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

Interconnection between Polarization-Detected and Population-Detected Signals: Theoretical Results and Ab Initio Simulations

Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales. In this work, we consider the fluorescence-detected (FD) N-wave-mixing (NWM) signal as a representative example of population-detected signals, derive a rigorous expression for this signal, and discuss its approximate variants suitable for numerical simulations. This leads us to the definition of the phenomenological FD (PFD) signal, which contains as a special case all definitions of FD signals available in the literature. Then we formulate and prove the population-polarization equivalence (PPE) theorem, which states that PFD NWM signals produced by (possibly strong) laser pulses can be evaluated as conventional PD signals in which the effective polarization is determined by the PFD transition dipole moment operator. We use the PPE theorem for the construction of the ab initio protocol for the simulation of PFD 4WM signals. As an example, we calculate electronic two-dimensional (2D) PFD spectra of the gas-phase pyrazine and compare them with the corresponding PD 2D spectra.

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.

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.

Pulse overlap ambiguities in multiple quantum coherence spectroscopy

Coherent two-dimensional electronic spectroscopy probes ultrafast dynamics using femtosecond pulses. In the case where the time scale of the studied dynamics become comparable to the pulse duration, pulse overlap effects may compromise the experimental data. Here, we perform one-dimensional coherence scans and study pulse overlap effects in clean two-level systems. We find parasitic multiple-quantum coherences as a consequence of the arbitrary time ordering during the temporal pulse overlap. Surprisingly, the coherence lifetimes exceed the pulse coherence time by a factor of 1.85. These findings have important implications for the interpretation of higher-order coherent two-dimensional and related spectroscopy experiments.

High-sensitivity fluorescence-detected multidimensional electronic spectroscopy through continuous pump-probe delay scan

Fluorescence-detected multidimensional electronic spectroscopy (fMES) promises high sensitivity compared to conventional approaches and is an emerging spectroscopic approach toward combining the advantages of MES with the spatial resolution of a microscope. Here, we present a visible white light continuum-based fMES spectrometer and systematically explore the sensitivity enhancement expected from fluorescence detection. As a demonstration of sensitivity, we report room temperature two-dimensional coherence maps of vibrational quantum coherences in a laser dye at optical densities of ∼2-3 orders of magnitude lower than conventional approaches. This high sensitivity is enabled by a combination of biased sampling along the optical coherence time axes and a rapid scan of the pump-probe waiting time T at each sample. A combination of this approach with acousto-optic phase modulation and phase-sensitive lock-in detection enables measurements of room temperature vibrational wavepackets even at the lowest ODs. Alternative faster data collection schemes, which are enabled by the flexibility of choosing a non-uniform undersampled grid in the continuous T scanning approach, are also demonstrated.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Beating signals in CdSe quantum dots measured by low-temperature 2D spectroscopy

Advances in ultrafast spectroscopy can provide access to dynamics involving nontrivial quantum correlations and their evolutions. In coherent 2D spectroscopy, the oscillatory time dependence of a signal is a signature of such quantum dynamics. Here we study such beating signals in electronic coherent 2D spectroscopy of CdSe quantum dots (CdSe QDs) at 77 K. The beating signals are analyzed in terms of their positive and negative Fourier components. We conclude that the beatings originate from coherent LO-phonons of CdSe QDs. No evidence for the quantum dot size dependence of the LO-phonon frequency was identified.

Phase-modulated rapid-scanning fluorescence-detected two-dimensional electronic spectroscopy

We present a rapid-scanning approach to fluorescence-detected two-dimensional electronic spectroscopy that combines acousto-optic phase-modulation with digital lock-in detection. This approach shifts the signal detection window to suppress 1/f laser noise and enables interferometric tracking of the time delays to allow for correction of spectral phase distortions and accurate phasing of the data. This use of digital lock-in detection enables acquisition of linear and nonlinear signals of interest in a single measurement. We demonstrate the method on a laser dye, measuring the linear fluorescence excitation spectrum as well as rephasing, non-rephasing, and absorptive fluorescence-detected two-dimensional electronic spectra.

