Two-quantum 2D FT electronic spectroscopy of biexcitons in GaAs quantum wells

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.

Superradiant Detection of Microscopic Optical Dipolar Interactions

The interaction between light and cold atoms is a complex phenomenon potentially featuring many-body resonant dipole interactions. A major obstacle toward exploring these quantum resources of the system is macroscopic light propagation effects, which not only limit the available time for the microscopic correlations to locally build up, but also create a directional, superradiant emission background whose variations can overwhelm the microscopic effects. In this Letter, we demonstrate a method to perform "background-free" detection of the microscopic optical dynamics in a laser-cooled atomic ensemble. This is made possible by transiently suppressing the macroscopic optical propagation over a substantial time, before a recall of superradiance that imprints the effect of the accumulated microscopic dynamics onto an efficiently detectable outgoing field. We apply this technique to unveil and precisely characterize a density-dependent, microscopic dipolar dephasing effect that generally limits the lifetime of optical spin-wave order in ensemble-based atom-light interfaces.

Many-Exciton Quantum Dynamics in a Ruddlesden-Popper Tin Iodide

We present a study on the many-body exciton interactions in a Ruddlesden-Popper tin halide, namely, (PEA)2SnI4 (PEA = phenylethylammonium), using coherent two-dimensional electronic spectroscopy. The optical dephasing times of the third-order polarization observed in these systems are determined by exciton many-body interactions and lattice fluctuations. We investigate the excitation-induced dephasing (EID) and observe a significant reduction of the dephasing time with increasing excitation density as compared to its lead counterpart (PEA)2PbI4, which we have previously reported in a separate publication [J. Chem. Phys.2020, 153, 164706]. Surprisingly, we find that the EID interaction parameter is four orders of magnitude higher in (PEA)2SnI4 than that in (PEA)2PbI4. This increase in the EID rate may be due to exciton localization arising from a more statically disordered lattice in the tin derivative. This is supported by the observation of multiple closely spaced exciton states and the broadening of the linewidth with increasing population time (spectral diffusion), which suggests a static disordered structure relative to the highly dynamic lead-halide. Additionally, we find that the exciton nonlinear coherent lineshape shows evidence of a biexcitonic state with low binding energy (<10 meV) not observed in the lead system. We model the lineshapes based on a stochastic scattering theory that accounts for the interaction with a nonstationary population of dark background excitations. Our study provides evidence of differences in the exciton quantum dynamics between tin- and lead-based Ruddlesden-Popper metal halides (RPMHs) and links them to the exciton-exciton interaction strength and the static disorder aspect of the crystalline structure.

Spatial Heterogeneity of Biexcitons in Two-Dimensional Ruddlesden-Popper Lead Iodide Perovskites

Quantum confinement in two-dimensional (2D) Ruddlesden-Popper (RP) perovskites leads to the formation of stable quasi-particles, including excitons and biexcitons, the latter of which may enable lasing in these materials. Due to their hybrid organic-inorganic structures and the solution phase synthesis, microcrystals of 2D RP perovskites can be quite heterogeneous, with variations in excitonic and biexcitonic properties between crystals from the same synthesis and even within individual crystals. Here, we employ one- and two-quantum two-dimensional white-light microscopy to systematically study the spatial variations of excitons and biexcitons in microcrystals of a series of 2D RP perovskites BA2MAn-1PbnI3n+1 (n = 2-4, BA= butylammonium, MA = methylammonium). We find that the average biexciton binding energy of around 60 meV is essentially independent of the perovskite layer thickness (n). We also resolve spatial variations of the exciton and biexciton energies on micron length scales within individual crystals. By comparing the one-quantum and two-quantum spectra at each pixel, we conclude that biexcitons are more sensitive to their environments than excitons. These results shed new light on the ways disorder can modify the energetic landscape of excitons and biexcitons in RP perovskites and how biexcitons can be used as a sensitive probe of the microscopic environment of a semiconductor.

