Two-dimensional electronic double-quantum coherence spectroscopy

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Unveiling Multiquantum Excitonic Correlations in Push-Pull Polymer Semiconductors

Bound and unbound Frenkel-exciton pairs are essential transient precursors for a variety of photophysical and biochemical processes. In this work, we identify bound and unbound Frenkel-exciton complexes in an electron push-pull polymer semiconductor using coherent two-dimensional spectroscopy. We find that the dominant A0-1 peak of the absorption vibronic progression is accompanied by a subpeak, each dressed by distinct vibrational modes. By considering the Liouville pathways within a two-exciton model, the imbalanced cross-peaks in one-quantum rephasing and nonrephasing spectra can be accounted for by the presence of pure biexcitons. The two-quantum nonrephasing spectra provide direct evidence for unbound exciton pairs and biexcitons with dominantly attractive force. In addition, the spectral features of unbound exciton pairs show mixed absorptive and dispersive character, implying many-body interactions within the correlated Frenkel-exciton pairs. Our work offers novel perspectives on the Frenkel-exciton complexes in semiconductor polymers.

Extracting double-quantum coherence in two-dimensional electronic spectroscopy under pump-probe geometry

Two-dimensional electronic spectroscopy (2DES) can be implemented with different geometries, e.g., BOXCARS, collinear, and pump-probe geometries. The pump-probe geometry has the advantage of overlapping only two beams and reducing phase cycling steps. However, its applications are typically limited to observing the dynamics with single-quantum coherence and population, leaving the challenge to measure the dynamics of the double-quantum (2Q) coherence, which reflects the many-body interactions. We demonstrate an experimental technique in 2DES under pump-probe geometry with a designed pulse sequence and the signal processing method to extract 2Q coherence. In the designed pulse sequence, with the probe pulse arriving earlier than the pump pulses, our measured signal includes the 2Q signal as well as the zero-quantum signal. With phase cycling and data processing using causality enforcement, we extract the 2Q signal. The proposal is demonstrated with rubidium atoms. We observe the collective resonances of two-body dipole-dipole interactions in both the D1 and D2 lines.

Full visible range two-dimensional electronic spectroscopy with high time resolution

Two-dimensional electronic spectroscopy (2DES) is a powerful method to study coherent and incoherent interactions and dynamics in complex quantum systems by correlating excitation and detection energies in a nonlinear spectroscopy experiment. Such dynamics can be probed with a time resolution limited only by the duration of the employed laser pulses and in a spectral range defined by the pulse spectrum. In the blue spectral range (<500 nm), the generation of sufficiently broadband ultrashort pulses with pulse durations of 10 fs or less has been challenging so far. Here, we present a 2DES setup based on a hollow-core fiber supercontinuum covering the full visible range (400-700 nm). Pulse compression via custom-made chirped mirrors yields a time resolution of <10 fs. The broad spectral coverage, in particular the extension of the pulse spectra into the blue spectral range, unlocks new possibilities for coherent investigations of blue-light absorbing and multichromophoric compounds, as demonstrated by a 2DES measurement of chlorophyll a.

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

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

Quantum interferometry and pathway selectivity in the nonlinear response of photosynthetic excitons

We propose a time-frequency resolved spectroscopic technique which employs nonlinear interferometers to study exciton-exciton scattering in molecular aggregates. A higher degree of control over the contributing Liouville pathways is obtained as compared to classical light. We show how the nonlinear response can be isolated from the orders-of-magnitude stronger linear background by either phase matching or polarization filtering. Both arise due to averaging the signal over a large number of noninteracting, randomly oriented molecules. We apply our technique to the Frenkel exciton model which excludes charge separation for the photosystem II reaction center. We show how the sum of the entangled photon frequencies can be used to select two-exciton resonances, while their delay times reveal the single-exciton levels involved in the optical process.

