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.

Dynamics of reduced perylene bisimide cyclophane redox species by ultrafast spectroelectrochemistry.

Charged molecules play essential roles in many natural and artificial functional processes, ranging from photosynthesis to photovoltaics to chemical reactions and more. It is often difficult to identify the optical dynamic properties of relevant redox species because they cannot be easily prepared, their spectra overlap, or they evolve on a femtosecond timescale. Here, we address these challenges by combining spectroelectrochemistry, ultrafast transient absorption spectroscopy, and suitable data analysis. We illustrate the method with the various redox species of a cyclophane composed of two perylene bisimide subunits. While singular-value decomposition is a well-established tool in the analysis of time-dependent spectra of a single molecular species, we here use it additionally to separate transient maps of individual redox species. This is relevant because at any specific applied electrochemical potential, several redox species coexist in the ensemble, and our procedure allows disentangling their spectroscopic response. In the second step, global analysis is then employed to retrieve the excited-state lifetimes and decay-associated difference spectra. Our approach is generally suitable for unraveling ultrafast dynamics in materials featuring charge-transfer processes.

Intersystem crossing of perylene bisimide neutral, radical anion, and dianion derivatives compared via ultrafast spectroelectrochemistry.

Perylene bisimides are widely studied due to their various applications. Most research is carried out on neutral molecules but charged species are essential in the context of organic electronics and photovoltaics. In this study, we carry out ultrafast transient absorption spectroelectrochemistry and coherent two-dimensional electronic spectroelectrochemistry on three different neutral perylene bisimide derivatives as well as their singly and doubly reduced species. We compare an unsubstituted, flat parent perylene bisimide with two twisted ones that introduce spin-orbit coupling, leading to enhanced intersystem crossing. The internal conversion from higher excited states to the lowest electronically excited state occurs in the picosecond regime with lifetimes significantly shorter for the charged species compared to the neutral ones. Coherent oscillations of the transients for the flat dianion of parent perylene bisimide indicate the occurrence of Fermi resonance. The corresponding vibrational coupling and the superposition of the participating vibrational modes may lead to an enhanced charge separation and triplet formation.

femtoPro: virtual-reality interactive training simulator of an ultrafast laser laboratory.

The huge field of optics and photonics research and development is in constant demand of well-trained experts. However, it is challenging to teach efficiently the setup process of complicated optical experiments due to limited hardware availability and eye-safety concerns, in particular, in the case of femtosecond lasers. We have developed an interactive simulation of an ultrafast laser laboratory ("femtoPro") for teaching and training, implementing physical models for the calculation and visualization of Gaussian laser beam propagation, ultrashort optical pulses, their modulation by typical optical elements, and linear as well as nonlinear light-matter interaction. This facilitates the setup and simulated measurement procedure, in virtual reality (VR) and at real-time speeds, of various typical optical arrangements and spectroscopy schemes such as telescopes, interferometers, or pulse characterization. femtoPro can be employed to supplement academic teaching in connection with regular courses in optics or spectroscopy, to train future scientists and engineers in the field of (ultrafast) optics in practical skills, to communicate to other researchers how to set up and align a particular experiment, to "test-build" and simulate new designs of optical setups, to simulate ultrafast spectroscopy data, to offer practical exercises to high-school students, and to reach out to the general public.

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.

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.

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.

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.

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.

Correlating Nanoscale Optical Coherence Length and Microscale Topography in Organic Materials by Coherent Two-Dimensional Microspectroscopy.

Many nanotechnology materials rely on a hierarchical structure ranging from the nanometer scale to the micrometer scale. Their interplay determines the nanoscale optical coherence length, which plays a key role in energy transport and radiative decay and, thus, the optoelectronic applications. However, it is challenging to detect optical coherence length in multiscale structures with existing methods. Techniques such as atomic force microscopy and transmission electron microscopy are not sensitive to optical coherence length. Linear absorption and fluorescence spectroscopy methods, on the other hand, were generally limited by inhomogeneous broadening, which often obstructs the determination of nanoscale coherence length. Here, we carry out coherent two-dimensional microspectroscopy to obtain a map of the local optical coherence length within a hierarchically structured molecular film. Interestingly, the nanoscale coherence length is found to correlate with microscale topography, suggesting a perspective for controlling structural coherence on molecular length scales by appropriate microscopic growth conditions.

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.

Spatial Variations in Femtosecond Field Dynamics within a Plasmonic Nanoresonator Mode.

Plasmonic resonators can be designed to support spectrally well-separated discrete modes. The associated characteristic spatial patterns of intense electromagnetic hot-spots can be exploited to enhance light-matter interaction. Here, we study the local field dynamics of individual hot-spots within a nanoslit resonator by detecting characteristic changes of the photoelectron emission signal on a scale of ∼12 nm using time-resolved photoemission electron microscopy (TR-PEEM) and by excitation with the output from a 20 fs, 1 MHz noncollinear optical parametric amplifier (NOPA). Surprisingly, we detect apparent spatial variations of the Q-factor and resonance frequency that are commonly considered to be global properties for a single mode. By using the concept of quasinormal modes we explain these local differences by crosstalk of adjacent resonator modes. Our findings are important in view of time-domain studies of plasmon-mediated strong light-matter coupling at ambient conditions.

Coherent two-dimensional fluorescence micro-spectroscopy.

