Exciton-exciton correlations revealed by two-quantum, two-dimensional fourier transform optical spectroscopy

Reference Energies for Double Excitations: Improvement and Extension

In the realm of photochemistry, the significance of double excitations (also known as doubly excited states), where two electrons are concurrently elevated to higher energy levels, lies in their involvement in key electronic transitions essential in light-induced chemical reactions as well as their challenging nature from the computational theoretical chemistry point of view. Based on state-of-the-art electronic structure methods (such as high-order coupled-cluster, selected configuration interaction, and multiconfigurational methods), we improve and expand our prior set of accurate reference excitation energies for electronic states exhibiting a substantial amount of double excitations [Loos et al. J. Chem. Theory Comput. 2019, 15, 1939]. This extended collection encompasses 47 electronic transitions across 26 molecular systems that we separate into two distinct subsets: (i) 28 "genuine" doubly excited states where the transitions almost exclusively involve doubly excited configurations and (ii) 19 "partial" doubly excited states which exhibit a more balanced character between singly and doubly excited configurations. For each subset, we assess the performance of high-order coupled-cluster (CC3, CCSDT, CC4, and CCSDTQ) and multiconfigurational methods (CASPT2, CASPT3, PC-NEVPT2, and SC-NEVPT2). Using as a probe the percentage of single excitations involved in a given transition (%T1) computed at the CC3 level, we also propose a simple correction that reduces the errors of CC3 by a factor of 3, for both sets of excitations. We hope that this more complete and diverse compilation of double excitations will help future developments of electronic excited-state methodologies.

Expanding the bandwidth of fluorescence-detected two-dimensional electronic spectroscopy using a broadband continuum probe pulse pair

We demonstrate fluorescence-detected two-dimensional electronic spectroscopy (F-2DES) with a broadband, continuum probe pulse pair in the pump-probe geometry. The approach combines a pump pulse pair generated by an acousto-optic pulse-shaper with precise control of the relative pump pulse phase and time delay with a broadband, continuum probe pulse pair created using the Translating Wedge-based Identical pulses eNcoding System (TWINS). The continuum probe expands the spectral range of the detection axis and lengthens the waiting times that can be accessed in comparison to implementations of F-2DES using a single pulse-shaper. We employ phase-cycling of the pump pulse pair and take advantage of the separation of signals in the frequency domain to isolate rephasing and non-rephasing signals and optimize the signal-to-noise ratio. As proof of principle, we demonstrate broadband F-2DES on a laser dye and bacteriochlorophyll a.

Perturbed free induction decay obscures early time dynamics in two-dimensional electronic spectroscopy: The case of semiconductor nanocrystals

Two-dimensional electronic spectroscopy (2DES) has recently been gaining popularity as an alternative to the more common transient absorption spectroscopy due to the combination of high frequency and time resolution of 2DES. In order to advance the reliable analysis of population dynamics and to optimize the time resolution of the method, one has to understand the numerous field matter interactions that take place at an early and negative time. These interactions have historically been discussed in one-dimensional spectroscopy as coherent artifacts and have been assigned to both resonant and non-resonant system responses during or before the pulse overlap. These coherent artifacts have also been described in 2DES but remain less well-understood due to the complexity of 2DES and the relative novelty of the method. Here, we present 2DES results in two model nanocrystal samples, CdSe and CsPbI₃. We demonstrate non-resonant signals due to solvent response during the pulse overlap and resonant signals, which we assign to perturbed free induction decay (PFID), both before and during the pulse overlap. The simulations of the 2DES response functions at early and negative time delays reinforce the assignment of the negative time delay signals to PFID. Modeling reveals that the PFID signals will severely distort the initial picture of the resonant population dynamics. By including these effects in models of 2DES spectra, one is able to push forward the extraction of early time dynamics in 2DES.

Phase stable, shot-to-shot measurement of third- and fifth-order two-quantum correlation spectra using a pulse shaper in the pump-probe geometry

We demonstrate the first phase stable measurement of a third-order 2Q spectrum using a pulse shaper in the pump-probe geometry. This measurement was achieved by permuting the time-ordering of the pump pulses, thus rearranging the signal pathways that are emitted in the probe direction. The third-order 2Q spectrum is self-heterodyned by the probe pulse. Using this method, one can interconvert between a 1Q experiment and a 2Q experiment by simply reprogramming a pulse shaper or delay stage. We also measure a fifth-order absorptive 2Q spectrum in the pump-probe geometry, which contains similar information as a third-order experiment but does not suffer from dispersive line shapes. To do so, we introduce methods to minimize saturation-induced artifacts of the pulse shaper, improving fifth-order signals. These techniques add new capabilities for 2D spectrometers that use pulse shapers in the pump-probe beam geometry.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

