phonons. Analysis of beating maps combined with simulations provides the exciton–phonon coupling. We get a Huang–Rhys factor ~1, larger than in most other inorganic semiconductor nanostructures. Our technique offers a unique tool to measure exciton–phonon coupling also in other heterogeneous semiconducting systems, with a spatial resolution ~260 nm, and provides design-relevant parameters for the development of optoelectronic devices.

The exciton–phonon coupling (EXPC) affects the opto-electronic properties of atomically thin semiconductors. Here, the authors develop two-dimensional micro-spectroscopy to determine the EXPC of monolayer MoSe₂.

Coherent 2D electronic spectroscopy with complete characterization of excitation pulses during all scanning steps

Coherent two-dimensional (2D) electronic spectroscopy has become a standard tool in ultrafast science. Thus it is relevant to consider the accuracy of data considering both experimental imperfections and theoretical assumptions about idealized conditions. It is already known that chirped excitation pulses can affect 2D line shapes. In the present work, we demonstrate performance-efficient, automated characterization of the full electric field of each individual multipulse sequence employed during a 2D scanning procedure. Using Fourier-transform spectral interferometry, we analyze how the temporal intensity and phase profile varies from scanning step to scanning step and extract relevant pulse-sequence parameters. This takes into account both random and systematic variations during the scan that may be caused, for example, by femtosecond pulse-shaping artifacts. Using the characterized fields, we simulate and compare 2D spectra obtained with idealized and real shapes obtained from an LCD-based pulse shaper. Exemplarily, we consider fluorescence of a molecular dimer and multiphoton photoemission of a plasmonic nanoslit. The deviations from pulse-shaper artifacts in our specific case do not distort strongly the population-based multidimensional data. The characterization procedure is applicable to other pulses-shaping technologies or excitation geometries, including also pump-probe geometry with multipulse excitation and coherent detection, and allows for accurate consideration of realistic optical excitation fields at all inter-pulse time-delays.

Development of interface-/surface-specific two-dimensional electronic spectroscopy

Structures, kinetics, and chemical reactivities at interfaces and surfaces are key to understanding many of the fundamental scientific problems related to chemical, material, biological, and physical systems. These steady-state and dynamical properties at interfaces and surfaces require even-order techniques with time-resolution and spectral-resolution. Here, we develop fourth-order interface-/surface-specific two-dimensional electronic spectroscopy, including both two-dimensional electronic sum frequency generation (2D-ESFG) spectroscopy and two-dimensional electronic second harmonic generation (2D-ESHG) spectroscopy, for structural and dynamics studies of interfaces and surfaces. The 2D-ESFG and 2D-ESHG techniques were based on a unique laser source of broadband short-wave IR from 1200 nm to 2200 nm from a home-built optical parametric amplifier. With the broadband short-wave IR source, surface spectra cover most of the visible light region from 480 nm to 760 nm. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate a phase-locked pulse pair for coherent excitation in the 2D-ESFG and 2D-ESHG. As an example, we demonstrated surface dark states and their interactions of the surface states at p-type GaAs (001) surfaces with the 2D-ESFG and 2D-ESHG techniques. These newly developed time-resolved and interface-/surface-specific 2D spectroscopies would bring new information for structure and dynamics at interfaces and surfaces in the fields of the environment, materials, catalysis, and biology.

Resolving Electron-Electron Scattering in Plasmonic Nanorod Ensembles Using Two-Dimensional Electronic Spectroscopy

The use of two-dimensional electronic spectroscopy (2DES) to study electron-electron scattering dynamics in plasmonic gold nanorods is described. The 2DES resolved the time-dependent plasmon homogeneous line width Γ_h(t), which was sensitive to changes in Fermi-level carrier densities. This approach was effective because electronic excitation accelerated plasmon dephasing, which broadened Γ_h. Analysis of Γ_h(t) indicated plasmon coherence times were decreased by 20-50%, depending on excitation conditions. Electron-electron scattering rates of approximately 0.01 fs^-1 were obtained by fitting the time-dependent Γ_h broadening; rates increased quadratically with both excitation pulse energy and frequency. This rate dependence agreed with Fermi-liquid theory-based predictions. Hot electron thermalization through electron-phonon scattering resulted in Γ_h narrowing. To our knowledge, this is the first use of the plasmon Γ_h(t) to isolate electron-electron scattering dynamics in colloidal metal nanoparticles. These results illustrate the effectiveness of 2DES for studying hot electron dynamics of solution-phase plasmonic ensembles.

