Separating single- from multi-particle dynamics in nonlinear spectroscopy.

Quantum states depend on the coordinates of all their constituent particles, with essential multi-particle correlations. Time-resolved laser spectroscopy1 is widely used to probe the energies and dynamics of excited particles and quasiparticles such as electrons and holes2,3, excitons4-6, plasmons7, polaritons8 or phonons9. However, nonlinear signals from single- and multiple-particle excitations are all present simultaneously and cannot be disentangled without a priori knowledge of the system4,10. Here, we show that transient absorption-the most commonly used nonlinear spectroscopy-with N prescribed excitation intensities allows separation of the dynamics into N increasingly nonlinear contributions; in systems well-described by discrete excitations, these N contributions systematically report on zero to N excitations. We obtain clean single-particle dynamics even at high excitation intensities and can systematically increase the number of interacting particles, infer their interaction energies and reconstruct their dynamics, which are not measurable via conventional means. We extract single- and multiple-exciton dynamics in squaraine polymers11,12 and, contrary to common assumption6,13, we find that the excitons, on average, meet several times before annihilating. This surprising ability of excitons to survive encounters is important for efficient organic photovoltaics14,15. As we demonstrate on five diverse systems, our procedure is general, independent of the measured system or type of observed (quasi)particle and straightforward to implement. We envision future applicability in the probing of (quasi)particle interactions in such diverse areas as plasmonics7, Auger recombination2 and exciton correlations in quantum dots5,16,17, singlet fission18, exciton interactions in two-dimensional materials19 and in molecules20,21, carrier multiplication22, multiphonon scattering9 or polariton-polariton interaction8.

High-order pump-probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers.

Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump-probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump-probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump-probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.

Direct comparison of molecular-beam vs liquid-phase pump-probe and two-dimensional spectroscopy on the example of azulene.

Although azulene's anomalous fluorescence originating from S2 rather than from S1 is a textbook example for the violation of Kasha's rule, an understanding of the underlying processes is still a subject of investigation. Here, we use action-based coherent two-dimensional electronic spectroscopy (2DES) to measure a single Liouville-space response pathway from S0 via S1 to the S2 state of azulene. We directly compare this sequential excitation in the liquid phase detecting S2 fluorescence and in a molecular beam detecting photoionized cations, using the S2 anomalous emission to our advantage. We complement the 2DES study with pump-probe measurements of S1 excitation dynamics, including vibrational relaxation and passage through a conical intersection. A direct comparison of the liquid and gas phase allows us to assess the effect of the solvent and the interplay of intra- and intermolecular energy relaxation.

Fluorescence band exchange narrowing in a series of squaraine oligomers: energetic vs. structural disorder.

The influence of oligosquaraine chain length on the energies and shape of absorption and emission bands and the exciton coherence length is studied in CHCl3 where the oligomers adopt a random coil structure. From the observed fluorescence band narrowing an effective coherence length of Ncoh = 2.5 was estimated for the nonamer. Applying a theoretical Frenkel exciton model the absorption and emission spectra were simulated which confirmed the experimental results. From the relative amplitude of the 00 peak to the vibronic shoulder the coherence length was estimated which yields a somewhat higher saturation value of Ncoh≈ 3 for the nonamer, which is in very good agreement with the theoretical amplitude ratio. The coherence length is much smaller than the geometrical length because the electronic delocalisation is reduced by structural disorder. Taking into account the energetic (diagonal) and structural (off-diagonal) disorder we observed a different influence on the absorption and fluorescence spectra. For the emission spectra, exciton delocalisation leads to a narrowing of the band caused by averaging over energetic disorder, but for the absorption band the spectra are broadened by excitonic splitting and structural disorder.

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.

Fluorescence-Detected Pump-Probe Spectroscopy.

We introduce a new approach to transient spectroscopy, fluorescence-detected pump-probe (F-PP) spectroscopy, that overcomes several limitations of traditional PP. F-PP suppresses excited-state absorption, provides background-free detection, removes artifacts resulting from pump-pulse scattering, from non-resonant solvent response, or from coherent pulse overlap, and allows unique extraction of excited-state dynamics under certain conditions. Despite incoherent detection, time resolution of F-PP is given by the duration of the laser pulses, independent of the fluorescence lifetime. We describe the working principle of F-PP and provide its theoretical description. Then we illustrate specific features of F-PP by direct comparison with PP, theoretically and experimentally. For this purpose, we investigate, with both techniques, a molecular squaraine heterodimer, core-shell CdSe/ZnS quantum dots, and fluorescent protein mCherry. F-PP is broadly applicable to chemical systems in various environments and in different spectral regimes.

