Resonance lineshapes in two-dimensional Fourier transform spectroscopy

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.

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.

High-order pump-probe and high-order two-dimensional electronic spectroscopy on the example of squaraine oligomers

Time-resolved spectroscopy is commonly used to study diverse phenomena in chemistry, biology, and physics. Pump-probe experiments and coherent two-dimensional (2D) spectroscopy have resolved site-to-site energy transfer, visualized electronic couplings, and much more. In both techniques, the lowest-order signal, in a perturbative expansion of the polarization, is of third order in the electric field, which we call a one-quantum (1Q) signal because in 2D spectroscopy it oscillates in the coherence time with the excitation frequency. There is also a two-quantum (2Q) signal that oscillates in the coherence time at twice the fundamental frequency and is fifth order in the electric field. We demonstrate that the appearance of the 2Q signal guarantees that the 1Q signal is contaminated by non-negligible fifth-order interactions. We derive an analytical connection between an nQ signal and (2n + 1)th-order contaminations of an rQ (with r < n) signal by studying Feynman diagrams of all contributions. We demonstrate that by performing partial integrations along the excitation axis in 2D spectra, we can obtain clean rQ signals free of higher-order artifacts. We exemplify the technique using optical 2D spectroscopy on squaraine oligomers, showing clean extraction of the third-order signal. We further demonstrate the analytical connection with higher-order pump-probe spectroscopy and compare both techniques experimentally. Our approach demonstrates the full power of higher-order pump-probe and 2D spectroscopy to investigate multi-particle interactions in coupled systems.

Studies of Local DNA Backbone Conformation and Conformational Disorder Using Site-Specific Exciton-Coupled Dimer Probe Spectroscopy

The processes of genome expression, regulation, and repair require direct interactions between proteins and DNA at specific sites located at and near single-stranded-double-stranded DNA (ssDNA-dsDNA) junctions. Here, we review the application of recently developed spectroscopic methods and analyses that combine linear absorbance and circular dichroism spectroscopy with nonlinear 2D fluorescence spectroscopy to study the local conformations and conformational disorder of the sugar-phosphate backbones of ssDNA-dsDNA fork constructs that have been internally labeled with exciton-coupled cyanine (iCy3)2 dimer probes. With the application of these methods, the (iCy3)2 dimer can serve as a reliable probe of the mean local conformations and conformational distributions of the sugar-phosphate backbones of dsDNA at various critical positions. The results of our studies suggest a possible structural framework for understanding the roles of DNA breathing in driving the processes of protein-DNA complex assembly and function.

Encapsulating Semiconductor Quantum Dots in Supramolecular Cages Enables Ultrafast Guest-Host Electron and Vibrational Energy Transfer

In the field of supramolecular chemistry, host-guest systems have been extensively explored to encapsulate a wide range of substrates, owing to emerging functionalities in nanoconfined space that cannot be achieved in dilute solutions. However, host-guest chemistry is still limited to encapsulation of small guests. Herein, we construct a water-soluble metallo-supramolecular hexagonal prism with a large hydrophobic cavity by anchoring multiple polyethylene glycol chains onto the building blocks. Then, assembled prisms are able to encapsulate quantum dots (QDs) with diameters of less than 5.0 nm. Furthermore, we find that the supramolecular cage around each QD strongly modifies the photophysics of the QD by universally increasing the rates of QD relaxation processes via ultrafast electron and vibrational energy transfer. Taken together, these efforts expand the scope of substrates in host-guest systems and provide a new approach to tune the optical properties of QDs.

Rapid multiplex ultrafast nonlinear microscopy for material characterization

We demonstrate rapid imaging based on four-wave mixing (FWM) by assessing the quality of advanced materials through measurement of their nonlinear response, exciton dephasing, and exciton lifetimes. We use a WSe₂ monolayer grown by chemical vapor deposition as a canonical example to demonstrate these capabilities. By comparison, we show that extracting material parameters such as FWM intensity, dephasing times, excited state lifetimes, and distribution of dark/localized states allows for a more accurate assessment of the quality of a sample than current prevalent techniques, including white light microscopy and linear micro-reflectance spectroscopy. We further discuss future improvements of the ultrafast FWM techniques by modeling the robustness of exponential decay fits to different spacing of the sampling points. Employing ultrafast nonlinear imaging in real-time at room temperature bears the potential for rapid in-situ sample characterization of advanced materials and beyond.