Photon Correlation Spectroscopy as a Witness for Quantum Coherence

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

Interface-Specific Two-Dimensional Electronic Sum Frequency Generation Spectroscopy

High even-order surface/interface specific spectroscopy has the potential to provide more structural and dynamical information about surfaces and interfaces. In this work, we developed a novel fourth-order interface-specific two-dimensional electronic sum frequency generation (2D-ESFG) for structures and dynamics at surfaces and interfaces. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate phase-locked pulse pairs for coherent pump beams in 2D-ESFG. As a proof-of-principle experiment, fourth-order 2D-ESFG spectroscopy was used to demonstrate couplings of surface states for both n-type and p-type GaAs (100). We found surface dark state within the bandgap of the GaAs in 2D-ESFG spectra, which could not be observed in one-dimensional ESFG spectra. To our best knowledge, this is a first demonstration of interface-specific two-dimensional electronic spectroscopy. The development of the 2D-ESFG spectroscopy will provide new structural probes of spectral diffusion, conformational dynamics, energy transfer, and charge transfer for surfaces and interfaces.

Coherently and fluorescence-detected two-dimensional electronic spectroscopy: direct comparison on squaraine dimers

Optical two-dimensional electronic spectroscopy (2DES) is now widely utilized to study excitonic structure and dynamics of a broad range of systems, from molecules to solid state. Besides the traditional experimental implementation using phase matching and coherent signal field detection, action-based approaches that detect incoherent signals such as fluorescence have been gaining popularity in recent years. While incoherent detection extends the range of applicability of 2DES, the observed spectra are not equivalent to the coherently detected ones. This raises questions about their interpretation and the sensitivity of the technique. Here we directly compare, both experimentally and theoretically, four-wave mixing coherently and fluorescence-detected 2DES of a series of squaraine dimers of increasing electronic coupling. All experiments are qualitatively well reproduced by a Frenkel exciton model with secular Redfield theory description of excitation dynamics. We contrast the spectral features and the sensitivities of both techniques with respect to exciton energies, delocalization, coherent and dissipative dynamics, and exciton-exciton annihilation. Discussing the fundamental and practical differences, we demonstrate the degree of complementarity of the techniques.

Spatially Resolved Photogenerated Exciton and Charge Transport in Emerging Semiconductors

We review recent advances in the characterization of electronic forms of energy transport in emerging semiconductors. The approaches described all temporally and spatially resolve the evolution of initially localized populations of photogenerated excitons or charge carriers. We first provide a comprehensive background for describing the physical origin and nature of electronic energy transport both microscopically and from the perspective of the observer. We introduce the new family of far-field, time-resolved optical microscopies developed to directly resolve not only the extent of this transport but also its potentially temporally and spatially dependent rate. We review a representation of examples from the recent literature, including investigation of energy flow in colloidal quantum dot solids, organic semiconductors, organic-inorganic metal halide perovskites, and 2D transition metal dichalcogenides. These examples illustrate how traditional parameters like diffusivity are applicable only within limited spatiotemporal ranges and how the techniques at the core of this review,especially when taken together, are revealing a more complete picture of the spatiotemporal evolution of energy transport in complex semiconductors, even as a function of their structural heterogeneities.

From wavelike to sub-diffusive motion: exciton dynamics and interaction in squaraine copolymers of varying length

Exciton transport and exciton-exciton interactions in molecular aggregates and polymers are of great importance in natural photosynthesis, organic electronics, and related areas of research. Both the experimental observation and theoretical description of these processes across time and length scales, including the transition from the initial wavelike motion to the following long-range exciton transport, are highly challenging. Therefore, while exciton dynamics at small scales are often treated explicitly, long-range exciton transport is typically described phenomenologically by normal diffusion. In this work, we study the transition from wavelike to diffusive motion of interacting exciton pairs in squaraine copolymers of varying length. To this end we use a combination of the recently introduced exciton-exciton-interaction two-dimensional (EEI2D) electronic spectroscopy and microscopic theoretical modelling. As we show by comparison with the model, the experimentally observed kinetics include three phases, wavelike motion dominated by immediate exciton-exciton annihilation (10-100 fs), sub-diffusive behavior (0.1-10 ps), and excitation relaxation (0.01-1 ns). We demonstrate that the key quantity for the transition from wavelike to diffusive dynamics is the exciton delocalization length relative to the length of the polymer: while in short polymers wavelike motion of rapidly annihilating excitons dominates, in long polymers the excitons become locally trapped and exhibit sub-diffusive behavior. Our findings indicate that exciton transport through conjugated systems emerging from the excitonic structure is generally not governed by normal diffusion. Instead, to characterize the material transport properties, the diffusion presence and character should be determined.