Time-Frequency Signatures of Electronic Coherence of Colloidal CdSe Quantum Dot Dimer Assemblies Probed at Room Temperature by Two-Dimensional Electronic Spectroscopy

Electronic coherence signatures can be directly identified in the time-frequency maps measured in two-dimensional electronic spectroscopy (2DES). Here, we demonstrate the theory and discuss the advantages of this approach via the detailed application to the fast-femtosecond beatings of a wide variety of electronic coherences in ensemble dimers of quantum dots (QDs), assembled from QDs of 3 nm in diameter, with 8% size dispersion in diameter. The observed and computed results can be consistently characterized directly in the time-frequency domain by probing the polarization in the 2DES setup. The experimental and computed time-frequency maps are found in very good agreement, and several electronic coherences are characterized at room temperature in solution, before the extensive dephasing due to the size dispersion begins. As compared to the frequency-frequency maps that are commonly used in 2DES, the time-frequency maps allow exploiting electronic coherences without additional post-processing and with fewer 2DES measurements. Towards quantum technology applications, we also report on the modeling of the time-frequency photocurrent response of these electronic coherences, which paves the way to integrating QD devices with classical architectures, thereby enhancing the quantum advantage of such technologies for parallel information processing at room temperature.

Pulse overlap artifacts and double quantum coherence spectroscopy

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

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.

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.

Vibrational response functions for multidimensional electronic spectroscopy in the adiabatic regime: A coherent-state approach

Multi-dimensional spectroscopy represents a particularly insightful tool for investigating the interplay of nuclear and electronic dynamics, which plays an important role in a number of photophysical processes and photochemical reactions. Here, we present a coherent state representation of the vibronic dynamics and of the resulting response functions for the widely used linearly displaced harmonic oscillator model. Analytical expressions are initially derived for the case of third-order response functions in an N-level system, with ground state initialization of the oscillator (zero-temperature limit). The results are then generalized to the case of Mth order response functions, with arbitrary M. The formal derivation is translated into a simple recipe, whereby the explicit analytical expressions of the response functions can be derived directly from the Feynman diagrams. We further generalize to the whole set of initial coherent states, which form an overcomplete basis. This allows one, in principle, to derive the dependence of the response functions on arbitrary initial states of the vibrational modes and is here applied to the case of thermal states. Finally, a non-Hermitian Hamiltonian approach is used to include in the above expressions the effect of vibrational relaxation.

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 Interactions between Silicon-Vacancy Centers in Diamond

We report tunable excitation-induced dipole-dipole interactions between silicon-vacancy color centers in diamond at cryogenic temperatures. These interactions couple centers into collective states, and excitation-induced shifts tag the excitation level of these collective states against the background of excited single centers. By characterizing the phase and amplitude of the spectrally resolved interaction-induced signal, we observe oscillations in the interaction strength and population state of the collective states as a function of excitation pulse area. Our results demonstrate that excitation-induced dipole-dipole interactions between color centers provide a route to manipulating collective intercenter states in the context of a congested, inhomogeneous ensemble.

Enhanced TEMPO Algorithm for Quantum Path Integrals with Off-Diagonal System-Bath Coupling: Applications to Photonic Quantum Networks

Multitime system correlation functions are relevant in various areas of physics and science, dealing with system-bath interaction including spectroscopy and quantum optics, where many of these schemes include an off-diagonal system bath interaction. Here we extend the enhanced time-evolving matrix product operator (eTEMPO) algorithm for quantum path integrals using tensor networks [Phys. Rev. Lett. 123, 240602 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.240602 to open quantum systems with off-diagonal coupling beyond a single two level system. We exemplify the approach on a coupled cavity waveguide system with spatially separated quantum two-state emitters, though many other applications in material science are possible, including entangled photon propagation, photosynthesis spectroscopy, and on-chip quantum optics with realistic dissipation.

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.

Third-order pump-probe spectroscopy applied to molecular dimers: characterization of relaxation dynamics and exciton–exciton annihilation

Exciton–exciton annihilation in a dimer, described within the basis of localizes monomer states.

Multidimensional spectroscopy of magneto-excitons at high magnetic fields

We perform two-dimensional Fourier transform spectroscopy on magneto-excitons in GaAs at magnetic fields and observe Zeeman splitting of the excitons. The Zeeman components are clearly resolved as separate peaks due to the two-dimensional nature of the spectra, leading to a more accurate measurement of the Zeeman splitting and the Landé g factors. Quantum coherent coupling between Zeeman components is observed using polarization dependent one-quantum two-dimensional spectroscopy. We use two-quantum two-dimensional spectroscopy to investigate higher four-particle correlations at high magnetic fields and reveal the role of the Zeeman splitting on the two-quantum transitions. The experimental two-dimensional spectra are simulated using the optical Bloch equations, where many-body effects are included phenomenologically.