Direct Observation of Higher Multiexciton Formation and Annihilation in CdSe Quantum Dots

Most experiments on multiexcitons (MX) in quantum dots focused on the biexciton (XX), which is now well-understood. In contrast, there is little understanding of higher MX in quantum dots as a result of their difficulty to observe. Here, we apply time-resolved photoluminescence (t-PL) spectroscopy with 3 ps time resolution, sufficient to directly resolve previously unobserved spectral dynamics of a higher MX in CdSe quantum dots. These experiments resolve the controversy of the sequence of MX emissions, revealing that the higher channels sequentially populate the lower channels. There is a strong dependence of MX recombination kinetics upon a higher MX state, following a universal volume scaling law for Auger recombination for larger dots. Smaller dots show deviations for higher MX. In addition to triexcitons (3X), these experiments reveal MX up to the tetraexciton (4X). These experiments provide a direct observation of MX formation and annihilation in quantum dots. The impact of this observation is a step toward designing quantum dots to exploit higher MX processes.

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.

Increasing Pump-Probe Signal toward Asymptotic Limits

Optimization of pump-probe signal requires a complete understanding of how signal scales with experimental factors. In simple systems, signal scales quadratically with molar absorptivity, and linearly with fluence, concentration, and path length. In practice, scaling factors weaken beyond certain thresholds (e.g., OD > 0.1) due to asymptotic limits related to optical density, fluence and path length. While computational models can accurately account for subdued scaling, quantitative explanations often appear quite technical in the literature. This Perspective aims to present a simpler understanding of the subject with concise formulas for estimating absolute magnitudes of signal under both ordinary and asymptotic scaling conditions. This formulation may be more appealing for spectroscopists seeking rough estimates of signal or relative comparisons. We identify scaling dependencies of signal with respect to experimental parameters and discuss applications for improving signal under broad conditions. We also review other signal enhancement methods, such as local-oscillator attenuation and plasmonic enhancement, and discuss respective benefits and challenges regarding asymptotic limits that signal cannot exceed.

Separating single- from multi-particle dynamics in nonlinear spectroscopy

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

Fluorescence-Detected Two-Quantum Photon Echoes via Cogwheel Phase Cycling

Two-dimensional (2D) electronic spectroscopy can separate homogeneous and inhomogeneous broadening. While established methods usually probe a photon-echo signal, i.e., a third-order response, to access the homogeneous line width of singly excited states, the homogeneous line width of doubly excited states remained spectroscopically inaccessible. Here we demonstrate the acquisition of two-quantum (2Q) photon echoes using fluorescence-detected 2D spectroscopy. In these eighth-order signals, 2Q coherences are rephased with themselves, leading to line-narrowed 2Q-2Q 2D spectra. By using cogwheel phase cycling, adapted from nuclear magnetic resonance spectroscopy, we isolate the 2Q-2Q 2D spectra of a squaraine dimer and a squaraine polymer and verify the same selectivity of cogwheel phase cycling compared to traditional "nested" phase cycling. The observed difference, between the two systems, in the homogeneous line width of the biexciton can be rationalized as a signature of the interplay of exciton-exciton annihilation, exciton diffusion, and exciton delocalization.

Entangled photons enabled time-frequency-resolved coherent Raman spectroscopy and applications to electronic coherences at femtosecond scale

Quantum entanglement has emerged as a great resource for spectroscopy and its importance in two-photon spectrum and microscopy has been demonstrated. Current studies focus on the two-photon absorption, whereas the Raman spectroscopy with quantum entanglement still remains elusive, with outstanding issues of temporal and spectral resolutions. Here we study the new capabilities provided by entangled photons in coherent Raman spectroscopy. An ultrafast frequency-resolved Raman spectroscopy with entangled photons is developed for condensed-phase molecules, to probe the electronic and vibrational coherences. Using quantum correlation between the photons, the signal shows the capability of both temporal and spectral resolutions not accessible by either classical pulses or the fields without entanglement. We develop a microscopic theory for this Raman spectroscopy, revealing the electronic coherence dynamics even at timescale of 50fs. This suggests new paradigms of optical signals and spectroscopy, with potential to push detection below standard quantum limit.