Interplay Between J- and H-Type Coupling in Aggregates of π-Conjugated Polymers: A Single-Molecule Perspective

Strong dipole–dipole coupling within and between π‐conjugated segments shifts electronic transitions, and modifies vibronic coupling and excited‐state lifetimes. Since J‐type coupling between monomers along the conjugated‐polymer (CP) chain and H‐type coupling of chromophores between chains of a CP compete, a superposition of the spectral modifications arising from each type of coupling emerges, making the two couplings hard to discern in the ensemble. We introduce a single‐molecule H‐type aggregate of fixed spacing and variable length of up to 10 nm. HJ‐type aggregate formation is visualized intuitively in the scatter of single‐molecule spectra.

Rapid multiple-quantum three-dimensional fluorescence spectroscopy disentangles quantum pathways

Coherent two-dimensional spectroscopy is a powerful tool for probing ultrafast quantum dynamics in complex systems. Several variants offer different types of information but typically require distinct beam geometries. Here we introduce population-based three-dimensional (3D) electronic spectroscopy and demonstrate the extraction of all fourth- and multiple sixth-order nonlinear signal contributions by employing 125-fold (1⨯5⨯5⨯5) phase cycling of a four-pulse sequence. Utilizing fluorescence detection and shot-to-shot pulse shaping in single-beam geometry, we obtain various 3D spectra of the dianion of TIPS-tetraazapentacene, a fluorophore with limited stability at ambient conditions. From this, we recover previously unknown characteristics of its electronic two-photon state. Rephasing and nonrephasing sixth-order contributions are measured without additional phasing that hampered previous attempts using noncollinear geometries. We systematically resolve all nonlinear signals from the same dataset that can be acquired in 8 min. The approach is generalizable to other incoherent observables such as external photoelectrons, photocurrents, or photoions.

Transient Two-Dimensional Electronic Spectroscopy: Coherent Dynamics at Arbitrary Times along the Reaction Coordinate

Recent advances in two-dimensional electronic spectroscopy (2DES) have enabled identification of fragile quantum coherences in condensed-phase systems near the equilibrium molecular geometry. In general, traditional 2DES cannot measure such coherences associated with photophysical processes that occur at times significantly after the initially prepared state has dephased, such as the evolution of the initial excited state into a charge transfer state. We demonstrate the use of transient two-dimensional electronic spectroscopy (t-2DES) to probe coherences in an electron donor-acceptor dyad consisting of a perylenediimide (PDI) acceptor and a perylene (Per) donor. An actinic pump pulse prepares the lowest excited singlet state of PDI followed by formation of the PDI^•--Per^•+ ion pair, which is probed at different times following the actinic pulse using 2DES. Analysis of the observed coherences provides information about electronic, vibronic, and vibrational interactions at any time along the reaction coordinate for ion pair formation.

Near-Field Spectroscopy of Nanoscale Molecular Aggregates

When molecules are assembled into an aggregate, their mutual dipole-dipole interaction leads to electronic eigenstates that are coherently delocalized over many molecules. Knowledge about these states is important to understand the optical and transfer properties of the aggregates. Optical spectroscopy, in principle, allows one to infer information on these eigenstates and about the interactions between the molecules. However, traditional optical techniques using an electromagnetic field which is uniform over the relevant size of the aggregate cannot access most of the excited states because of selection rules. We demonstrate that by using localized fields one can obtain information about these otherwise inaccessible states. As an example, we discuss in detail the case of local excitation via radiation from the apex of a metallic tip, which allows also scanning across the aggregate. The resulting spatially resolved spectra provide extensive information on the eigenenergies and wave functions. Finally we show that the technique will elucidate the anomalous temperature dependence of superradiance found recently for two-dimensional aggregates of the semiconductor PTCDA formed on a KCl surface.

Understanding the influence of disorder on the exciton dynamics and energy transfer in Zn-phthalocyanine H-aggregates

The photophysics of 9(19),16(17),23(24)-tri-tert-butyl-2-[ethynyl-(4-carboxymethyl)phenyl]phthalocyaninatozinc(ii) and its H-aggregates is studied in different solvents by means of ultrafast non-linear optical spectroscopy and computational modeling. In non-coordinating solvents, both stationary and time-resolved spectroscopies highlight the formation of extended molecular aggregates, whose dimension and spectral properties depends on the concentration. In all the explored experimental conditions, time-resolved transient absorption experiments show multi exponential decay of the signals. Additional insights into the excited state relaxation mechanisms of the system is obtained with 2D electronic spectroscopy, which is employed to compare the deactivation channels in the absence or presence of aggregates. In ethanol and diethylether, where only monomers are present, an ultrafast relaxation process among the two non-degenerate Q-states of the molecule is evidenced by the appearance of a cross peak in the 2D-maps. In chloroform or CCl4, where disordered H-aggregates are formed, an energy transfer channel among aggregates with different composition and size is observed, leading to the non-radiative decay towards the lower energy dark state of the aggregates. Efficient coupling between less and more aggregated species is highlighted in two-dimensional electronic spectra by the appearance of a cross peak. The kinetics and intensity of the latter depend on the concentration of the solution. Finally, the linear spectroscopic properties of the aggregate are reproduced using a simplified structural model of an extended aggregate, based on Frenkel Hamiltonian Calculations and on an estimate of the electronic couplings between each dimer composing the aggregate computed at DFT level.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

