Using fluorescence detected two-dimensional spectroscopy to investigate initial exciton delocalization between coupled chromophores

Coherent Vibrations Promote Charge-Transfer across a Graphene-Based Interface

Discerning the impact of the coherent motion of the nuclei on the timing and efficiency of charge transfer at the donor-acceptor interface is essential for designing performance-enhanced optoelectronic devices. Here, we employ an experimental approach using photocurrent detection in coherent multidimensional spectroscopy to excite a donor aromatic macrocycle and collect the charge transferred to a 2D acceptor layer. For this purpose, we prepared a cobalt phthalocyanine-graphene (CoPc-Gr) interface. Unlike blends, the well-ordered architecture achieved through the physical separation of the two layers allows us to unambiguously collect the electrical signal from graphene alone and associate it with a microscopic understanding of the whole process. The CoPc-Gr interface exhibits an ultrafast electron-transfer signal, stemming from an interlayer mechanism. Remarkably, the signal presents an oscillating time evolution modulated by coherent vibrations originating from the laser-excited CoPc states. By performing Fourier analysis on the beatings and correlating it with the Raman features, along with a comprehensive first-principles characterization of the vibrational coupling in the CoPc excited states, we successfully identify both the orbitals and molecular vibrations that promote the charge transfer at the interface.

Nonlinear Optical Spectroscopy of Molecular Assemblies: What Is Gained and Lost in Action Detection?

This study elucidates the information content that is extracted from action-2D electronic spectroscopy (A-2DES) when the output intensity is not proportional to the number of excitations generated. Such a scenario can be realized in both fluorescence and photocurrent detection because of direct interaction like exciton-exciton annihilation or indirect effects in the signal generation or detection. By means of an intuitive probabilistic model supported by nonlinear response theory, the study concludes that in molecular assemblies the ground-state bleaching contribution can dominate the nonlinear signal and partially or completely hide the stimulated emission. In this case, the spectral effect resembles incoherent mixing, even in the absence of exciton-exciton annihilation, implying reduced information about the excited-state dynamics with an increasing number of chromophores. This finding has important implications for the selection of samples for A-2DES as well as for its interpretation.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. II. Analysis of early-time signals

Developing fluorescence-encoded infrared (FEIR) vibrational spectroscopy for single-molecule applications requires a detailed understanding of how the molecular response and external experimental parameters manifest in the detected signals. In Paper I [L. Whaley-Mayda, A. Guha, and A. Tokmakoff, J. Chem. Phys. 159, 194201 (2023)] we introduced a nonlinear response function theory to describe vibrational dynamics, vibronic coupling, and transition dipole orientation in FEIR experiments with ultrashort pulses. In this second paper, we apply the theory to investigate the role of intermode vibrational coherence, the orientation of vibrational and electronic transition dipoles, and the effects of finite pulse durations in experimental measurements. We focus on measurements at early encoding delays-where signal sizes are largest and therefore of most value for single-molecule experiments, but where many of these phenomena are most pronounced and can complicate the appearance of data. We compare experiments on coumarin dyes with finite-pulse response function simulations to explain the time-dependent behavior of FEIR spectra. The role of the orientational response is explored by analyzing polarization-dependent experiments and their ability to resolve relative dipole angles in the molecular frame. This work serves to demonstrate the molecular information content of FEIR experiments, and develop insight and guidelines for their interpretation.

Multimode vibrational dynamics and orientational effects in fluorescence-encoded infrared spectroscopy. I. Response function theory

Fluorescence-encoded infrared (FEIR) spectroscopy is an emerging technique for performing vibrational spectroscopy in solution with detection sensitivity down to single molecules. FEIR experiments use ultrashort pulses to excite a fluorescent molecule's vibrational and electronic transitions in a sequential, time-resolved manner, and are therefore sensitive to intervening vibrational dynamics on the ground state, vibronic coupling, and the relative orientation of vibrational and electronic transition dipole moments. This series of papers presents a theoretical treatment of FEIR spectroscopy that describes these phenomena and examines their manifestation in experimental data. This first paper develops a nonlinear response function description of Fourier-transform FEIR experiments for a two-level electronic system coupled to multiple vibrations, which is then applied to interpret experimental measurements in the second paper [L. Whaley-Mayda et al., J. Chem. Phys. 159, 194202 (2023)]. Vibrational coherence between pairs of modes produce oscillatory features that interfere with the vibrations' population response in a manner dependent on the relative signs of their respective Franck-Condon wavefunction overlaps, leading to time-dependent distortions in FEIR spectra. The orientational response of population and coherence contributions are analyzed and the ability of polarization-dependent experiments to extract relative transition dipole angles is discussed. Overall, this work presents a framework for understanding the full spectroscopic information content of FEIR measurements to aid data interpretation and inform optimal experimental design.