Pulse area dependence of multiple quantum coherence signals in dilute thermal gases

In the general framework of open quantum systems, we assess the impact of the pulse area on single and double quantum coherence (1QC and 2QC) signals extracted from fluorescence emitted by dilute thermal gases. We show that 1QC and 2QC signals are periodic functions of the pulse area, with distinctive features that reflect the particles' interactions via photon exchange, the polarizations of the laser pulses, and the observation direction.

Multidimensional electronic spectroscopy in high-definition-Combining spectral, temporal, and spatial resolutions

Over the past two decades, coherent multidimensional spectroscopies have been implemented across the terahertz, infrared, visible, and ultraviolet regions of the electromagnetic spectrum. A combination of coherent excitation of several resonances with few-cycle pulses, and spectral decongestion along multiple spectral dimensions, has enabled new insights into wide ranging molecular scale phenomena, such as energy and charge delocalization in natural and artificial light-harvesting systems, hydrogen bonding dynamics in monolayers, and strong light-matter couplings in Fabry-Pérot cavities. However, measurements on ensembles have implied signal averaging over relevant details, such as morphological and energetic inhomogeneity, which are not rephased by the Fourier transform. Recent extension of these spectroscopies to provide diffraction-limited spatial resolution, while maintaining temporal and spectral information, has been exciting and has paved a way to address several challenging questions by going beyond ensemble averaging. The aim of this Perspective is to discuss the technological developments that have eventually enabled spatially resolved multidimensional electronic spectroscopies and highlight some of the very recent findings already made possible by introducing spatial resolution in a powerful spectroscopic tool.

Photocurrent-Detected 2D Electronic Spectroscopy Reveals Ultrafast Hole Transfer in Operating PM6/Y6 Organic Solar Cells

The performance of nonfullerene-acceptor-(NFA)-based organic solar cells is rapidly approaching the efficiency of inorganic cells. The chemical versatility of NFAs extends the light-harvesting range to the infrared, while preserving a considerably high open-circuit-voltage, crucial to achieve power-conversion efficiencies >17%. Such low voltage losses in the charge separation process have been attributed to a low-driving-force and efficient exciton dissociation. Here, we address the nature of the subpicosecond dynamics of electron/hole transfer in PM6/Y6 solar cells. While previous reports focused on active layers only, we developed a photocurrent-detected two-dimensional spectroscopy to follow the charge transfer in fully operating devices. Our measurements reveal an efficient hole-transfer from the Y6-acceptor to the PM6-donor on the subpicosecond time scale. On the contrary, at the same time scale, no electron-transfer is seen from the donor to the acceptor. These findings, putting ultrafast spectroscopy in action on operating optoelectronic devices, provide insight for further enhancing NFA solar cell performance.

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.

Observing Multiexciton Correlations in Colloidal Semiconductor Quantum Dots via Multiple-Quantum Two-Dimensional Fluorescence Spectroscopy

Correlations between excitons, that is, electron-hole pairs, have a great impact on the optoelectronic properties of semiconductor quantum dots and thus are relevant for applications such as lasers and photovoltaics. Upon multiphoton excitation, these correlations lead to the formation of multiexciton states. It is challenging to observe these states spectroscopically, especially higher multiexciton states, because of their short lifetimes and nonradiative decay. Moreover, solvent contributions in experiments with coherent signal detection may complicate the analysis. Here we employ multiple-quantum two-dimensional (2D) fluorescence spectroscopy on colloidal CdSe_1-xS_x/ZnS alloyed core/shell quantum dots. We selectively map the electronic structure of multiexcitons and their correlations by using two- and three-quantum 2D spectroscopy, conducted in a simultaneous measurement. Our experiments reveal the characteristics of biexcitons and triexcitons such as transition dipole moments, binding energies, and correlated transition energy fluctuations. We determine the binding energies of the first six biexciton states by simulating the two-quantum 2D spectrum. By analyzing the line shape of the three-quantum 2D spectrum, we find strong correlations between biexciton and triexciton states. Our method contributes to a more comprehensive understanding of multiexcitonic species in quantum dots and other semiconductor nanostructures.

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.