Fluorescence-Detected Two-Quantum and One-Quantum-Two-Quantum 2D Electronic Spectroscopy

We demonstrate two-quantum (2Q) coherent two-dimensional (2D) electronic spectroscopy using a shot-to-shot-modulated pulse shaper and fluorescence detection. Broadband collinear excitation is realized with the supercontinuum output of an argon-filled hollow-core fiber, enabling us to excite multiple transitions simultaneously in the visible range. The 2Q contribution is extracted via a three-pulse sequence with 16-fold phase cycling and simulated employing cresyl violet as a model system. Furthermore, we report the first experimental realization of one-quantum-two-quantum (1Q-2Q) 2D spectroscopy, offering less congested spectra as compared with the 2Q implementation. We avoid scattering artifacts and nonresonant solvent contributions by using fluorescence as the observable. This allows us to extract quantitative information about doubly excited states that agree with literature expectations. The high sensitivity and background-free nature of fluorescence detection allow for a general applicability of this method to many other systems.

Recent advances in multidimensional ultrafast spectroscopy

Multidimensional ultrafast spectroscopies are one of the premier tools to investigate condensed phase dynamics of biological, chemical and functional nanomaterial systems. As they reach maturity, the variety of frequency domains that can be explored has vastly increased, with experimental techniques capable of correlating excitation and emission frequencies from the terahertz through to the ultraviolet. Some of the most recent innovations also include extreme cross-peak spectroscopies that directly correlate the dynamics of electronic and vibrational states. This review article summarizes the key technological advances that have permitted these recent advances, and the insights gained from new multidimensional spectroscopic probes.

Two-dimensional electronic spectroscopy as a tool for tracking molecular conformations in DNA/RNA aggregates

A computational strategy to simulate two-dimensional electronic spectra (2DES) is introduced, which allows characterising ground state conformations of flexible nucleobase aggregates that play a crucial role in nucleic acid photochemistry.

Quantum Coherent Excitation Energy Transfer by Carotenoids in Photosynthetic Light Harvesting

It remains an open question whether quantum coherence and molecular excitons created by delocalization of electronic excited states are essential features of the mechanisms that enable efficient light capture and excitation energy transfer to reaction centers in photosynthetic organisms. The peridinin-chlorophyll a protein from marine dinoflagellates is an example of a light-harvesting system with tightly clustered antenna chromophores in which quantum coherence has long been suspected, but unusually it features the carotenoid peridinin as the principal light absorber for mid-visible photons. We report that broad-band two-dimensional electronic spectroscopy indeed reveals the initial presence of exciton relaxation pathways that enable transfer of excitation from peridinin to chlorophyll a in <20 fs, but the quantum coherence that permits this is very short-lived. Strongly coupled excited-state vibrational distortions of the peridinins trigger a dynamic transition of the electronic structure of the system and a rapid conversion to incoherent energy transfer mechanisms.

Ultrafast Solvation Dynamics and Vibrational Coherences of Halogenated Boron-Dipyrromethene Derivatives Revealed through Two-Dimensional Electronic Spectroscopy

Boron-dipyrromethene (BODIPY) chromophores have a wide range of applications, spanning areas from biological imaging to solar energy conversion. Understanding the ultrafast dynamics of electronically excited BODIPY chromophores could lead to further advances in these areas. In this work, we characterize and compare the ultrafast dynamics of halogenated BODIPY chromophores through applying two-dimensional electronic spectroscopy (2DES). Through our studies, we demonstrate a new data analysis procedure for extracting the dynamic Stokes shift from 2DES spectra revealing an ultrafast solvent relaxation. In addition, we extract the frequency of the vibrational modes that are strongly coupled to the electronic excitation, and compare the results of structurally different BODIPY chromophores. We interpret our results with the aid of DFT calculations, finding that structural modifications lead to changes in the frequency, identity, and magnitude of Franck-Condon active vibrational modes. We attribute these changes to differences in the electron density of the electronic states of the structurally different BODIPY chromophores.