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Unifying Nonlinear Response and Incoherent Mixing in Action-2D Electronic Spectroscopy

Action-detection has expanded the scope and applicability of 2D electronic spectroscopy, while posing new challenges for the unambiguous interpretation of spectral features. In this context, identifying the origin of cross-peaks at early waiting times is not trivial, and incoherent mixing is often invoked as an unwanted contribution masking the nonlinear signal. In this work, we elaborate on the relation between the nonlinear response and the incoherent mixing contribution by analyzing the action signal in terms of one- and two-particle observables. Considering a weakly interacting molecular dimer, we show how cross-peaks at early waiting times, reflecting exciton-exciton annihilation dynamics, can be equivalently interpreted as arising from incoherent mixing. This equivalence, on the one hand, highlights the information content of spectral features related to incoherent mixing and, on the other hand, provides an efficient numerical scheme to simulate the action response of weakly interacting systems.

Optical two-dimensional coherent spectroscopy of many-body dipole-dipole interactions and correlations in atomic vapors

Many-body interactions and correlations in atomic ensembles are fundamental in understanding many-body effects such as collective and emergent phenomena and also play an important role in various atom-based applications. Optical two-dimensional coherent spectroscopy (2DCS) provides a powerful tool to measure many-body interactions and correlations. Here, we present the study of many-body dipole-dipole interactions and correlations in potassium and rubidium atomic vapors by using double-quantum and multi-quantum 2DCS. The results show that double-quantum 2DCS provides sensitive and background-free detection of weak dipole-dipole interaction between atoms with a mean separation up to about 16 μm, and multi-quantum 2DCS can excite and detect multi-atom states (Dicke states) with up to eight correlated atoms. The technique of optical 2DCS can provide a new approach to study many-body physics in atomic ensembles and can be potentially implemented to measure many-body effects in cold atoms and other atomic/molecular systems.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

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

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

Signatures of exciton dynamics and interaction in coherently and fluorescence-detected four- and six-wave-mixing two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) can be realized in increasing nonlinear orders of interaction with the electric field, bringing new information about single- and multi-particle properties and dynamics. Furthermore, signals can be detected both coherently (C-2DES) and by fluorescence (F-2DES), with fundamental and practical differences. We directly compare the simultaneous measurements of four- and six-wave mixing C-2DES and F-2DES on an excitonic heterodimer of squaraine molecules. Spectral features are described in increasing orders of nonlinearity by an explicit excitonic model. We demonstrate that the four-wave-mixing spectra are sensitive to one-exciton energies, their delocalization and dynamics, while the six-wave-mixing spectra include information on bi-exciton and higher excited states including the state energies, electronic coupling, and exciton-exciton annihilation. We focus on the possibility to extract the dynamics arising from exciton-exciton interaction directly from the six-wave-mixing spectra. To this end, in analogy to previously demonstrated fifth-order coherently detected exciton-exciton-interaction 2DES (EEI2D spectroscopy), we introduce a sixth-order fluorescence-detected EEI2D spectroscopy variant.

Polaritons and excitons: Hamiltonian design for enhanced coherence

The primary questions motivating this report are: Are there ways to increase coherence and delocalization of excitation among many molecules at moderate electronic coupling strength? Coherent delocalization of excitation in disordered molecular systems is studied using numerical calculations. The results are relevant to molecular excitons, polaritons, and make connections to classical phase oscillator synchronization. In particular, it is hypothesized that it is not only the magnitude of electronic coupling relative to the standard deviation of energetic disorder that decides the limits of coherence, but that the structure of the Hamiltonian-connections between sites (or molecules) made by electronic coupling-is a significant design parameter. Inspired by synchronization phenomena in analogous systems of phase oscillators, some properties of graphs that define the structure of different Hamiltonian matrices are explored. The report focuses on eigenvalues and ensemble density matrices of various structured, random matrices. Some reasons for the special delocalization properties and robustness of polaritons in the single-excitation subspace (the star graph) are discussed. The key result of this report is that, for some classes of Hamiltonian matrix structure, coherent delocalization is not easily defeated by energy disorder, even when the electronic coupling is small compared to disorder.