Coherent Nonlinear Spectroscopy with Multiple Mode-Locked Lasers

Coherent multidimensional spectroscopy has been widely used to study the structure and dynamics of chemical and biological systems. Each ultrashort pulse from a single mode-locked laser is split into multiple pulses by beam splitters. Their arrival times at a given molecular sample are controlled with mechanical time-delay generators for time-resolved measurements of molecular responses. Such nonlinear vibrational, electronic, or vibrational-electronic spectroscopy can now be carried out with multiple mode-locked lasers with highly stabilized repetition and sometimes carrier-envelope-offset frequencies. By precisely controlling the repetition frequencies of multiple mode-locked lasers, one can achieve automatic delay time scanning, known as asynchronous optical sampling, to investigate various relaxation processes associated with photochemical or photobiological phenomena at one sweep in time. In this Perspective, the current developments and applications of multiple mode-locked laser-based techniques to time-resolved nonlinear spectroscopy of chromophores in condensed phases are discussed. The author's perspective on this approach is also presented.

Theory of two-dimensional spectroscopy with intense laser fields

Two-dimensional vibrational and electronic spectroscopic observables of isotropically oriented molecular samples in solution are sensitive to laser field intensities and polarization. The third-order response function formalism predicts a signal that grows linearly with the field strength of each laser pulse, thus lacking a way of accounting for non-trivial intensity-dependent effects, such as saturation and finite bleaching. An analytical expression to describe the orientational part of the molecular response, which, in the weak-field limit, becomes equivalent to a four-point correlation function, is presented. Such an expression is evaluated for Liouville-space pathways accounting for diagonal and cross peaks for all-parallel and cross-polarized pulse sequences, in both the weak- and strong-field conditions, via truncation of a Taylor series expansion at different orders. The results obtained in the strong-field conditions suggest how a careful analysis of two-dimensional spectroscopic experimental data should include laser pulse intensity considerations when determining molecular internal coordinates.

Two-dimensional pattern recognition methods for rapidly recording and interpreting high resolution coherent three-dimensional spectra

High resolution coherent multidimensional spectroscopy has the ability to reduce congestion and automatically sort peaks by species and quantum numbers, even for simple mixtures and molecules that are extensively perturbed. The two-dimensional version is relatively simple to carry out, and the results are easy to interpret, but its ability to deal with severe spectral congestion is limited. Three-dimensional spectroscopy is considerably more complicated and time-consuming than two-dimensional spectroscopy, but it provides the spectral resolution needed for more challenging systems. This paper describes how to design high resolution coherent 3D spectroscopy experiments so that a small number of strategically positioned 2D scans may be used instead of recording all the data required for a 3D plot. This faster and simpler approach uses new pattern recognition methods to interpret the results. Key factors that affect the resulting patterns include the scanning strategy and the four wave mixing process. Optimum four wave mixing (FWM) processes and scanning strategies have been identified, and methods for identifying the FWM process from the observed patterns have been developed. Experiments based on nonparametric FWM processes provide significant pattern recognition and efficiency advantages over those based on parametric processes. Alternative scanning strategies that use synchronous scanning and asynchronous scanning to create new kinds of patterns have also been identified. Rotating the resulting patterns in 3D space leads to an insight into similarities in the patterns produced by different FWM processes.

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.

Manipulating Core Excitations in Molecules by X-Ray Cavities

Core excitations on different atoms are highly localized and therefore decoupled. By placing molecules in an x-ray cavity the core transitions become coupled via the exchange of cavity photons and form delocalized hybrid light-matter excitations known as core polaritons. We demonstrate these effects for the two inequivalent carbon atoms in 1,1-difluoroethylene. Polariton signatures in the x-ray absorption, two-photon absorption, and multidimensional four-wave mixing signals are predicted.

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.