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.

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.

How reduced excitonic coupling enhances light harvesting in the main photosynthetic antennae of diatoms.

Strong excitonic interactions are a key design strategy in photosynthetic light harvesting, expanding the spectral cross-section for light absorption and creating considerably faster and more robust excitation energy transfer. These molecular excitons are a direct result of exceptionally densely packed pigments in photosynthetic proteins. The main light-harvesting complexes of diatoms, known as fucoxanthin-chlorophyll proteins (FCPs), are an exception, displaying surprisingly weak excitonic coupling between their chlorophyll (Chl) a's, despite a high pigment density. Here, we show, using single-molecule spectroscopy, that the FCP complexes of Cyclotella meneghiniana switch frequently into stable, strongly emissive states shifted 4-10 nm toward the red. A few percent of isolated FCPa complexes and ∼20% of isolated FCPb complexes, on average, were observed to populate these previously unobserved states, percentages that agree with the steady-state fluorescence spectra of FCP ensembles. Thus, the complexes use their enhanced sensitivity to static disorder to increase their light-harvesting capability in a number of ways. A disordered exciton model based on the structure of the main plant light-harvesting complex explains the red-shifted emission by strong localization of the excitation energy on a single Chl a pigment in the terminal emitter domain due to very specific pigment orientations. We suggest that the specific construction of FCP gives the complex a unique strategy to ensure that its light-harvesting function remains robust in the fluctuating protein environment despite limited excitonic interactions.

Ultrafast energy relaxation in single light-harvesting complexes.

Energy relaxation in light-harvesting complexes has been extensively studied by various ultrafast spectroscopic techniques, the fastest processes being in the sub-100-fs range. At the same time, much slower dynamics have been observed in individual complexes by single-molecule fluorescence spectroscopy (SMS). In this work, we use a pump-probe-type SMS technique to observe the ultrafast energy relaxation in single light-harvesting complexes LH2 of purple bacteria. After excitation at 800 nm, the measured relaxation time distribution of multiple complexes has a peak at 95 fs and is asymmetric, with a tail at slower relaxation times. When tuning the excitation wavelength, the distribution changes in both its shape and position. The observed behavior agrees with what is to be expected from the LH2 excited states structure. As we show by a Redfield theory calculation of the relaxation times, the distribution shape corresponds to the expected effect of Gaussian disorder of the pigment transition energies. By repeatedly measuring few individual complexes for minutes, we find that complexes sample the relaxation time distribution on a timescale of seconds. Furthermore, by comparing the distribution from a single long-lived complex with the whole ensemble, we demonstrate that, regarding the relaxation times, the ensemble can be considered ergodic. Our findings thus agree with the commonly used notion of an ensemble of identical LH2 complexes experiencing slow random fluctuations.

Robust light harvesting by a noisy antenna.

Photosynthetic light harvesting can be very efficient in solar energy conversion while taking place in a highly disordered and noisy physiological environment. This efficiency is achieved by the ultrafast speed of the primary photosynthetic processes, which is enabled by a delicate interplay of quantum effects, thermodynamics and environmental noise. The primary processes take place in light-harvesting antennas built from pigments bound to a fluctuating protein scaffold. Here, we employ ultrafast single-molecule spectroscopy to follow fluctuations of the femtosecond energy transfer times in individual LH2 antenna complexes of purple bacteria. By combining single molecule results with ensemble spectroscopy through a unified theoretical description of both, we show how the protein fluctuations alter the excitation energy transfer dynamics. We find that from the thirteen orders of magnitude of possible timescales from picoseconds to minutes, the relevant fluctuations occur predominantly on a biological timescale of seconds, i.e. in the domain of slow protein motion. The measured spectra and dynamics can be explained by the protein modulating pigment excitation energies only. Moreover, we find that the small spread of pigment mean energies allows for excitation delocalization between the coupled pigments to survive. These unique features provide fast energy transport even in the presence of disorder. We conclude that this is the mechanism that enables LH2 to operate as a robust light-harvester, in spite of its intrinsically noisy biological environment.

The Role of Resonant Vibrations in Electronic Energy Transfer.

Nuclear vibrations play a prominent role in the spectroscopy and dynamics of electronic systems. As recent experimental and theoretical studies suggest, this may be even more so when vibrational frequencies are resonant with transitions between the electronic states. Herein, a vibronic multilevel Redfield model is reported for excitonically coupled electronic two-level systems with a few explicitly included vibrational modes and interacting with a phonon bath. With numerical simulations the effects of the quantized vibrations on the dynamics of energy transfer and coherence in a model dimer are illustrated. The resonance between the vibrational frequency and energy gap between the sites leads to a large delocalization of vibronic states, which then results in faster energy transfer and longer-lived mixed coherences.