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.

High-resolution two-dimensional electronic spectroscopy reveals the homogeneous line profile of chromophores solvated in nanoclusters

Doped clusters in the gas phase provide nanoconfined model systems for the study of system-bath interactions. To gain insight into interaction mechanisms between chromophores and their environment, the ensemble inhomogeneity has to be lifted and the homogeneous line profile must be accessed. However, such measurements are very challenging at the low particle densities and low signal levels in cluster beam experiments. Here, we dope cryogenic rare-gas clusters with phthalocyanine molecules and apply action-detected two-dimensional electronic spectroscopy to gain insight into the local molecule-cluster environment for solid and superfluid cluster species. The high-resolution homogeneous linewidth analysis provides a benchmark for the theoretical modelling of binding configurations and shows a promising route for high-resolution molecular two-dimensional spectroscopy.

Understanding the interaction of single chromophores with nanoparticles remains a challenging task in nanoscience. Here the authors provide insight into the interaction between isolated base-free phthalocyanine molecules and He and Ne nanoclusters in the gas phase using high-resolution two-dimensional spectroscopy.

Double-quantum-zero-quantum 2D coherent spectroscopy reveals quantum coherence between collective states in an atomic vapor

We report a novel, to the best of our knowledge, double-quantum-zero-quantum two-dimensional coherent spectroscopy (2DCS) that allows direct detection of the quantum coherence between multiparticle collective states. Through correlating the double-quantum coherence and the zero-quantum coherence, signatures for coherence between collective states can be well isolated as side peaks and readily identified in the 2D spectrum. The experiment is implemented in a vapor of rubidium atoms in a collinear 2DCS setup. Good agreement with a theoretical simulation using density matrix confirms the essential role of the interatomic correlation effect in generating the side peak signals. This 2D spectrum technique paves a new avenue for studying the coherent coupling of highly excited states and many-body properties.

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.

Nonlinear rotational spectroscopy reveals many-body interactions in water molecules

Because of their central importance in chemistry and biology, water molecules have been the subject of decades of intense spectroscopic investigations. Rotational spectroscopy of water vapor has yielded detailed information about the structure and dynamics of isolated water molecules, as well as water dimers and clusters. Nonlinear rotational spectroscopy in the terahertz regime has been developed recently to investigate the rotational dynamics of linear and symmetric-top molecules whose rotational energy levels are regularly spaced. However, it has not been applied to water or other lower-symmetry molecules with irregularly spaced levels. We report the use of recently developed two-dimensional (2D) terahertz rotational spectroscopy to observe high-order rotational coherences and correlations between rotational transitions that were previously unobservable. The results include two-quantum (2Q) peaks at frequencies that are shifted slightly from the sums of distinct rotational transitions on two different molecules. These results directly reveal the presence of previously unseen metastable water complexes with lifetimes of 100 ps or longer. Several such peaks observed at distinct 2Q frequencies indicate that the complexes have multiple preferred bimolecular geometries. Our results demonstrate the sensitivity of rotational correlations measured in 2D terahertz spectroscopy to molecular interactions and complexation in the gas phase.

Optical two-dimensional coherent spectroscopy of many-body dipole-dipole interactions and correlations in atomic vapors

Many-body interactions and correlations in atomic ensembles are fundamental in understanding many-body effects such as collective and emergent phenomena and also play an important role in various atom-based applications. Optical two-dimensional coherent spectroscopy (2DCS) provides a powerful tool to measure many-body interactions and correlations. Here, we present the study of many-body dipole-dipole interactions and correlations in potassium and rubidium atomic vapors by using double-quantum and multi-quantum 2DCS. The results show that double-quantum 2DCS provides sensitive and background-free detection of weak dipole-dipole interaction between atoms with a mean separation up to about 16 μm, and multi-quantum 2DCS can excite and detect multi-atom states (Dicke states) with up to eight correlated atoms. The technique of optical 2DCS can provide a new approach to study many-body physics in atomic ensembles and can be potentially implemented to measure many-body effects in cold atoms and other atomic/molecular systems.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

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.