Dephasing Processes in the Molecular Dye Lumogen-F Orange Characterized by Two-Dimensional Electronic Spectroscopy

Molecular dyes are finding more and more applications in photonics and quantum technologies, such as polaritonic optical microcavities, organic quantum batteries and single-photon emitters for quantum sensing and metrology. For all these applications, it is of crucial importance to characterize the dephasing mechanisms. In this work we use two-dimensional electronic spectroscopy (2DES) to study the temperature dependent dephasing processes in the prototypical organic dye Lumogen-F orange. We model the 2DES maps using the Bloch equations for a two-level system and obtain a dephasing time T₂ = 53 fs at room temperature, which increases to T₂ = 94 fs at 86 K. Furthermore, spectral diffusion processes are observed and modeled by a combination of underdamped and overdamped Brownian oscillators. Our results provide useful design parameters for advanced optoelectronic and photonic devices incorporating dye molecules.

Stochastic exciton-scattering theory of optical lineshapes: Renormalized many-body contributions

Spectral line-shapes provide a window into the local environment coupled to a quantum transition in the condensed phase. In this paper, we build upon a stochastic model to account for non-stationary background processes produced by broad-band pulsed laser stimulation. In particular, we consider the contribution of pair-fluctuations arising from the full bosonic many-body Hamiltonian within a mean-field approximation, treating the coupling to the system as a stochastic noise term. Using the It{\^o} transformation, we consider two limiting cases for our model which lead to a connection between the observed spectral fluctuations and the spectral density of the environment. In the first case, we consider a Brownian environment and show that this produces spectral dynamics that relax to form dressed excitonic states and recover an Anderson-Kubo-like form for the spectral correlations. In the second case, we assume that the spectrum is Anderson-Kubo like, and invert to determine the corresponding background. Using the Jensen inequality, we obtain an upper limit for the spectral density of the background. The results presented here provide the technical tools for applying the stochastic model to a broad range of problems.

Imaging dynamic exciton interactions and coupling in transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) are regarded as a possible material platform for quantum information science and related device applications. In TMD monolayers, the dephasing time and inhomogeneity are crucial parameters for any quantum information application. In TMD heterostructures, coupling strength and interlayer exciton lifetimes are also parameters of interest. However, many demonstrations in TMDs can only be realized at specific spots on the sample, presenting a challenge to the scalability of these applications. Here, using multi-dimensional coherent imaging spectroscopy, we shed light on the underlying physics—including dephasing, inhomogeneity, and strain—for a MoSe2 monolayer and identify both promising and unfavorable areas for quantum information applications. We, furthermore, apply the same technique to a MoSe2/WSe2 heterostructure. Despite the notable presence of strain and dielectric environment changes, coherent and incoherent coupling and interlayer exciton lifetimes are mostly robust across the sample. This uniformity is despite a significantly inhomogeneous interlayer exciton photoluminescence distribution that suggests a bad sample for device applications. This robustness strengthens the case for TMDs as a next-generation material platform in quantum information science and beyond.

Plasmon-Enhanced Exciton Delocalization in Squaraine-Type Molecular Aggregates

Enlarging exciton coherence lengths in molecular aggregates is critical for enhancing the collective optical and transport properties of molecular thin film nanostructures or devices. We demonstrate that the exciton coherence length of squaraine aggregates can be increased from 10 to 24 molecular units at room temperature when preparing the aggregated thin film on a metallic rather than a dielectric substrate. Two-dimensional electronic spectroscopy measurements reveal a much lower degree of inhomogeneous line broadening for aggregates on a gold film, pointing to a reduced disorder. The result is corroborated by simulations based on a Frenkel exciton model including exciton-plasmon coupling effects. The simulation shows that localized, energetically nearly resonant excitons on spatially well separated segments can be radiatively coupled via delocalized surface plasmon polariton modes at a planar molecule-gold interface. Such plasmon-enhanced delocalization of the exciton wave function is of high importance for improving the coherent transport properties of molecular aggregates on the nanoscale. Additionally, it may help tailor the collective optical response of organic materials for quantum optical applications.