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

Frenkel biexcitons in hybrid HJ photophysical aggregates

Frenkel excitons are unequivocally responsible for the optical properties of organic semiconductors and are predicted to form bound exciton pairs (biexcitons). These are key intermediates, ubiquitous in many photophysical processes such as the exciton bimolecular annihilation dynamics in such systems. Because of their spectral ambiguity, there has been, to date, only scant direct evidence of bound biexcitons. By using nonlinear coherent spectroscopy, we identify here bound biexcitons in a model polymeric semiconductor. We find, unexpectedly, that excitons with interchain vibronic dispersion reveal intrachain biexciton correlations and vice versa. Moreover, using a Frenkel exciton model, we relate the biexciton binding energy to molecular parameters quantified by quantum chemistry, including the magnitude and sign of the exciton-exciton interaction the intersite hopping energies. Therefore, our work promises general insights into the many-body electronic structure in polymeric semiconductors and beyond, e.g., other excitonic systems such as organic semiconductor crystals, molecular aggregates, photosynthetic light-harvesting complexes, or DNA.

OPA-driven hollow-core fiber as a tunable, broadband source for coherent multidimensional spectroscopy

Despite the impressive abilities of coherent multi-dimensional spectroscopy (CMDS), its' implementation is limited due to the complexity of continuum generation and required phase stability between the pump pulse pair. In light of this, we have implemented a system producing sub-10 fs pulses with tunable central wavelength. Using a commercial OPA to drive a hollow-core fiber, the system is extremely simple. Output pulse energies lie in the 40-80 μJ range, more than sufficient for transmission through the pulse shaping optics and beam splitters necessary for CMDS. Power fluctuations are minimal, mode quality is excellent, and spectral phase is well behaved at the output. To demonstrate the strength of this source, we measure the two-dimensional spectrum of CdSe quantum dots over a range of population times and find clean signals and clear phonon vibrations. This combination of OPA and hollow-core fiber provides a substantial extension to the capabilities of CMDS.

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.

Two-dimensional electronic spectroscopy of bacteriochlorophyll a with synchronized dual mode-locked lasers

How atoms and electrons in a molecule move during a chemical reaction and how rapidly energy is transferred to or from the surroundings can be studied with flashes of laser light. However, despite prolonged efforts to develop various coherent spectroscopic techniques, the lack of an all-encompassing method capable of both femtosecond time resolution and nanosecond relaxation measurement has hampered various applications of studying correlated electron dynamics and vibrational coherences in functional materials and biological systems. Here, we demonstrate that two broadband (>300 nm) synchronized mode-locked lasers enable two-dimensional electronic spectroscopy (2DES) study of chromophores such as bacteriochlorophyll a in condensed phases to measure both high-resolution coherent vibrational spectrum and nanosecond electronic relaxation. We thus anticipate that the dual mode-locked laser-based 2DES developed and demonstrated here would be of use for unveiling the correlation between the quantum coherence and exciton dynamics in light-harvesting protein complexes and semiconducting materials.

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.

Atomic fluctuations in electronic materials revealed by dephasing

The microscopic origin and timescale of the fluctuations of the energies of electronic states has a significant impact on the properties of interest of electronic materials, with implication in fields ranging from photovoltaic devices to quantum information processing. Spectroscopic investigations of coherent dynamics provide a direct measurement of electronic fluctuations. Modern multidimensional spectroscopy techniques allow the mapping of coherent processes along multiple time or frequency axes and thus allow unprecedented discrimination between different sources of electronic dephasing. Exploiting modern abilities in coherence mapping in both amplitude and phase, we unravel dissipative processes of electronic coherences in the model system of CdSe quantum dots (QDs). The method allows the assignment of the nature of the observed coherence as vibrational or electronic. The expected coherence maps are obtained for the coherent longitudinal optical (LO) phonon, which serves as an internal standard and confirms the sensitivity of the technique. Fast dephasing is observed between the first two exciton states, despite their shared electron state and common environment. This result is contrary to predictions of the standard effective mass model for these materials, in which the exciton levels are strongly correlated through a common size dependence. In contrast, the experiment is in agreement with ab initio molecular dynamics of a single QD. Electronic dephasing in these materials is thus dominated by the realistic electronic structure arising from fluctuations at the atomic level rather than static size distribution. The analysis of electronic dephasing thereby uniquely enables the study of electronic fluctuations in complex materials.