Theory of molecular emission power spectra. I. Macroscopic quantum electrodynamics formalism

We study the emission power spectrum of a molecular emitter with multiple vibrational modes in the framework of macroscopic quantum electrodynamics. The theory we present is general for a molecular spontaneous emission spectrum in the presence of arbitrary inhomogeneous, dispersive, and absorbing media. Moreover, the theory shows that the molecular emission power spectra can be decomposed into the electromagnetic environment factor and lineshape function. In order to demonstrate the validity of the theory, we investigate the lineshape function in two limits. In the incoherent limit (single molecules in a vacuum), the lineshape function exactly corresponds to the Franck-Condon principle. In the coherent limit (single molecules strongly coupled with single polaritons or photons) together with the condition of high vibrational frequency, the lineshape function exhibits a Rabi splitting, the spacing of which is exactly the same as the magnitude of exciton-photon coupling estimated by our previous theory [S. Wang et al., J. Chem. Phys. 151, 014105 (2019)]. Finally, we explore the influence of exciton-photon and electron-phonon interactions on the lineshape function of a single molecule in a cavity. The theory shows that the vibronic structure of the lineshape function does not always disappear as the exciton-photon coupling increases, and it is related to the loss of a dielectric environment.

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.

Optical Gain from Biexcitons in CsPbBr3 Nanocrystals Revealed by Two-dimensional Electronic Spectroscopy

Perovskite semiconductor nanocrystals (NCs) exhibit highly efficient optical gain, which is promising for laser applications. However, the intrinsic mechanism of optical gain in perovskite NCs, particularly whether more than one exciton per NCs is required, remains poorly understood. Here, we use two-dimensional electronic spectroscopy to resonantly probe the interplay between near-band-edge transitions during the buildup of optical gain in CsPbBr₃ NCs. We find compelling evidence to conclude that optical gain in CsPbBr₃ NCs is generated through stimulated emission from strongly interacting biexcitons. The threshold is largely determined by the competition between stimulated emission from biexcitons and excited-state absorption from single exciton to biexciton states. The findings in this work may guide future explorations of NC materials with low-threshold optical gain.

Fluorescence-detected two-quantum and one-quantum-two-quantum 2D electronic spectros-copy of Rhodamine 700

We demonstrate the simultaneous acquisition of three fourth-order nonlinear signal contributions using a shot-to-shot-modulating pulse shaper and fluorescence detection. Beside the 1Q photon echo, two different species of two-quantum contributions can be isolated without any background via phase cycling.

Direct observation of exciton-exciton interactions

Natural light harvesting as well as optoelectronic and photovoltaic devices depend on efficient transport of energy following photoexcitation. Using common spectroscopic methods, however, it is challenging to discriminate one-exciton dynamics from multi-exciton interactions that arise when more than one excitation is present in the system. Here we introduce a coherent two-dimensional spectroscopic method that provides a signal only in case that the presence of one exciton influences the behavior of another one. Exemplarily, we monitor exciton diffusion by annihilation in a perylene bisimide-based J-aggregate. We determine quantitatively the exciton diffusion constant from exciton–exciton-interaction 2D spectra and reconstruct the annihilation-free dynamics for large pump powers. The latter enables for ultrafast spectroscopy at much higher intensities than conventionally possible and thus improves signal-to-noise ratios for multichromophore systems; the former recovers spatio–temporal dynamics for a broad range of phenomena in which exciton interactions are present.

Some photo-physical processes in multichromophore systems might get triggered only if two excitations are present. Here, the authors introduce exciton–exciton-interaction 2D spectroscopy, which is a non-linear optical method that can selectively track the time evolution of such effects.

Frequency-Comb Based Double-Quantum Two-Dimensional Spectrum Identifies Collective Hyperfine Resonances in Atomic Vapor Induced by Dipole-Dipole Interactions

Frequency-comb based multidimensional coherent spectroscopy is a novel optical method that enables high-resolution measurement in a short acquisition time. The method's resolution makes multidimensional coherent spectroscopy relevant for atomic systems that have narrow resonances. We use double-quantum multidimensional coherent spectroscopy to reveal collective hyperfine resonances in rubidium vapor at 100 °C induced by dipole-dipole interactions. We observe tilted and elongated line shapes in the double-quantum 2D spectra, which have never been reported for Doppler-broadened systems. The elongated line shapes suggest that the signal is predominately from the interacting atoms that have a near zero relative velocity.

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.