Measuring Exciton Fine-Structure in Randomly Oriented Perovskite Nanocrystal Ensembles Using Nonlinear Optical Spectroscopy: Theory

Lead halide perovskite nanocrystals (PNCs) exhibit unique optoelectronic properties, many of which originate from a purported bright-triplet exciton fine-structure. A major impediment to measuring this fine-structure is inhomogeneous spectral broadening, which has limited most experimental studies to single-nanocrystal spectroscopies. It is shown here that the linearly polarized single-particle selection rules in PNCs are preserved in nonlinear spectroscopies of randomly oriented ensembles. Simulations incorporating rotational averaging demonstrate that techniques such as transient absorption and two-dimensional coherent spectroscopy are capable of resolving exciton fine-structure in PNCs, even in the presence of inhomogeneous broadening and orientation disorder.

Temperature-dependent local conformations and conformational distributions of cyanine dimer labeled single-stranded-double-stranded DNA junctions by 2D fluorescence spectroscopy

DNA replication and the related processes of genome expression require binding, assembly, and function of protein complexes at and near single-stranded (ss)-double-stranded (ds) DNA junctions. These central protein-DNA interactions are likely influenced by thermally induced conformational fluctuations of the DNA scaffold across an unknown distribution of functionally relevant states to provide regulatory proteins access to properly conformed DNA binding sites. Thus, characterizing the nature of conformational fluctuations and the associated structural disorder at ss-dsDNA junctions is critical for understanding the molecular mechanisms of these central biological processes. Here, we describe spectroscopic studies of model ss-dsDNA fork constructs that contain dimers of "internally labeled" cyanine (iCy3) chromophore probes that have been rigidly inserted within the sugar-phosphate backbones of the DNA strands. Our combined analyses of absorbance, circular dichroism, and two-dimensional fluorescence spectroscopy permit us to characterize the local conformational parameters and conformational distributions. We find that the DNA sugar-phosphate backbones undergo abrupt successive changes in their local conformations-initially from a right-handed and ordered DNA state to a disordered splayed-open structure and then to a disordered left-handed conformation-as the dimer probes are moved across the ss-dsDNA junction. Our results suggest that the sugar-phosphate backbones at and near ss-dsDNA junctions adopt specific position-dependent local conformations and exhibit varying extents of conformational disorder that deviate widely from the Watson-Crick structure. We suggest that some of these conformations can function as secondary-structure motifs for interaction with protein complexes that bind to and assemble at these sites.

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.

Analysis of complex multidimensional optical spectra by linear prediction

We apply Linear Prediction from Singular Value Decomposition (LPSVD) to two-dimensional complex optical data in the time-domain to generate spectra with advantages over discrete Fourier transformation (DFT). LPSVD is a non-iterative procedure that fits time-domain complex data to the sum of damped sinusoids, or Lorentzian peaks in the spectral domain. Because the fitting is linear, it is not necessary to give initial guess parameters as in nonlinear fits. Although LPSVD is a one-dimensional algorithm, it can be performed column-wise on two-dimensional data. The method has been extensively used in 2D NMR spectroscopy, where spectral peaks are typically nearly ideal Lorentzians, but to our knowledge has not been applied in the analogous optical technique, where peaks can be far from Lorentzian. We apply LPSVD to the analysis of zero, one, and two quantum electronic two-dimensional spectra from a semiconductor microcavity. The spectra consist of non-ideal, often overlapping peaks. We find that LPSVD achieves a very good fit even on non-ideal data. It reduces noise and eliminates discrete distortions inherent in the DFT. We also use it to isolate and analyze weak features of interest.