Efficient Charge Generation via Hole Transfer in Dilute Organic Donor-Fullerene Blends

Efficient organic photovoltaics (OPVs) require broadband charge photogeneration with near-unity quantum yield. This can only be achieved by exploiting all pathways that generate charge. Electron transfer from organic donors to acceptors has been well-studied and is considered the primary path to charge photogeneration in OPVs. In contrast, much less is known about the hole transfer pathway. Here we study charge photogeneration in an archetypal system comprising tetraphenyldibenzoperiflanthene:C₇₀ blends using our recently developed multispectral two-dimensional electronic spectroscopy (M-2DES), supported by time-dependent density functional theory and fully quantum-mechanical Fermi's golden rule rate calculations. Our approach identifies in real time two rapid charge transfer pathways that are confirmed through computational analysis. Surprisingly, we find that both electron and hole transfer occur with comparable rates and efficiencies, facilitated by donor-acceptor electronic interactions. Our results highlight the importance of the hole transfer pathway for optimizing the efficiency of OPV devices employing small-molecule heterojunctions.

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.

Vibronic structure of photosynthetic pigments probed by polarized two-dimensional electronic spectroscopy and ab initio calculations

Bacteriochlorophyll a (Bchl a) and chlorophyll a (Chl a) play important roles as light absorbers in photosynthetic antennae and participate in the initial charge-separation steps in photosynthetic reaction centers. Despite decades of study, questions remain about the interplay of electronic and vibrational states within the Q-band and its effect on the photoexcited dynamics. Here we report results of polarized two-dimensional electronic spectroscopic measurements, performed on penta-coordinated Bchl a and Chl a and their interpretation based on state-of-the-art time-dependent density functional theory calculations and vibrational mode analysis for spectral shapes. We find that the Q-band of Bchl a is comprised of two independent bands, that are assigned following the Gouterman model to Q x and Q y states with orthogonal transition dipole moments. However, we measure the angle to be ∼75°, a finding that is confirmed by ab initio calculations. The internal conversion rate constant from Q x to Q y is found to be 11 ps-1. Unlike Bchl a, the Q-band of Chl a contains three distinct peaks with different polarizations. Ab initio calculations trace these features back to a spectral overlap between two electronic transitions and their vibrational replicas. The smaller energy gap and the mixing of vibronic states result in faster internal conversion rate constants of 38-50 ps-1. We analyze the spectra of penta-coordinated Bchl a and Chl a to highlight the interplay between low-lying vibronic states and their relationship to photoinduced relaxation. Our findings shed new light on the photoexcited dynamics in photosynthetic systems where these chromophores are primary pigments.

Investigating exciton structure and dynamics in colloidal CdSe quantum dots with two-dimensional electronic spectroscopy

Two-Dimensional Electronic Spectroscopy (2DES) is performed on CdSe colloidal quantum dots. These experiments reveal new observations on exciton structure and dynamics in quantum dots, expanding upon prior transient absorption measurements of excitonics in these systems. The 2DES method enables the separation of line broadening mechanisms, thereby better revealing the excitonic lineshapes and biexcitonic interactions. 2DES enables more information rich spectral probing of coherent phonons and their coupling to excitons. The data show spectral modulations and drifts, with differences based upon whether one monitors the excitation energy (E₁) or emission energy (E₃). These measurements reveal both homogeneous and inhomogeneous broadenings, as well as static and dynamic line broadening. The longitudinal optical phonon modulates the dynamic absorption spectrum both in energy and linewidth. These experiments enable measurement of hot exciton cooling with improved resolution in energy and time. These 2DES results are consistent with prior excitonic state-resolved transient absorption measurements, albeit with the addition of contributions due to coherent phonons. Finally these 2DES experiments enable disentangling of coupling versus relaxation contributions to the signals, further offering a test of electronic structure theory.

Seeing Multiexcitons through Sample Inhomogeneity: Band-Edge Biexciton Structure in CdSe Nanocrystals Revealed by Two-Dimensional Electronic Spectroscopy

The electronic structure of multiexcitons significantly impacts the performance of nanostructures in lasing and light-emitting applications. However, these multiexcitons remain poorly understood due to their complexity arising from many-body physics. Standard transient-absorption and photoluminescence spectroscopies are unable to unambiguously distinguish effects of sample inhomogeneity from exciton-biexciton interactions. Here, we exploit the energy and time resolution of two-dimensional electronic spectroscopy to access the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots. By removing effects of inhomogeneities, we show that the band-edge biexciton structure must consist of a discrete manifold of electronic states. Furthermore, the biexciton states within the manifold feature distinctive binding energies. Our findings have direct implications for optical gain thresholds and efficiency droop in light-emitting devices and provide experimental measures of many-body physics in nanostructures.