Inhomogeneous Biexciton Binding in Perovskite Semiconductor Nanocrystals Measured with Two-Dimensional Spectroscopy

Perovskite semiconductor nanocrystals have emerged as an excellent family of materials for optoelectronic applications, where biexciton interaction is essential for optical gain generation and quantum light emission. However, the strength of biexciton interaction remains highly controversial due to the entangled spectral features of the exciton- and biexciton-related transitions in conventional measurement approaches. Here, we tackle the limitation by using polarization-dependent two-dimensional electronic spectroscopy and quantify the excitation energy-dependent biexciton binding energy at cryogenic temperatures. The biexciton binding energy increases with excitation energy, which can be modeled as a near inverse-square size dependence in the effective mass approximation considering the quantum confinement effect. The spectral line width for the exciton-biexciton transition is much broader than that for the ground state to exciton transition, suggesting weakly correlated broadening between these transitions. These inhomogeneity effects should be carefully considered for the future demonstration of optoelectronic applications relying on coherent exciton-biexciton interactions.

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.

Stochastic scattering theory for excitation-induced dephasing: Time-dependent nonlinear coherent exciton lineshapes

We develop a stochastic theory that treats time-dependent exciton-exciton s-wave scattering and that accounts for dynamic Coulomb screening, which we describe within a mean-field limit. With this theory, we model excitation-induced dephasing effects on time-resolved two-dimensional coherent optical lineshapes and we identify a number of features that can be attributed to the many-body dynamics occurring in the background of the exciton, including dynamic line narrowing, mixing of real and imaginary spectral components, and multi-quantum states. We test the model by means of multidimensional coherent spectroscopy on a two-dimensional metal-halide semiconductor that hosts tightly bound excitons and biexcitons that feature strong polaronic character. We find that the exciton nonlinear coherent lineshape reflects many-body correlations that give rise to excitation-induced dephasing. Furthermore, we observe that the exciton lineshape evolves with the population time over time windows in which the population itself is static in a manner that reveals the evolution of the multi-exciton many-body couplings. Specifically, the dephasing dynamics slow down with time, at a rate that is governed by the strength of exciton many-body interactions and on the dynamic Coulomb screening potential. The real part of the coherent optical lineshape displays strong dispersive character at zero time, which transforms to an absorptive lineshape on the dissipation timescale of excitation-induced dephasing effects, while the imaginary part displays converse behavior. Our microscopic theoretical approach is sufficiently flexible to allow for a wide exploration of how system-bath dynamics contribute to linear and non-linear time-resolved spectral behavior.

Fast phase cycling in non-collinear optical two-dimensional coherent spectroscopy

As optical two-dimensional coherent spectroscopy (2DCS) is extended to a broader range of applications, it is critical to improve the detection sensitivity of optical 2DCS. We developed a fast phase-cycling scheme in a non-collinear optical 2DCS implementation by using liquid crystal phase retarders to modulate the phases of two excitation pulses. The background in the signal can be eliminated by combining either two or four interferograms measured with a proper phase configuration. The effectiveness of this method was validated in optical 2DCS measurements of an atomic vapor. This fast phase-cycling scheme will enable optical 2DCS in novel emerging applications that require enhanced detection sensitivity.

Excitation Ladder of Cavity Polaritons

Multidimensional coherent spectroscopy directly unravels multiply excited states that overlap in a linear spectrum. We report multidimensional coherent optical photocurrent spectroscopy in a semiconductor polariton diode and explore the excitation ladder of cavity polaritons. We measure doubly and triply avoided crossings for pairs and triplets of exciton polaritons, demonstrating the strong coupling between light and dressed doublet and triplet semiconductor excitations. These results demonstrate that multiply excited excitonic states strongly coupled to a microcavity can be described as two coupled quantum-anharmonic ladders.