Phonon-Assisted Intervalley Scattering Determines Ultrafast Exciton Dynamics in MoSe_{2} Bilayers

While valleys (energy extrema) are present in all band structures of solids, their preeminent role in determining exciton resonances and dynamics in atomically thin transition metal dichalcogenides (TMDC) is unique. Using two-dimensional coherent electronic spectroscopy, we find that exciton decoherence occurs on a much faster timescale in MoSe_{2} bilayers than that in the monolayers. We further identify two population relaxation channels in the bilayer, a coherent and an incoherent one. Our microscopic model reveals that phonon-emission processes facilitate scattering events from the K valley to other lower-energy Γ and Λ valleys in the bilayer. Our combined experimental and theoretical studies unequivocally establish different microscopic mechanisms that determine exciton quantum dynamics in TMDC monolayers and bilayers. Understanding exciton quantum dynamics provides critical guidance to the manipulation of spin-valley degrees of freedom in TMDC bilayers.

Pump Slice Amplitudes: A Simple and Robust Method for Connecting Two-Dimensional Infrared and Fourier Transform Infrared Spectra

Ultrafast two-dimensional infrared (2D IR) spectroscopy and Fourier transform infrared (FTIR) spectroscopy are often performed in tandem, with FTIR typically used to interpret and provide hypotheses for 2D IR experiments. Comparisons between 2D IR and FTIR spectra can also be used to examine the structure and orientation in systems of coupled vibrational chromophores. The most common method for comparing 2D IR and FTIR lineshapes, the diagonal slice method, contains significant artifacts when applied to oscillators with low anharmonicities. Here, we introduce a new technique, the pump slice amplitude (PSA) method, for relating 2D IR lineshapes to FTIR lineshapes and compare PSAs against diagonal slices using theoretical and experimental spectra. We find that PSAs are significantly more similar to FTIR lineshapes than diagonal slices in systems with low anharmonicity.

Exciton linewidth broadening induced by exciton-phonon interactions in CsPbBr3 nanocrystals

Quantum dephasing of excitonic transitions in CsPbBr₃ nanocrystals has been studied using two-dimensional electronic spectroscopy at cryogenic temperatures. The exciton-phonon interactions for acoustic and optical modes exhibit different effects on the coherent dynamics of excitonic transitions. The homogeneous linewidth shows a proportional dependence on the temperature, suggesting the primary dephasing channel of the elastic scattering between exciton and acoustic modes. The exciton-optical mode interaction is manifested as the beatings of off-diagonal signals in the population time domain at the frequencies of 29 and 51 cm^-1, indicating phonon replicas of excitonic transitions arising from coherent exciton-phonon interaction. The insight information of exciton homogeneous broadening in perovskite nanocrystals is essential for the potential application of quantum light sources.

Toward Engineering Intrinsic Line Widths and Line Broadening in Perovskite Nanoplatelets

Perovskite nanoplatelets possess extremely narrow absorption and emission line widths, which are crucial characteristics for many optical applications. However, their underlying intrinsic and extrinsic line-broadening mechanisms are poorly understood. Here, we apply multidimensional coherent spectroscopy to determine the homogeneous line broadening of colloidal perovskite nanoplatelet ensembles. We demonstrate a dependence of not only their intrinsic line widths but also of various broadening mechanisms on platelet geometry. We find that decreasing nanoplatelet thickness by a single monolayer results in a 2-fold reduction of the inhomogeneous line width and a 3-fold reduction of the intrinsic homogeneous line width to the sub-millielectronvolts regime. In addition, our measurements suggest homogeneously broadened exciton resonances in two-layer (but not necessarily three-layer) nanoplatelets at room-temperature.

Multidimensional coherent spectroscopy reveals triplet state coherences in cesium lead-halide perovskite nanocrystals

Advances in optoelectronics require materials with novel and engineered characteristics. A class of materials that has garnered tremendous interest is metal-halide perovskites, stimulated by meteoric increases in photovoltaic efficiencies of perovskite solar cells. In addition, recent advances have applied perovskite nanocrystals (NCs) in light-emitting devices. It was found recently that, for cesium lead-halide perovskite NCs, their unusually efficient light emission may be due to a unique excitonic fine structure composed of three bright triplet states that minimally interact with a proximal dark singlet state. To study this fine structure without isolating single NCs, we use multidimensional coherent spectroscopy at cryogenic temperatures to reveal coherences involving triplet states of a CsPbI₃ NC ensemble. Picosecond time scale dephasing times are measured for both triplet and inter-triplet coherences, from which we infer a unique exciton fine structure level ordering composed of a dark state energetically positioned within the bright triplet manifold.