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

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

Recent advances in multidimensional ultrafast spectroscopy

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

Coherent Two-Quantum Two-Dimensional Electronic Spectroscopy Using Incoherent Light

Two-quantum two-dimensional electronic spectroscopy (2Q 2D ES) may provide a measure of electron-correlation energies in molecules. Attempts to obtain this profound but elusive signal have relied on experimental implementations using femtosecond laser pulses, which induce an overwhelming background signal of nonresonant response. Here we explore theoretically the signatures of electron correlation in coherent 2Q 2D ES measurements that use spectrally incoherent light, I⁽⁴⁾ 2Q 2D ES. One can use such fields to suppress nonresonant response, and therefore this method may better isolate the desired signature of electron correlation. Using an appropriate treatment of the multilevel Bloch electronic system, we find that I⁽⁴⁾ 2Q 2D ES presents an opportunity to measure electron-correlation energies in molecules.

Strong Local-Field Enhancement of the Nonlinear Soft-Mode Response in a Molecular Crystal

The nonlinear response of soft-mode excitations in polycrystalline acetylsalicylic acid (aspirin) is studied with two-dimensional terahertz spectroscopy. We demonstrate that the correlation of CH_{3} rotational modes with collective oscillations of π electrons drives the system into the nonperturbative regime of light-matter interaction, even for a moderate strength of the THz driving field on the order of 50  kV/cm. Nonlinear absorption around 1.1 THz leads to a blueshifted coherent emission at 1.7 THz, revealing the dynamic breakup of the strong electron-phonon correlations. The observed behavior is reproduced by theoretical calculations including dynamic local-field correlations.

Correlated Fluctuations and Intraband Dynamics of J-Aggregates Revealed by Combination of 2DES Schemes

The intraband exciton dynamics of molecular aggregates is a crucial initial step to determine the possibly coherent nature of energy transfer and its implications for the ensuing interband relaxation pathways in strongly coupled excitonic systems. In this work, we fully characterize the intraband dynamics in linear J-aggregates of porphyrins, good model systems for multichromophoric assemblies in biological antenna complexes. Using different 2D electronic spectroscopy schemes together with Raman spectroscopy and theoretical modeling, we provide a full characterization of the inner structure of the main one-exciton band of the porphyrin aggregates. We find that the redistribution of population within the band occurs with a characteristic time of 280 fs and dominates the modulation of an electronic coherence. While we do not find that the coupling to vibrations significantly affects the dynamics of excitonic coherence, our results suggest that exciton fluctuations are nevertheless highly correlated.

Two-Dimensional Visible Spectroscopy For Studying Colloidal Semiconductor Nanocrystals

Possibilities offered by 2D visible spectroscopy for the investigation of the properties of excitons in colloidal semiconductor nanocrystals are overviewed, with a particular focus on their ultrafast dynamics. The technique of 2D electronic spectroscopy is illustrated with several examples showing its advantages compared to 1D ultrafast spectroscopic techniques (transient absorption and time-resolved photoluminescence).

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Mapping the Vibronic Structure of a Molecule by Few-Cycle Continuum Two-Dimensional Spectroscopy in a Single Pulse

Accurate mapping of the electronic and vibrational structure of a molecular system is a basic goal of chemistry as it underpins reactivity and function. Experimentally, the challenge is to uncover the intramolecular interactions and ensuing dynamics that define this structure. Multidimensional coherent spectroscopy can map such interactions analogous to the way in which nuclear magnetic resonance provides access to the nuclear spin structure. Here we present two-dimensional coherent spectra measured using few-cycle continuum light. Critically, our approach instantaneously maps the energy landscape of a complex molecular system in a single laser pulse across 350 nm of bandwidth, thereby making it suitable for rapid molecular fingerprinting. We envision few-cycle supercontinuum spectroscopy based on the nonlinear optical response as a powerful tool to examine molecules in the condensed phase at the extremes of time, space, and energy.