We have developed coherent two-dimensional (2D) fluorescence micro-spectroscopy which probes the nonlinear optical response at surfaces via fluorescence detection with sub-micron spatial resolution. This enables the investigation of microscopic variations in heterogeneous systems. An LCD-based pulse shaper in 4f geometry is used to create collinear trains of 12-fs visible/NIR laser pulses in the focus of an NA = 1.4 immersion-oil microscope objective. We demonstrate the capabilities of the new method by presenting 2D spectra, analyzed via phase cycling, as a function of position of selected sub-micron regions from a laterally nanostructured polycrystalline thin film of fluorinated zinc phthalocyanine (F16ZnPc).

Disentangling the photochemistry of benzocyclobutenedione.

The ultrafast photophysics and photochemistry of benzocyclobutenedione (BCBD) dissolved in dichloromethane is investigated by transient absorption spectroscopy in both the IR and the UV/Vis regime. The molecule is excited at 300 nm to the S3 (ππ*) state and a time scale from roughly 100 fs to several nanoseconds is covered. The initially excited S3 deactivates quickly to the lower-lying S1 (nπ*) state. Three parallel photochemical reaction pathways starting in the S1 state that compete with deactivation to S0 are identified in the transient IR spectra, two of them consisting of a sequence of steps. DFT/TDDFT calculations of the normal modes of the reactant and various photoproducts support the analysis of the transient spectra. The rapid internal conversion (IC) to the S1 state of BCBD is followed by a sub-picosecond vibrational relaxation (VR) to S1 (ν = 0). In parallel BCBD loses one carbonyl group and forms benzocyclopropenone, which subsequently rearranges to cyclopentadienylidene ketene. Ring opening in the S1 (ν = 0) state produces vibrationally hot bisketene, which cools within 22 ps. This reaction competes with the intramolecular rearrangement to singlet oxacarbene, which subsequently converts into the triplet carbene via intersystem crossing (ISC). The late-time product identified in the transient UV/Vis spectra is probably due to dimerization of the carbene. Molecular dynamics (MD) simulations of the early-time photochemistry of BCBD successfully reproduce the formation of the three main photoproducts.

Solvent-Templated Folding of Perylene Bisimide Macrocycles into Coiled Double-String Ropes with Solvent-Sensitive Optical Signatures.

A series of semirigid perylene bisimide (PBI) macrocycles with varied ring size containing two to nine PBI chromophores were synthesized in a one-pot reaction and their photophysical properties characterized by fluorescence, steady-state, and transient absorption spectroscopy as well as femtosecond stimulated Raman spectroscopy. These macrocycles show solvent-dependent conformational equilibria and excited-state properties. In dichloromethane, the macrocycles prevail in wide-stretched conformations and upon photoexcitation exhibit symmetry-breaking charge separation followed by charge recombination to triplet states, which photosensitize singlet oxygen formation. In contrast, in aromatic solvents folding of the macrocycles with a distinct odd-even effect regarding the number of PBI chromophore units was observed in steady-state and time-resolved absorption and fluorescence spectroscopy as well as femtosecond stimulated Raman spectroscopy. These distinctive optical properties are attributable to the folding of the even-membered macrocycles into exciton-vibrational coupled dimer pairs in aromatic solvents. Studies in a variety of aromatic solvents indicate that these solvents embed between PBI dimer pairs and accordingly template the folding of even-membered PBI macrocycles into ropelike folded conformations that give rise to solvent-specific exciton-vibrational couplings in UV-vis absorption spectra. As a consequence of the embedding of solvent molecules in the coiled double-string rope architecture, highly solvent specific intensity ratios are observed for the two lowest-energy exciton-vibrational bands, enabling assignment of the respective solvent simply based on the absorption spectra measured for the tetramer macrocycle.

Rapid-scan coherent 2D fluorescence spectroscopy.

We developed pulse-shaper-assisted coherent two-dimensional (2D) electronic spectroscopy in liquids using fluorescence detection. A customized pulse shaper facilitates shot-to-shot modulation at 1 kHz and is employed for rapid scanning over all time delays. A full 2D spectrum with 15 × 15 pixels is obtained in approximately 6 s of measurement time (plus further averaging if needed). Coherent information is extracted from the incoherent fluorescence signal via 27-step phase cycling. We exemplify the technique on cresyl violet in ethanol and recover literature-known oscillations as a function of population time. Signal-to-noise behavior is analyzed as a function of the amount of averaging. Rapid scanning provides a 2D spectrum with a root-mean-square error of < 0.05 after 1 min of measurement time.

Generating laser-pulse enantiomers.

We present an optical setup capable of mirroring an arbitrary, potentially time-varying, polarization state of an ultrashort laser pulse. The incident beam is split up in two and the polarization of one beam is mirrored by reflection off a mirror in normal incidence. Afterwards, both beams are recombined in time and space such that two collinear ultrashort laser pulses with mutually mirrored polarization, i.e., laser-pulse enantiomers, leave the setup. We employ the Jones formalism to describe the function of the setup and analyze the influence of alignment errors before describing the experimental implementation and alignment protocol. Since no wave plates are utilized, broadband pulses in a large wavelength range can be processed. In particular, we show that the setup outperforms broadband achromatic wave plates. Furthermore, since the two beams travel separately through the optical system they can be blocked independently. This opens the possibility for circular dichroism, ellipsometry, and anisotropy spectroscopy with shot-to-shot chopping and detection schemes as well as chiral coherent control applications.