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.

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.

Lineshape characterization of excitons in monolayer WS2 by two-dimensional electronic spectroscopy

The optical properties of monolayer transition metal dichalcogenides (TMDCs), an important family of two-dimensional (2D) semiconductors for optoelectronic applications, are dominated by two excitons A (XA) and B (XB) located at K/K's valleys. The lineshape of the excitons is an indicator of the interaction of the excitons with other particles and also largely determines the performance of TMDC-based optoelectronic devices. In this work, we apply 2D electronic spectroscopy (2DES), which enables separation of the intrinsic homogeneous linewidth and the extrinsic inhomogeneous linewidth, to dissect the lineshape of XA in monolayer WS₂. With a home-built broadband optical parametric amplifier, the 2D spectra give the exciton linewidth values for extensive ranges of excitation densities and temperatures, reflecting inter-exciton and exciton-phonon interactions. Meanwhile, the time-domain evolution of the lineshape reveals a similar rate of spectral diffusion to that in quantum wells (QWs) based on III-V semiconductors.

Exciton Polarons in Two-Dimensional Hybrid Metal-Halide Perovskites

While polarons, charges bound to a lattice deformation induced by electron-phonon coupling, are primary photoexcitations in bulk metal-halide hybrid organic-inorganic perovskites (HOIPs), excitons, Coulomb-bound electron-hole pairs, are the stable quasi-particles in their two-dimensional (2D) analogues. However, are polaronic effects consequential for excitons in 2D-HOIPs? We argue that they are manifested intrinsically in the exciton spectral structure, which is composed of multiple nondegenerate resonances with constant interpeak energy spacing. We highlight population and dephasing dynamics that point to the apparently deterministic role of polaronic effects. We contend that an interplay of long-range and short-range exciton-lattice couplings gives rise to exciton polarons, which fundamentally establishes their effective mass and radius and, consequently, their quantum dynamics. Finally, we highlight opportunities for the community to develop the rigorous description of exciton polarons in 2D-HOIPs to advance their fundamental understanding as model systems for condensed-phase materials with strong lattice-mediated correlations.

Encapsulation narrows excitonic homogeneous linewidth of exfoliated MoSe2 monolayer

We use collinear multidimensional coherent spectroscopy to measure van der Waals structures with a nearly diffraction-limited spot size. Encapsulation by boron nitride narrows the homogeneous and inhomogeneous linewidths of excitonic resonances in MoSe2.

Diagonal slice four-wave mixing: natural separation of coherent broadening mechanisms

We present an ultrafast coherent spectroscopy data acquisition scheme that samples slices of the time domain used in multidimensional coherent spectroscopy to achieve faster data collection than full spectra. We derive analytical expressions for resonance lineshapes using this technique that completely separate homogeneous and inhomogeneous broadening contributions into separate projected lineshapes for arbitrary inhomogeneous broadening. These lineshape expressions are also valid for slices taken from full multidimensional spectra and allow direct measurement of the parameters contributing to the lineshapes in those spectra as well as our own.

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.

Advances in multi-dimensional coherent spectroscopy of semiconductor nanostructures

Multi-dimensional coherent spectroscopy (MDCS) has become an extremely versatile and sensitive technique for elucidating the structure, composition, and dynamics of condensed matter, atomic, and molecular systems. The appeal of MDCS lies in its ability to resolve both individual-emitter and ensemble-averaged dynamics of optically created excitations in disordered systems. When applied to semiconductors, MDCS enables unambiguous separation of homogeneous and inhomogeneous contributions to the optical linewidth, pinpoints the nature of coupling between resonances, and reveals signatures of many-body interactions. In this review, we discuss the implementation of MDCS to measure the nonlinear optical response of excitonic transitions in semiconductor nanostructures. Capabilities of the technique are illustrated with recent experimental studies that advance our understanding of optical decoherence and dissipation, energy transfer, and many-body phenomena in quantum dots and quantum wells, semiconductor microcavities, layered semiconductors, and photovoltaic materials.