Fifth-order two-quantum absorptive two-dimensional electronic spectroscopy of CdSe quantum dots

Two-quantum variants of two-dimensional electronic spectroscopy (2DES) have previously been used to characterize multi-exciton interactions in molecules and semiconductor nanostructures though many implementations are limited by phasing procedures or non-resonant signals. We implement 2DES using phase-cycling to simultaneously measure one-quantum and two-quantum spectra in colloidal CdSe quantum dots. In the pump-probe geometry, fully absorptive spectra are automatically acquired by measuring the sum of the rephasing and nonrephasing signals. Fifth-order two-quantum spectroscopy allows for direct access to multi-exciton states that may be obscured in excited state absorption signals due to population relaxation or third-order two-quantum spectra due to the non-resonant response.

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.

Effects of high pulse intensity and chirp in two-dimensional electronic spectroscopy of an atomic vapor

The effects of high pulse intensity and chirp on two-dimensional electronic spectroscopy signals are experimentally investigated in the highly non-perturbative regime using atomic rubidium vapor as clean model system. Data analysis is performed based on higher-order Feynman diagrams and non-perturbative numerical simulations of the system response. It is shown that higher-order contributions may lead to a fundamental change of the static appearance and beating-maps of the 2D spectra and that chirped pulses enhance or suppress distinct higher-order pathways. We further give an estimate of the threshold intensity beyond which the high-intensity effects become visible for the system under consideration.

Molecular Coherent Three-Quantum Two-Dimensional Fluorescence Spectroscopy

We introduce molecular coherent three-quantum (3Q) two-dimensional (2D) fluorescence spectroscopy with phase cycling via shot-to-shot pulse shaping at a 1 kHz repetition rate. This allows us to acquire simultaneously, within a single scan, three fourth-order and six sixth-order signals correlating various one-quantum, two-quantum, and 3Q coherences. We demonstrate the approach on the dye molecule rhodamine 700 and reproduce all nine 2D data sets, including their absolute signal strengths, with simulations using a single, consistent set of model parameters. We observe a linear concentration dependence of all nonlinear signals, evidencing the absence of cascades and many-particle signals of noninteracting molecules. The single-beam, background-free implementation allows direct comparability between various nonlinear signal types and provides information about multiple excited states. Apart from molecules, the method is expected to be applicable to supramolecular systems, polymers, and solid-state materials with the prospect of revealing signatures of bi- and triexcitonic states.

Strong-field control of H3 + production from methanol dications: Selecting between local and extended formation mechanisms

Using the CD₃OH isotopologue of methanol, the ratio of D₂H⁺ to D₃ ⁺ formation is manipulated by changing the characteristics of the intense femtosecond laser pulse. Detection of D₂H⁺ indicates a formation process involving two hydrogen atoms from the methyl side of the molecule and a proton from the hydroxyl side, while detection of D₃ ⁺ indicates local formation involving only the methyl group. Both mechanisms are thought to involve a neutral D₂ moiety. An adaptive control strategy that employs image-based feedback to guide the learning algorithm results in an enhancement of the D₂H⁺/D₃ ⁺ ratio by a factor of approximately two. The optimized pulses have secondary structures 110-210 fs after the main pulse and result in photofragments that have different kinetic energy release distributions than those produced from near transform limited pulses. Systematic changes to the linear chirp and higher order dispersion terms of the laser pulse are compared to the results obtained with the optimized pulse shapes.

Synthesis, Photophysical and Electronic Properties of New Red-to-NIR Emitting Donor-Acceptor Pyrene Derivatives

We synthesized new pyrene derivatives with strong bis(para-methoxyphenyl)amine donors at the 2,7-positions and n-azaacene acceptors at the K-region of pyrene. The compounds possess a strong intramolecular charge transfer, leading to unusual properties such as emission in the red to NIR region (700 nm), which has not been reported before for monomeric pyrenes. Detailed photophysical studies reveal very long intrinsic lifetimes of >100 ns for the new compounds, which is typical for 2,7-substituted pyrenes but not for K-region substituted pyrenes. The incorporation of strong donors and acceptors leads to very low reduction and oxidation potentials, and spectroelectrochemical studies show that the compounds are on the borderline between localized Robin-Day class-II and delocalized Robin-Day class-III species.

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.