Estimation of damped oscillation associated spectra from ultrafast transient absorption spectra.

When exciting a complex molecular system with a short optical pulse, all chromophores present in the system can be excited. The resulting superposition of electronically and vibrationally excited states evolves in time, which is monitored with transient absorption spectroscopy. We present a methodology to resolve simultaneously the contributions of the different electronically and vibrationally excited states from the complete data. The evolution of the excited states is described with a superposition of damped oscillations. The amplitude of a damped oscillation cos(ωnt)exp(-γnt) as a function of the detection wavelength constitutes a damped oscillation associated spectrum DOASn(λ) with an accompanying phase characteristic φn(λ). In a case study, the cryptophyte photosynthetic antenna complex PC612 which contains eight bilin chromophores was excited by a broadband optical pulse. Difference absorption spectra from 525 to 715 nm were measured until 1 ns. The population dynamics is described by four lifetimes, with interchromophore equilibration in 0.8 and 7.5 ps. We have resolved 24 DOAS with frequencies between 130 and 1649 cm-1 and with damping rates between 0.9 and 12 ps-1. In addition, 11 more DOAS with faster damping rates were necessary to describe the "coherent artefact." The DOAS contains both ground and excited state features. Their interpretation is aided by DOAS analysis of simulated transient absorption signals resulting from stimulated emission and ground state bleach.

The role of exciton delocalization in the major photosynthetic light-harvesting antenna of plants.

In the major peripheral plant light-harvesting complex LHCII, excitation energy is transferred between chlorophylls along an energetic cascade before it is transmitted further into the photosynthetic assembly to be converted into chemical energy. The efficiency of these energy transfer processes involves a complicated interplay of pigment-protein structural reorganization and protein dynamic disorder, and the system must stay robust within the fluctuating protein environment. The final, lowest energy site has been proposed to exist within a trimeric excitonically coupled chlorophyll (Chl) cluster, comprising Chls a610-a611-a612. We studied an LHCII monomer with a site-specific mutation resulting in the loss of Chls a611and a612, and find that this mutant exhibits two predominant overlapping fluorescence bands. From a combination of bulk measurements, single-molecule fluorescence characterization, and modeling, we propose the two fluorescence bands originate from differing conditions of exciton delocalization and localization realized in the mutant. Disruption of the excitonically coupled terminal emitter Chl trimer results in an increased sensitivity of the excited state energy landscape to the disorder induced by the protein conformations. Consequently, the mutant demonstrates a loss of energy transfer efficiency. On the contrary, in the wild-type complex, the strong resonance coupling and correspondingly high degree of excitation delocalization within the Chls a610-a611-a612 cluster dampens the influence of the environment and ensures optimal communication with neighboring pigments. These results indicate that the terminal emitter trimer is thus an essential design principle for maintaining the efficient light-harvesting function of LHCII in the presence of protein disorder.

Exciton annihilation and diffusion length in disordered multichromophoric nanoparticles.

Efficient exciton transport is the essential property of natural and synthetic light-harvesting (LH) devices. Here we investigate exciton transport properties in LH organic polymer nanoparticles (ONPs) of 40 nm diameter. The ONPs are loaded with a rhodamine B dye derivative and bulky counterion, enabling dye loadings as high as 0.3 M, while preserving fluorescence quantum yields larger than 30%. We use time-resolved fluorescence spectroscopy to monitor exciton-exciton annihilation (EEA) kinetics within the ONPs dispersed in water. We demonstrate that unlike the common practice for photoluminescence investigations of EEA, the non-uniform intensity profile of the excitation light pulse must be taken into account to analyse reliably intensity-dependent population dynamics. Alternatively, a simple confocal detection scheme is demonstrated, which enables (i) retrieving the correct value for the bimolecular EEA rate which would otherwise be underestimated by a typical factor of three, and (ii) revealing minor EEA by-products otherwise unnoticed. Considering the ONPs as homogeneous rigid solutions of weakly interacting dyes, we postulate an incoherent exciton hoping mechanism to infer a diffusion constant exceeding 0.003 cm2 s-1 and a diffusion length as large as 70 nm. This work demonstrates the success of the present ONP design strategy at engineering efficient exciton transport in disordered multichromophoric systems.

Higher-Order Multidimensional and Pump-Probe Spectroscopies.

Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.