Neutral and charged inter-valley biexcitons in monolayer MoSe2

In atomically thin transition metal dichalcogenides (TMDs), reduced dielectric screening of the Coulomb interaction leads to strongly correlated many-body states, including excitons and trions, that dominate the optical properties. Higher-order states, such as bound biexcitons, are possible but are difficult to identify unambiguously using linear optical spectroscopy methods. Here, we implement polarization-resolved two-dimensional coherent spectroscopy (2DCS) to unravel the complex optical response of monolayer MoSe₂ and identify multiple higher-order correlated states. Decisive signatures of neutral and charged inter-valley biexcitons appear in cross-polarized two-dimensional spectra as distinct resonances with respective ∼20 and ∼5 meV binding energies—similar to recent calculations using variational and Monte Carlo methods. A theoretical model considering the valley-dependent optical selection rules reveals the quantum pathways that give rise to these states. Inter-valley biexcitons identified here, comprising of neutral and charged excitons from different valleys, offer new opportunities for developing ultrathin biexciton lasers and polarization-entangled photon sources.

Atomically thin transition metal dichalcogenides host excitons and trions, however higher-order states, although possible, are difficult to identify experimentally. Here, the authors perform polarization-resolved coherent spectroscopy to unveil the signature of neutral and charged inter-valley biexcitons in monolayer MoSe₂.

Trion Valley Coherence in Monolayer Semiconductors

The emerging field of valleytronics aims to exploit the valley pseudospin of electrons residing near Bloch band extrema as an information carrier. Recent experiments demonstrating optical generation and manipulation of exciton valley coherence (the superposition of electron-hole pairs at opposite valleys) in monolayer transition metal dichalcogenides (TMDs) provide a critical step towards control of this quantum degree of freedom. The charged exciton (trion) in TMDs is an intriguing alternative to the neutral exciton for control of valley pseudospin because of its long spontaneous recombination lifetime, its robust valley polarization, and its coupling to residual electronic spin. Trion valley coherence has however been unexplored due to experimental challenges in accessing it spectroscopically. In this work, we employ ultrafast two-dimensional coherent spectroscopy to resonantly generate and detect trion valley coherence in monolayer MoSe₂ demonstrating that it persists for a few-hundred femtoseconds. We conclude that the underlying mechanisms limiting trion valley coherence are fundamentally different from those applicable to exciton valley coherence.

Conformational Homogeneity in the Pr Isomer of Phytochrome Cph1

Numerous time-resolved studies of the P_r to P_fr photoisomerization in phytochrome Cph1 have revealed multiphasic excited-state decay kinetics. It remains unclear whether these kinetics arise from multiple ground-state conformational subpopulations or from a single ground-state conformation that undergoes an excited-state photoisomerization process-either branching on the excited state or relaxing through multiple sequential intermediates. Many studies have attempted to resolve this debate by fitting the measured dynamics to proposed kinetic models, arriving at different conclusions. Here we probe spectral signatures of ground-state heterogeneity of P_r. Two-dimensional electronic spectra display negligible inhomogeneous line broadening, and vibrational coherence spectra extracted from transient absorption measurements do not contain nodes and phase shifts at the fluorescence maximum. These spectroscopic results support the homogeneous model, in which the primary photochemical transformation of P_r to Lumi-R occurs adiabatically on the excited-state potential energy surface.

Vibronic coupling in organic semiconductors for photovoltaics

Ultrafast two-dimensional electronic spectroscopy reveals vibronically-assisted coherent charge transport and separation in organic materials and opens up new perspectives for artificial light-to-current conversion.

