Optical two-dimensional Fourier transform spectroscopy of semiconductors

Ultrafast Coherent Exciton Couplings and Many-Body Interactions in Monolayer WS2

Transition metal dichalcogenides (TMDs) are quantum confined systems with interesting optoelectronic properties, governed by Coulomb interactions in the monolayer (1L) limit, where strongly bound excitons provide a sensitive probe for many-body interactions. Here, we use two-dimensional electronic spectroscopy (2DES) to investigate many-body interactions and their dynamics in 1L-WS2 at room temperature and with sub-10 fs time resolution. Our data reveal coherent interactions between the strongly detuned A and B exciton states in 1L-WS2. Pronounced ultrafast oscillations of the transient optical response of the B exciton are the signature of a coherent 50 meV coupling and coherent population oscillations between the two exciton states. Supported by microscopic semiconductor Bloch equation simulations, these coherent dynamics are rationalized in terms of Dexter-like interactions. Our work sheds light on the role of coherent exciton couplings and many-body interactions in the ultrafast temporal evolution of spin and valley states in TMDs.

Phonon-driven intra-exciton Rabi oscillations in CsPbBr3 halide perovskites

Coupling electromagnetic radiation with matter, e.g., by resonant light fields in external optical cavities, is highly promising for tailoring the optoelectronic properties of functional materials on the nanoscale. Here, we demonstrate that even internal fields induced by coherent lattice motions can be used to control the transient excitonic optical response in CsPbBr₃ halide perovskite crystals. Upon resonant photoexcitation, two-dimensional electronic spectroscopy reveals an excitonic peak structure oscillating persistently with a 100-fs period for up to ~2 ps which does not match the frequency of any phonon modes of the crystals. Only at later times, beyond 2 ps, two low-frequency phonons of the lead-bromide lattice dominate the dynamics. We rationalize these findings by an unusual exciton-phonon coupling inducing off-resonant 100-fs Rabi oscillations between 1s and 2p excitons driven by the low-frequency phonons. As such, prevailing models for the electron-phonon coupling in halide perovskites are insufficient to explain these results. We propose the coupling of characteristic low-frequency phonon fields to intra-excitonic transitions in halide perovskites as the key to control the anharmonic response of these materials in order to establish new routes for enhancing their optoelectronic properties.

Coherent Nonlinear Spectroscopy with Multiple Mode-Locked Lasers

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

Development of interface-/surface-specific two-dimensional electronic spectroscopy

Structures, kinetics, and chemical reactivities at interfaces and surfaces are key to understanding many of the fundamental scientific problems related to chemical, material, biological, and physical systems. These steady-state and dynamical properties at interfaces and surfaces require even-order techniques with time-resolution and spectral-resolution. Here, we develop fourth-order interface-/surface-specific two-dimensional electronic spectroscopy, including both two-dimensional electronic sum frequency generation (2D-ESFG) spectroscopy and two-dimensional electronic second harmonic generation (2D-ESHG) spectroscopy, for structural and dynamics studies of interfaces and surfaces. The 2D-ESFG and 2D-ESHG techniques were based on a unique laser source of broadband short-wave IR from 1200 nm to 2200 nm from a home-built optical parametric amplifier. With the broadband short-wave IR source, surface spectra cover most of the visible light region from 480 nm to 760 nm. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate a phase-locked pulse pair for coherent excitation in the 2D-ESFG and 2D-ESHG. As an example, we demonstrated surface dark states and their interactions of the surface states at p-type GaAs (001) surfaces with the 2D-ESFG and 2D-ESHG techniques. These newly developed time-resolved and interface-/surface-specific 2D spectroscopies would bring new information for structure and dynamics at interfaces and surfaces in the fields of the environment, materials, catalysis, and biology.