Pulse shaping based two-dimensional electronic spectroscopy in a background free geometry

We demonstrate a "drop-in" modification of the pulse-shaped pump-probe geometry two-dimensional Fourier transform spectrometer that significantly improves its performance by making the measurement background-free. The modification uses a hybrid diffractive optic/pulse-shaping approach that combines the advantages of background-free detection with the precise timing and phase-cycling capabilities enabled by pulse-shaping. In addition, we present a simple new method for accurate phasing of optically heterodyned two-dimensional spectra. We demonstrate the high quality of data obtainable with this approach by reporting two-dimensional Fourier transform electronic spectra of chlorophyll a in glycerol/water at 77 K.

Two-dimensional electronic spectroscopy using incoherent light: theoretical analysis

Electronic energy transfer in photosynthesis occurs over a range of time scales and under a variety of intermolecular coupling conditions. Recent work has shown that electronic coupling between chromophores can lead to coherent oscillations in two-dimensional electronic spectroscopy measurements of pigment-protein complexes measured with femtosecond laser pulses. A persistent issue in the field is to reconcile the results of measurements performed using femtosecond laser pulses with physiological illumination conditions. Noisy-light spectroscopy can begin to address this question. In this work we present the theoretical analysis of incoherent two-dimensional electronic spectroscopy, I((4)) 2D ES. Simulations reveal diagonal peaks, cross peaks, and coherent oscillations similar to those observed in femtosecond two-dimensional electronic spectroscopy experiments. The results also expose fundamental differences between the femtosecond-pulse and noisy-light techniques; the differences lead to new challenges and new opportunities.

Coherent fifth-order visible-infrared spectroscopies: ultrafast nonequilibrium vibrational dynamics in solution

Obtaining a detailed description of photochemical reactions in solution requires measuring time-evolving structural dynamics of transient chemical species on ultrafast time scales. Time-resolved vibrational spectroscopies are sensitive probes of molecular structure and dynamics in solution. In this work, we develop doubly resonant fifth-order nonlinear visible-infrared spectroscopies to probe nonequilibrium vibrational dynamics among coupled high-frequency vibrations during an ultrafast charge transfer process using a heterodyne detection scheme. The method enables the simultaneous collection of third- and fifth-order signals, which respectively measure vibrational dynamics occurring on electronic ground and excited states on a femtosecond time scale. Our data collection and analysis strategy allows transient dispersed vibrational echo (t-DVE) and dispersed pump-probe (t-DPP) spectra to be extracted as a function of electronic and vibrational population periods with high signal-to-noise ratio (S/N > 25). We discuss how fifth-order experiments can measure (i) time-dependent anharmonic vibrational couplings, (ii) nonequilibrium frequency-frequency correlation functions, (iii) incoherent and coherent vibrational relaxation and transfer dynamics, and (iv) coherent vibrational and electronic (vibronic) coupling as a function of a photochemical reaction.

Invited article: The coherent optical laser beam recombination technique (COLBERT) spectrometer: coherent multidimensional spectroscopy made easier

We have developed an efficient spectrometer capable of performing a wide variety of coherent multidimensional measurements at optical wavelengths. The two major components of the largely automated device are a spatial beam shaper which controls the beam geometry and a spatiotemporal pulse shaper which controls the temporal waveform of the femtosecond pulse in each beam. We describe how to construct, calibrate, and operate the device, and we discuss its limitations. We use the exciton states of a semiconductor nanostructure as a working example. A series of complex multidimensional spectra-displayed in amplitude and real parts-reveals increasingly intricate correlations among the excitons.

Two-quantum many-body coherences in two-dimensional fourier-transform spectra of exciton resonances in semiconductor quantum wells

We present experimental coherent two-dimensional Fourier-transform spectra of Wannier exciton resonances in semiconductor quantum wells generated by a pulse sequence that isolates two-quantum coherences. By measuring the real part of the signals, we determine that the spectra are dominated by two-quantum coherences due to mean-field many-body interactions, rather than bound biexcitons. Simulations performed using dynamics controlled truncation agree with the experiments.

Three-dimensional electronic spectroscopy of excitons in GaAs quantum wells

We demonstrate three-dimensional (3D) electronic Fourier transform spectroscopy of GaAs quantum wells using four fully phase-coherent, noncollinear optical fields. Since the full complex signal field is measured as a function of all three time intervals, nearly every peak in the resulting 3D spectral solid arises from a distinguishable sequence of transitions represented by a single Feynman pathway. We use the 3D spectral peaks to separate two pathways involving weakly bound mixed biexcitons generated in different time orders. In the process, we reveal a peak that was previously obscured by a correlated but unbound exciton pair coherence. We also demonstrate a calibration procedure for the carrier frequency which yields biexciton binding energy values with high accuracy.