Coherent Control of the Exciton-Biexciton System in an InAs Self-Assembled Quantum Dot Ensemble

Coherent control of a strongly inhomogeneously broadened system, namely, InAs self-assembled quantum dots, is demonstrated. To circumvent the deleterious effects of the inhomogeneous broadening, which usually masks the results of coherent manipulation, we use prepulse two-dimensional coherent spectroscopy to provide a size-selective readout of the ground, exciton, and biexciton states. The dependence on the timing of the prepulse is due to the dynamics of the coherently generated populations. To further validate the results, we performed prepulse polarization dependent measurements and confirmed the behavior expected from selection rules. All measured spectra can be excellently reproduced by solving the optical Bloch equations for a 4-level system.

Revealing and Characterizing Dark Excitons through Coherent Multidimensional Spectroscopy

Dark excitons are of fundamental importance in a broad range of contexts but are difficult to study using conventional optical spectroscopy due to their weak interaction with light. We show how coherent multidimensional spectroscopy can reveal and characterize dark states. Using this approach, we identify parity-forbidden and spatially indirect excitons in InGaAs/GaAs quantum wells and determine details regarding lifetimes, homogeneous and inhomogeneous linewidths, broadening mechanisms, and coupling strengths. The observations of coherent coupling between these states and bright excitons hint at a role for a multistep process by which excitons in the barrier can relax into the quantum wells.

Coherent and Incoherent Coupling Dynamics between Neutral and Charged Excitons in Monolayer MoSe2

The optical properties of semiconducting transition metal dichalcogenides are dominated by both neutral excitons (electron-hole pairs) and charged excitons (trions) that are stable even at room temperature. While trions directly influence charge transport properties in optoelectronic devices, excitons may be relevant through exciton-trion coupling and conversion phenomena. In this work, we reveal the coherent and incoherent nature of exciton-trion coupling and the relevant time scales in monolayer MoSe2 using optical two-dimensional coherent spectroscopy. Coherent interaction between excitons and trions is definitively identified as quantum beating of cross peaks in the spectra that persists for a few hundred femtoseconds. For longer times up to 10 ps, surprisingly, the relative intensity of the cross peaks increases, which is attributed to incoherent energy transfer likely due to phonon-assisted up-conversion and down-conversion processes that are efficient even at cryogenic temperature.

Exciton Dynamics in Monolayer Transition Metal Dichalcogenides

Since the discovery of semiconducting monolayer transition metal dichalcogenides, a variety of experimental and theoretical studies have been carried out seeking to understand the intrinsic exciton population recombination and valley relaxation dynamics. Reports of the exciton decay time range from hundreds of femtoseconds to ten nanoseconds, while the valley depolarization time can exceed one nanosecond. At present, however, a consensus on the microscopic mechanisms governing exciton radiative and non-radiative recombination is lacking. The strong exciton oscillator strength resulting in up to ~ 20% absorption for a single monolayer points to ultrafast radiative recombination. However, the low quantum yield and large variance in the reported lifetimes suggest that non-radiative Auger-type processes obscure the intrinsic exciton radiative lifetime. In either case, the electron-hole exchange interaction plays an important role in the exciton spin and valley dynamics. In this article, we review the experiments and theory that have led to these conclusions and comment on future experiments that could complement our current understanding.

Intrinsic homogeneous linewidth and broadening mechanisms of excitons in monolayer transition metal dichalcogenides

The band-edge optical response of transition metal dichalcogenides, an emerging class of atomically thin semiconductors, is dominated by tightly bound excitons localized at the corners of the Brillouin zone (valley excitons). A fundamental yet unknown property of valley excitons in these materials is the intrinsic homogeneous linewidth, which reflects irreversible quantum dissipation arising from system (exciton) and bath (vacuum and other quasiparticles) interactions and determines the timescale during which excitons can be coherently manipulated. Here we use optical two-dimensional Fourier transform spectroscopy to measure the exciton homogeneous linewidth in monolayer tungsten diselenide (WSe₂). The homogeneous linewidth is found to be nearly two orders of magnitude narrower than the inhomogeneous width at low temperatures. We evaluate quantitatively the role of exciton–exciton and exciton–phonon interactions and population relaxation as linewidth broadening mechanisms. The key insights reported here—strong many-body effects and intrinsically rapid radiative recombination—are expected to be ubiquitous in atomically thin semiconductors.