New Nonlinear Optical Crystal of Rhodamine 590 Acid Phthalate

The synthesis and crystal structure of rhodamine 590 acid phthalate (RhAP) have been reported. This novel solid-state rhodamine derivative not only has a longer fluorescence lifetime compared to rhodamine solid-state matrixes where emission is quenched but also possesses strong nonlinear optical characteristics. The static and dynamic first- and second-order hyperpolarizabilities were calculated using the time-dependent density functional theory at the B3LYP/6-31+G* level. The computed static values of β and γ of RhAP by the X-ray diffraction (XRD) structure were 31.9 × 10^-30 and 199.0 × 10^-36 esu, respectively. These values were about 62 times larger than the corresponding values in urea, an already well-known nonlinear optical material. The second-order hyperpolarizability of the compound was determined experimentally by measuring the two-photon absorption cross section using intensity-modulated light fields. The reported compound, excitable at near-infrared, exhibited frequency upconversion with the two-photon absorption coefficient enhanced by two orders of magnitude compared to that of the dye solution. Hosting the dye in the solid, at high concentrations, exploits the nonlinearity of the dye itself as well as results in significant excitonic effects including formation of broad exciton band and superradiance.

Compressed Sensing for Reconstructing Coherent Multidimensional Spectra

We apply two sparse reconstruction techniques, the least absolute shrinkage and selection operator (LASSO) and the sparse exponential mode analysis (SEMA), to two-dimensional (2D) spectroscopy. The algorithms are first tested on model data, showing that both are able to reconstruct the spectra using only a fraction of the data required by the traditional Fourier-based estimator. Through the analysis of the sparsely sampled experimental fluorescence-detected 2D spectra of LH2 complexes, we conclude that both SEMA and LASSO can be used to significantly reduce the required data, still allowing one to reconstruct the multidimensional spectra. Of the two techniques, it is shown that SEMA offers preferable performance, providing more accurate estimation of the spectral line widths and their positions. Furthermore, SEMA allows for off-grid components, enabling the use of a much smaller dictionary than that of the LASSO, thereby improving both the performance and the lowering of the computational complexity for reconstructing coherent multidimensional spectra.

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.

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.

Long range dipole-dipole interaction in low-density atomic vapors probed by double-quantum two-dimensional coherent spectroscopy

Optical double-quantum two-dimensional coherent spectroscopy (2DCS) was implemented to probe interatomic dipole-dipole interactions in both potassium and rubidium atomic vapors. The dipole-dipole interaction was detected at densities of 4.81×10⁸ cm ^-3 and 8.40×10⁹ cm ^-3 for potassium and rubidium, respectively, corresponding to a mean interatomic separation of 15.8 μm or 3.0×10⁵ a ₀ for potassium and 6.1 μm or 1.2×10⁵ a ₀ for rubidium, where a ₀ is the Bohr radius. The experimental results confirm the long range nature of the dipole-dipole interaction, which is critical for understanding many-body physics in atoms/molecules. The long range interaction also has implications in atom-based applications involving many-body interactions. Additionally, we demonstrated that double-quantum 2DCS is sufficiently sensitive to probe dipole-dipole interaction at densities that can be achieved with cold atom in a magneto-optical trap, paving the way for double-quantum 2DCS studies of cold atoms and molecules. The method can also open a new avenue to study long-range interactions in solid state systems such as quantum dots and color centers in diamonds.

Before Förster. Initial excitation in photosynthetic light harvesting

Electronic 2D spectroscopy allows nontrivial quantum effects to be explored in unprecedented detail. Here, we apply recently developed fluorescence detected coherent 2D spectroscopy to study the light harvesting antenna 2 (LH2) of photosynthetic purple bacteria. We report double quantum coherence 2D spectra which show clear cross peaks indicating correlated excitations. Similar results are found for rephasing and nonrephasing signals. Analysis of signal generating quantum pathways leads to the conclusion that, contrary to the currently prevailing physical picture, the two weakly coupled pigment rings of LH2 share the initial electronic excitation leading to quantum mechanical correlation between the two clearly separate absorption bands. These results are general and have consequences for the interpretation of initially created excited states not only in photosynthesis but in all light absorbing systems composed of weakly interacting pigments where the excitation transfer is commonly described by using Förster theory. Being able to spectrally resolve the nonequilibrium dynamics immediately following photoabsorption may provide a glimpse to the systems' transition into the Förster regime.

Simulating Fluorescence-Detected Two-Dimensional Electronic Spectroscopy of Multichromophoric Systems

We present a theory for modeling fluorescence-detected two-dimensional electronic spectroscopy of multichromophoric systems. The theory is tested by comparison of the predicted spectra of the light-harvesting complex LH2 with experimental data. A qualitative explanation of the strong cross-peaks as compared to conventional two-dimensional electronic spectra is given. The strong cross-peaks are attributed to the clean ground-state signal that is revealed when the annihilation of exciton pairs created on the same LH2 complex cancels oppositely signed signals from the doubly excited state. This annihilation process occurs much faster than the nonradiative relaxation. Furthermore, the line shape difference is attributed to slow dynamics, exciton delocalization within the bands, and intraband exciton-exciton annihilation. This is in line with existing theories presented for model systems. We further propose the use of time-resolved fluorescence-detected two-dimensional spectroscopy to study state-resolved exciton-exciton annihilation.