Electron heating and thermal relaxation of gold nanorods revealed by two-dimensional electronic spectroscopy

To elucidate the complex interplay between the size and shape of gold nanorods and their electronic, photothermal, and optical properties for molecular imaging, photothermal therapy, and optoelectronic devices, it is a prerequisite to characterize ultrafast electron dynamics in gold nanorods. Time-resolved transient absorption (TA) studies of plasmonic electrons in various nanostructures have revealed the time scales for electron heating, lattice vibrational excitation, and phonon relaxation processes in condensed phases. However, because linear spectroscopic and time-resolved TA signals are vulnerable to inhomogeneous line-broadening, pure dephasing and direct electron heating effects are difficult to observe. Here we show that femtosecond two-dimensional electronic spectroscopy, with its unprecedented time resolution and phase sensitivity, can be used to collect direct experimental evidence for ultrafast electron heating, anomalously strong coherent and transient electronic plasmonic responses, and homogenous dephasing processes resulting from electron-vibration couplings even for polydisperse gold nanorods.

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.

Two-dimensional coherent spectroscopy of a THz quantum cascade laser: observation of multiple harmonics

Two-dimensional spectroscopy is performed on a terahertz (THz) frequency quantum cascade laser (QCL) with two broadband THz pulses. Gain switching is used to amplify the first THz pulse and the second THz pulse is used to probe the system. Fourier transforms are taken with respect to the delay time between the two THz pulses and the sampling time of the THz probe pulse. The two-dimensional spectrum consists of three peaks at (ω_τ = 0, ω_t = ω₀), (ω_τ = ω₀, ω_t = ω₀), and (ω_τ = 2ω₀, ω_t = ω₀) where ω₀ denotes the lasing frequency. The peak at ω_τ = 0 represents the response of the probe to the zero-frequency (rectified) component of the instantaneous intensity and can be used to measure the gain recovery.

Biexciton Resonances Reveal Exciton Localization in Stacked Perovskite Quantum Wells

Quasi-two-dimensional lead halide perovskites, MA_n-1Pb_nX_3n+1, are quantum confined materials with an ever-developing range of optoelectronic device applications. Like other semiconductors, the correlated motion of electrons and holes dominates the material's response to optical excitation influencing its electrical and optical properties such as charge formation and mobility. However, the effects of many-particle correlation have been relatively unexplored in perovskite because of the difficultly of probing these states directly. Here, we use double quantum coherence spectroscopy to explore the formation and localization of multiexciton states in these materials. Between the most confined domains, we demonstrate the presence of an interwell, two-exciton excited state. This demonstrates that the four-body Coulomb interaction electronically couples neighboring wells despite weak electron/hole hybridization in these materials. Additionally, in contrast with inorganic semiconductor quantum wells, we demonstrate a rapid decrease in the dephasing time as wells become thicker, indicating that exciton delocalization is not limited by structural inhomogeneity in low-dimensional perovskite.

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.

An Introduction to Coherent Multidimensional Spectroscopy

Coherent multidimensional spectroscopy is a field that has drawn much attention as an optical analogue to multidimensional nuclear magnetic resonance imaging. Coherent multidimensional spectroscopic techniques produce spectra that show the magnitude of an optical signal as a function of two or more pulsed laser frequencies. Spectra can be collected in either the frequency or the time domain. In addition to improving resolution and overcoming spectral congestion, coherent multidimensional spectroscopy provides the ability to investigate and conduct studies based upon the relationship between different peaks. The purpose of this paper is to provide a general introduction to the area of coherent multidimensional spectroscopy, to provide a brief overview of current experimental approaches, and to discuss some emerging developments in this relatively young field.

Controlling S2 Population in Cyanine Dyes Using Shaped Femtosecond Pulses

Fast population transfer from higher to lower excited states occurs via internal conversion (IC) and is the basis of Kasha's rule, which states that spontaneous emission takes place from the lowest excited state of the same multiplicity. Photonic control over IC is of interest because it would allow direct influence over intramolecular nonradiative decay processes occurring in condensed phase. Here we tracked the S2 and S1 fluorescence yield for different cyanine dyes in solution as a function of linear chirp. For the cyanine dyes with polar solvation response IR144 and meso-piperidine substituted IR806, increased S2 emission was observed when using transform limited pulses, whereas chirped pulses led to increased S1 emission. The nonpolar solvated cyanine IR806, on the other hand, did not show S2 emission. A theoretical model, based on a nonperturbative solution of the equation of motion for the density matrix, is offered to explain and simulate the anomalous chirp dependence. Our findings, which depend on pulse properties beyond peak intensity, offer a photonic method to control S2 population thereby opening the door for the exploration of photochemical processes initiated from higher excited states.