The band-edge optical response of transition metal dichalcogenides is dominated by tightly bound valley excitons. Here, the authors use optical two-dimensional Fourier transform spectroscopy to determine the exciton homogeneous linewidth in monolayer tungsten diselenide.

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.

Analytical calculation of two-dimensional spectra

We demonstrate an analytical calculation of two-dimensional (2D) coherent spectra of electronic or vibrational resonances. Starting with the solution to the optical Bloch equations for a two-level system in the 2D time domain, we show that a fully analytical 2D Fourier transform can be performed if the projection-slice and Fourier-shift theorems of Fourier transforms are applied. Results can be fit to experimental 2D coherent spectra of resonances with arbitrary inhomogeneity.

Coherent coupling of excitons and trions in a photoexcited CdTe/CdMgTe quantum well

We present zero-, one-, and two-quantum two-dimensional coherent spectra of excitons and trions in a CdTe/(Cd,Mg)Te quantum well. The set of spectra provides a unique and comprehensive picture of the coherent nonlinear optical response. Distinct peaks in the spectra are manifestations of exciton-exciton and exciton-trion coherent coupling. Excellent agreement using density matrix calculations highlights the essential role of many-body effects on the coupling. Strong exciton-trion coherent interactions open up the possibility for novel conditional control schemes in coherent optoelectronics.

Coherent excitonic coupling in an asymmetric double InGaAs quantum well arises from many-body effects

We study an asymmetric double InGaAs quantum well using optical two-dimensional coherent spectroscopy. The collection of zero-quantum, one-quantum, and two-quantum two-dimensional spectra provides a unique and comprehensive picture of the double well coherent optical response. Coherent and incoherent contributions to the coupling between the two quantum well excitons are clearly separated. An excellent agreement with density matrix calculations reveals that coherent interwell coupling originates from many-body interactions.

Multidimensional coherent photocurrent spectroscopy of a semiconductor nanostructure

Multidimensional Coherent Optical Photocurrent Spectroscopy (MD-COPS) is implemented using unstabilized interferometers. Photocurrent from a semiconductor sample is generated using a sequence of four excitation pulses in a collinear geometry. Each pulse is frequency shifted by a unique radio frequency through acousto-optical modulation; the Four-Wave Mixing (FWM) signal is then selected in the frequency domain. The interference of an auxiliary continuous wave laser, which is sent through the same interferometers as the excitation pulses, is used to synthesize reference frequencies for lock-in detection of the photocurrent FWM signal. This scheme enables the partial compensation of mechanical fluctuations in the setup, achieving sufficient phase stability without the need for active stabilization. The method intrinsically provides both the real and imaginary parts of the FWM signal as a function of inter-pulse delays. This signal is subsequently Fourier transformed to create a multi-dimensional spectrum. Measurements made on the excitonic resonance in a double InGaAs quantum well embedded in a p-i-n diode demonstrate the technique.

Unraveling quantum pathways using optical 3D Fourier-transform spectroscopy

Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system’s nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system’s Hamiltonian.

Knowledge of the Hamiltonian of a quantum system is essential for predicting and controlling its behaviour. Li et al. use optical three-dimensional Fourier-transform spectroscopy to separate and study each pathway, gaining quantitative insight into the quantum pathways of an atomic vapour Hamiltonian.

Ultrafast field-resolved semiconductor spectroscopy utilizing quantum interference control of currents

We implement a versatile concept to time-resolve optical nonlinearities of semiconductors in amplitude and phase. A probe pulse transmitted through the optically pumped sample is superimposed with first subharmonic spectral components derived from the same laser source. This effective ω/2ω pulse pair induces a coherently controlled current in a time-integrating semiconductor detector. Current interferograms obtained by scanning the ω/2ω time delay then reveal the electric field of the 2ω part as well as its pump-induced modifications. As a paradigm we analyze the excitonic optical nonlinearity of a CdTe thin film at frequencies around 385 THz. We then move on to resolve the pump-induced amplitude- and phase-distortions of a probe pulse related to two-photon absorption and cross-phase modulation in ZnSe.