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.

Precise pulse shaping for quantum control of strong optical transitions

Advances of quantum control technology have led to nearly perfect single-qubit control of nuclear spins and atomic hyperfine ground states. In contrast, quantum control of strong optical transitions, even for free atoms, are far from being perfect. Developments of such quantum control appears to be limited by available laser technology for generating isolated, sub-nanosecond optical waveforms with 10's of GHz programming bandwidth. Here we propose a simple and robust method for the desired pulse shaping, based on precisely stacking multiple delayed picosecond pulses. Our proof-of-principal demonstration leads to arbitrarily shapeable optical waveforms with 30 GHz bandwidth and 100 ps duration. We confirm the stability of the waveforms by interfacing the pulses with laser-cooled atoms, resulting in "super-resolved" spectroscopic signals. This pulse shaping method may open exciting perspectives in quantum optics, and for fast laser cooling and atom interferometry with mode-locked lasers.

From wavelike to sub-diffusive motion: exciton dynamics and interaction in squaraine copolymers of varying length

Exciton transport and exciton-exciton interactions in molecular aggregates and polymers are of great importance in natural photosynthesis, organic electronics, and related areas of research. Both the experimental observation and theoretical description of these processes across time and length scales, including the transition from the initial wavelike motion to the following long-range exciton transport, are highly challenging. Therefore, while exciton dynamics at small scales are often treated explicitly, long-range exciton transport is typically described phenomenologically by normal diffusion. In this work, we study the transition from wavelike to diffusive motion of interacting exciton pairs in squaraine copolymers of varying length. To this end we use a combination of the recently introduced exciton-exciton-interaction two-dimensional (EEI2D) electronic spectroscopy and microscopic theoretical modelling. As we show by comparison with the model, the experimentally observed kinetics include three phases, wavelike motion dominated by immediate exciton-exciton annihilation (10-100 fs), sub-diffusive behavior (0.1-10 ps), and excitation relaxation (0.01-1 ns). We demonstrate that the key quantity for the transition from wavelike to diffusive dynamics is the exciton delocalization length relative to the length of the polymer: while in short polymers wavelike motion of rapidly annihilating excitons dominates, in long polymers the excitons become locally trapped and exhibit sub-diffusive behavior. Our findings indicate that exciton transport through conjugated systems emerging from the excitonic structure is generally not governed by normal diffusion. Instead, to characterize the material transport properties, the diffusion presence and character should be determined.

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.

Correction of Fabry-Pérot interference effects in phase and amplitude pulse shapers based on liquid crystal spatial light modulators

Broadband femtosecond laser pulses manipulated by pulse shapers based on a liquid crystal spatial light modulator (LC-SLM) inevitably experience periodic spectral distortions due to Fabry-Perot interference effects within the LC-SLM. We present a method, applicable to phase and amplitude pulse shapers based on dual LC-SLMs, that enables the calibration and suppression of the undesired spectral intensity modulations in a non-iterative fashion. We demonstrate that the method considerably improves the amplitude shaping fidelity of phase and amplitude pulse shapers without compromising the phase shaping properties.

Coherent two-dimensional Fourier transform spectroscopy using a 25 Tesla resistive magnet

We performed nonlinear optical two-dimensional Fourier transform spectroscopy measurements using an optical resistive high-field magnet on GaAs quantum wells. Magnetic fields up to 25 T can be achieved using the split helix resistive magnet. Two-dimensional spectroscopy measurements based on the coherent four-wave mixing signal require phase stability. Therefore, these measurements are difficult to perform in environments prone to mechanical vibrations. Large resistive magnets use extensive quantities of cooling water, which causes mechanical vibrations, making two-dimensional Fourier transform spectroscopy very challenging. Here, we report on the strategies we used to overcome these challenges and maintain the required phase-stability throughout the measurement. A self-contained portable platform was used to set up the experiments within the time frame provided by a user facility. Furthermore, this platform was floated above the optical table in order to isolate it from vibrations originating from the resistive magnet. Finally, we present two-dimensional Fourier transform spectra obtained from GaAs quantum wells at magnetic fields up to 25 T and demonstrate the utility of this technique in providing important details, which are obscured in one dimensional spectroscopy.