Methylene Blue Exciton States Steer Nonradiative Relaxation: Ultrafast Spectroscopy of Methylene Blue Dimer

The photochemistry and aggregation properties of methylene blue (MB) lead to its popular use in photodynamic therapy. The facile formation of strongly coupled "face-to-face" H-aggregates in concentrated aqueous solution, however, significantly changes its spectroscopic properties and photophysics. The photoinitiated dynamics of the simplest MB aggregate, MB2, was investigated over femtosecond to nanosecond time scales revealing sequential internal conversion events that fully relax the excited population. MB monomer dynamics were analyzed in tandem for a direct comparison. First, ultrafast internal conversion from the electric-dipole allowed upper exciton state to the lower forbidden exciton state was evaluated by use of broadband transient absorption (BBTA) and two-dimensional electronic spectroscopy (2DES) with a time resolution of ∼ 10 fs. Lineshape analysis of MB and MB2 2DES bands at 298 and 77 K show effectively no difference in the diagonal/antidiagonal line width ratio for the dimer, in marked contrast to the distinct reduction of the homogeneous line width for MB. This result is interpreted as ultrafast population relaxation imposing a limitation to the homogeneous line width, instead of pure dephasing as in the case of the monomer. Narrowband transient absorption was performed with the aid of target analysis, to model the dynamics at longer times. The MB dynamics were described by a sequential model featuring vibrational relaxation (1-10 ps) followed by intersystem crossing and internal conversion (τ ∼ 370 ps) leaving behind MB triplet species. Alternatively, the dimer dynamics were entirely quenched within ∼ 10 ps, yielding a ground state recovery time of 3-4 ps. Such fast and complete relaxation to the ground state demonstrates the effect of concentration quenching when monomers are brought into close proximity. The formation of exciton states introduces an initial energy funnel that eventually leads to population relaxation to the ground state, preventing even the dissociation of dimers despite having internal energies well above its binding energy.

Multidimensional Electronic Spectroscopy of Photochemical Reactions

Coherent multidimensional electronic spectroscopy can be employed to unravel various channels in molecular chemical reactions. This approach is thus not limited to analysis of energy transfer or charge transfer (i.e. processes from photophysics), but can also be employed in situations where the investigated system undergoes permanent structural changes (i.e. in photochemistry). Photochemical model reactions are discussed by using the example of merocyanine/spiropyran-based molecular switches, which show a rich variety of reaction channels, in particular ring opening and ring closing, cis-trans isomerization, coherent vibrational wave-packet motion, radical ion formation, and population relaxation. Using pump-probe, pump-repump-probe, coherent two-dimensional and three-dimensional, triggered-exchange 2D, and quantum-control spectroscopy, we gain intuitive pictures on which product emerges from which reactant and which reactive molecular modes are associated.

Biexciton formation and exciton coherent coupling in layered GaSe

Nonlinear two-dimensional Fourier transform (2DFT) and linear absorption spectroscopy are used to study the electronic structure and optical properties of excitons in the layered semiconductor GaSe. At the 1s exciton resonance, two peaks are identified in the absorption spectra, which are assigned to splitting of the exciton ground state into the triplet and singlet states. 2DFT spectra acquired for co-linear polarization of the excitation pulses feature an additional peak originating from coherent energy transfer between the singlet and triplet. At cross-linear polarization of the excitation pulses, the 2DFT spectra expose a new peak likely originating from bound biexcitons. The polarization dependent 2DFT spectra are well reproduced by simulations using the optical Bloch equations for a four level system, where many-body effects are included phenomenologically. Although biexciton effects are thought to be strong in this material, only moderate contributions from bound biexciton creation can be observed. The biexciton binding energy of ∼2 meV was estimated from the separation of the peaks in the 2DFT spectra. Temperature dependent absorption and 2DFT measurements, combined with "ab initio" theoretical calculations of the phonon spectra, indicate strong interaction with the A1 (') phonon mode. Excitation density dependent 2DFT measurements reveal excitation induced dephasing and provide a lower limit for the homogeneous linewidth of the excitons in the present GaSe crystal.