Single-Molecule Ultrafast Fluorescence-Detected Pump-Probe Microscopy.

We introduce fluorescence-detected pump-probe microscopy by combining a wavelength-tunable ultrafast laser with a confocal scanning fluorescence microscope, enabling access to the femtosecond time scale on the micrometer spatial scale. In addition, we obtain spectral information from Fourier transformation over excitation pulse-pair time delays. We demonstrate this new approach on a model system of a terrylene bisimide (TBI) dye embedded in a PMMA matrix and acquire the linear excitation spectrum as well as time-dependent pump-probe spectra simultaneously. We then push the technique toward single TBI molecules and analyze the statistical distribution of their excitation spectra. Furthermore, we demonstrate the ultrafast transient evolution of several individual molecules, highlighting their different behavior in contrast to the ensemble due to their individual local environment. By correlating the linear and nonlinear spectra, we assess the effect of the molecular environment on the excited-state energy.

Time-resolved circular dichroism of excitonic systems: theory and experiment on an exemplary squaraine polymer.

Experimental and theoretical foundations for femtosecond time-resolved circular dichroism (TRCD) spectroscopy of excitonic systems are presented. In this method, the system is pumped with linearly polarized light and the signal is defined as the difference between the transient absorption spectrum probed with left and with right circularly polarized light. We present a new experimental setup with a polarization grating as key element to generate circularly polarized pulses. Herein the positive (negative) first order of the diffracted light is left-(right-)circularly polarized and serves as a probe pulse in a TRCD experiment. The grating is capable of transferring ultrashort broadband pulses ranging from 470 nm to 720 nm into two separate beams with opposite ellipticity. By applying a specific chopping scheme we can switch between left and right circular polarizations and detect transient absorption (TA) and TRCD spectra on a shot-to-shot basis simultaneously. We perform experiments on a squaraine polymer, investigating excitonic dynamics, and we develop a general theory for TRCD experiments of excitonically coupled systems that we then apply to describe the experimental data in this particular example. At a magic angle of 54.7° between the pump-pulse polarization and the propagation direction of the probe pulse, the TRCD and TA signals become particularly simple to analyze, since the orientational average over random orientations of complexes factorizes into that of the interaction with the pump and the probe pulse, and the intrinsic electric quadrupole contributions to the TRCD signal average to zero for isotropic samples. Application of exciton theory to linear absorption and to linear circular dichroism spectra of squaraine polymers reveals the presence of two fractions of polymer conformations, a dominant helical conformation with close interpigment distances that are suggested to lead to short-range contributions to site energy shifts and excitonic couplings of the squaraine molecules, and a fraction of unfolded random coils. Theory demonstrates that TRCD spectra of selectively excited helices can resolve state populations that are practically invisible in TA spectroscopy due to the small dipole strength of these states. A qualitative interpretation of TRCD and TA spectra in the spectral window investigated experimentally is offered. The 1 ps time component found in these spectra is related to the slow part of exciton relaxation obtained between states of the helix in the low-energy half of the exciton manifold. The dominant 140 ps time constant reflects the decay of excited states to the electronic ground state.

Radiological and clinical outcome of screw placement in adolescent idiopathic scoliosis: evaluation with low-dose computed tomography.

Posterior corrective surgery using "all pedicle screw construct" carries risk of neurovascular complications. The study aims were to assess the screw placement in patients with adolescent idiopathic scoliosis using CT with low-radiation dose, and to evaluate the clinical outcome in patients with misplaced pedicle screws. CTs of 49 consecutive patients (873 screws, 79% thoracic) were retrospectively evaluated by two independent radiologists. A new grading system was developed to distinguish between lateral, medial and anterior cortical perforations, endplate perforation and foraminal perforation. The grading system is based on whether the cortical violation is partial or total rather than on mm-basis. The overall rate of screw misplacement was 17% (n = 149): 8% were laterally placed and 6.1% were medially placed. The rates of anterior cortical, endplate and foraminal perforation were 1.5, 0.9, and 0.5%, respectively. Lateral cortical perforation was more frequent in the thoracic spine (P = 0.005), whereas other types of misplacement including medial cortical perforation were more frequent on the left and the concave side of scoliotic curves (P = 0.002 and 0.003). No neurovascular complications were reported. The association between the occurrence of screw misplacement and the Cobb angle was statistically significant (P = 0.037). Misplacements exceeding half screw diameter should be classified as unacceptable. Low-dose CT implies exposing these young individuals to a significantly lower radiation dose than do other protocols used in daily clinical practice. We recommend using low-dose CT and the grading system proposed here in the postoperative assessment of screw placement.