Coherent and dissipative quantum process tensor reconstructions in two-dimensional electronic spectroscopy

A major goal of time-resolved spectroscopy is to resolve the dynamical processes that follow photoexcitation. This amounts to identifying all the quantum states involved and the rates of population transfer between them. Unfortunately, such quantum state and kinetic reconstructions are ambiguous using one-dimensional methods such as transient absorption even when all the states of the system are fully resolved. Higher-dimensionality methods like two-dimensional spectroscopy lift some of the ambiguity, but unless the spectral features are well-separated, current inversion methods generally fail. Here, we show that, using both coherence and population signals of the nonlinear response, it is indeed possible to accurately extract both static and dynamic information from the 2D spectrum even when features are highly congested. Coherences report on the positions of the vibronic states of the system, providing a useful constraint for extracting the full kinetic scheme. We model time-resolved 2D photon echo spectra using a sum-over-states approach and show in which regimes the Hamiltonian and kinetic schemes may be recovered. Furthermore, we discuss how such algorithms may be applied to experimental data and where some of the underlying assumptions may fail. The ability to systematically extract the maximal information content of multidimensional spectroscopic data is an important step toward utilizing the full power of these techniques and elucidating the structure and dynamics of increasingly complex molecular systems.

Probing biexciton structure in CdSe nanocrystals using 2D optical spectroscopy

Coherent Multi-dimensional Spectroscopy is ideally suited to investigate many-body effects in semiconductor nanostructures. Here we employ 2D optical spectroscopy on the model system of CdSe quantum dots to reveal the structure of the bandedge biexciton.

Delocalized excitons and interaction effects in extremely dilute thermal ensembles

Long-range interparticle interactions are revealed in extremely dilute thermal atomic ensembles using highly sensitive nonlinear femtosecond spectroscopy. Delocalized excitons are detected in the atomic systems at particle densities where the mean interatomic distance (>10 μm) is much greater than the laser wavelength and multi-particle coherences should destructively interfere over the ensemble average. With a combined experimental and theoretical analysis, we identify an effective interaction mechanism, presumably of dipolar nature, as the origin of the excitonic signals. Our study implies that even in highly-dilute thermal atom ensembles, significant transition dipole-dipole interaction networks may form that require advanced modeling beyond the nearest neighbor approximation to quantitatively capture the details of their many-body properties.

Two-dimensional UV spectroscopy: a new insight into the structure and dynamics of biomolecules

Two-dimensional ultraviolet spectroscopy has the potential to deliver rich structural and dynamical information on biomolecules such as DNA and proteins.

Biexcitons in monolayer transition metal dichalcogenides tuned by magnetic fields

We present time-integrated four-wave mixing measurements on monolayer MoSe₂ in magnetic fields up to 25 T. The experimental data together with time-dependent density function theory calculations provide interesting insights into the biexciton formation and dynamics. In the presence of magnetic fields the coherence at negative and positive time delays is dominated by intervalley biexcitons. We demonstrate that magnetic fields can serve as a control to enhance the biexciton formation and help search for more exotic states of matter, including the creation of multiple exciton complexes and excitonic condensates.

Biexciton complexes in atomically thin transition metal dichalcogenides have unusually large binding energies. Here, the authors explore biexciton formation dynamics in monolayer MoSe₂ in the presence of magnetic fields up to 25 T.

Coherent two-dimensional electronic mass spectrometry

Coherent two-dimensional (2D) optical spectroscopy has revolutionized our ability to probe many types of couplings and ultrafast dynamics in complex quantum systems. The dynamics and function of any quantum system strongly depend on couplings to the environment. Thus, studying coherent interactions for different environments remains a topic of tremendous interest. Here we introduce coherent 2D electronic mass spectrometry that allows 2D measurements on effusive molecular beams and thus on quantum systems with minimum system–bath interaction and employ this to identify the major ionization pathway of 3d Rydberg states in NO₂. Furthermore, we present 2D spectra of multiphoton ionization, disclosing distinct differences in the nonlinear response functions leading to the ionization products. We also realize the equivalent of spectrally resolved transient-absorption measurements without the necessity for acquiring weak absorption changes. Using time-of-flight detection introduces cations as an observable, enabling the 2D spectroscopic study on isolated systems of photophysical and photochemical reactions.

Multidimensional spectroscopy is a powerful tool in exploring photo-induced dynamics and electron coupling processes in molecules. Here the authors demonstrate coherent two-dimensional electronic mass spectrometry on molecular beams and its application to photoionization studies of the NO₂ molecule.

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.

Deconvolution of optical multidimensional coherent spectra

Optical coherent multidimensional spectroscopy is a powerful technique for unraveling complex and congested spectra by spreading them across multiple dimensions, removing the effects of inhomogeneity, and revealing underlying correlations. As the technique matures, the focus is shifting from understanding the technique itself to using it to probe the underlying dynamics in the system being studied. However, these dynamics can be difficult to discern because they are convolved with the nonlinear optical response of the system. Inspired by methods used to deblur images, we present a method for deconvolving the underlying dynamics from the optical response. To demonstrate the method, we extract the many-particle diffusion Green's functions for excitons in a semiconductor quantum well from two-dimensional coherent spectra.

Photochemical Control of Exciton Superradiance in Light-Harvesting Nanotubes

Photosynthetic antennae and organic electronic materials use topological, structural, and molecular control of delocalized excitons to enhance and direct energy transfer. Interactions between the transition dipoles of individual chromophore units allow for coherent delocalization across multiple molecular sites. This delocalization, for specific geometries, greatly enhances the transition dipole moment of the lowest energy excitonic state relative to the chromophore and increases its radiative rate, a phenomenon known as superradiance. In this study, we show that ordered, self-assembled light-harvesting nanotubes (LHNs) display excitation-induced photobrightening and photodarkening. These changes in quantum yield arise due to changes in energetic disorder, which in turn increases/decreases excitonic superradiance. Through a combination of experiment and modeling, we show that intense illumination induces different types of chemical change in LHNs that reproducibly alter absorption and fluorescence properties, indicating control over excitonic delocalization. We also show that changes in spectral width and shift can be sensitive measures of system dimensionality, illustrating the mixed 1-2D nature of LHN excitons. Our results demonstrate a path forward for mastery of energetic disorder in an excitonic antenna, with implications for fundamental studies of coherent energy transport.

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.

Ultrafast Four-Dimensional Coherent Spectroscopy by Projection Reconstruction

Multidimensional coherent spectroscopy provides insights into the vibronic structure and dynamics of complex systems. In general, the higher the dimensionality, the better the spectral discrimination and the more information that may be extracted about the system. A major impediment to widespread implementation of these methods, however, is that the acquisition time generally increases exponentially with dimensionality, prohibiting practical implementation. We demonstrate the use of nonuniform sampling based on the projection-slice theorem and inverse Radon transform within the context of a fifth-order, 4D technique (GAMERS) designed to correlate the vibrational contributions to different electronic states. Projection-reconstruction (PRO GAMERS) greatly reduces the data sampling requirements without sacrificing frequency resolution. The sensitivity of this technique is demonstrated to surpass conventional uniform sampling by orders of magnitude. The incorporation of projection-reconstruction into multidimensional coherent spectroscopy opens up the possibility to study the structure of complex chemical, biological, and physical systems with unprecedented detail.

Coherent two-dimensional fluorescence micro-spectroscopy

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