Size-Dependent Hot Carrier Dynamics in Perovskite Nanocrystals Revealed by Two-Dimensional Electronic Spectroscopy

The lifetimes of hot carriers have been predicted to be prolonged in small nanocrystals with an inter-level spacing larger than phonon energy. Nevertheless, whether such a phonon bottleneck is present in perovskite semiconductor nanocrystals remains highly controversial. Here we report compelling evidence of a phonon bottleneck in CsPbI₃ nanocrystals with marked size-dependent relaxation of hot carriers by using broadband two-dimensional electronic spectroscopy (2DES). By combining high resolutions in both the time (<10 fs) and excitation energy domains, 2DES allows the clear disentanglement of the thermalization and cooling processes. The lifetime is over doubled for hot carriers when the average edge length of the nanocrystals decreases from 8.2 nm down to 4.6 nm. The confirmation of the phonon bottleneck effect suggests the feasibility of controlling hot carrier dynamics in perovskite semiconductors with nanocrystal size for potential applications of hot carrier devices.

Evidence for the Dominance of Carrier-Induced Band Gap Renormalization over Biexciton Formation in Cryogenic Ultrafast Experiments on MoS2 Monolayers

Transition-metal dichalcogenides (TMDs) such as MoS₂ display promising electrical and optical properties in the monolayer limit. Due to strong quantum confinement, TMDs provide an ideal environment for exploring excitonic physics using ultrafast spectroscopy. However, the interplay between collective excitation effects on single excitons such as band gap renormalization/exciton binding energy (BGR/EBE) change and multiexciton effects such biexciton formation remains poorly understood. Using two-dimensional electronic spectroscopy, we observe the dominance of single-exciton BGR/EBE signals over optically induced biexciton formation. We make this determination based on a lack of strong PIA features at T = 0 fs in the cryogenic spectra. By means of nodal line slope analysis, we determine that spectral diffusion occurs faster than BGR/EBE change, indicative of distinct processes. These results indicate that at higher sub-Mott limit fluences, collective effects on single excitons dominate biexciton formation.

Interface-Specific Two-Dimensional Electronic Sum Frequency Generation Spectroscopy

High even-order surface/interface specific spectroscopy has the potential to provide more structural and dynamical information about surfaces and interfaces. In this work, we developed a novel fourth-order interface-specific two-dimensional electronic sum frequency generation (2D-ESFG) for structures and dynamics at surfaces and interfaces. A translating wedge-based identical pulses encoding system (TWINs) was introduced to generate phase-locked pulse pairs for coherent pump beams in 2D-ESFG. As a proof-of-principle experiment, fourth-order 2D-ESFG spectroscopy was used to demonstrate couplings of surface states for both n-type and p-type GaAs (100). We found surface dark state within the bandgap of the GaAs in 2D-ESFG spectra, which could not be observed in one-dimensional ESFG spectra. To our best knowledge, this is a first demonstration of interface-specific two-dimensional electronic spectroscopy. The development of the 2D-ESFG spectroscopy will provide new structural probes of spectral diffusion, conformational dynamics, energy transfer, and charge transfer for surfaces and interfaces.

Implementation of continuous fast scanning detection in femtosecond Fourier-transform two-dimensional vibrational-electronic spectroscopy to decrease data acquisition time

Femtosecond Fourier transform two-dimensional vibrational-electronic (2D VE) spectroscopy is a recently developed third-order nonlinear spectroscopic technique to measure coupled electronic and vibrational motions in the condensed phase. The viability of femtosecond multidimensional spectroscopy as an analytical tool requires improvements in data collection and processing to enhance the signal-to-noise ratio and increase the amount of data collected in these experiments. Here a continuous fast scanning technique for the efficient collection of 2D VE spectroscopy is described. The resulting 2D VE spectroscopic method gains sensitivity by reducing the effect of laser drift, as well as decreasing the data collection time by a factor of 10 for acquiring spectra with a high signal-to-noise ratio within 3 dB of the more time intensive step scanning methods. This work opens the door to more comprehensive studies where 2D VE spectra can be collected as a function of external parameters such as temperature, pH, and polarization of the input electric fields.

Biexciton Resonances Reveal Exciton Localization in Stacked Perovskite Quantum Wells

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

Two-Dimensional Visible Spectroscopy For Studying Colloidal Semiconductor Nanocrystals

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

Strong Quantum Coherence between Fermi Liquid Mahan Excitons

In modulation doped quantum wells, the excitons are formed as a result of the interactions of the charged holes with the electrons at the Fermi edge in the conduction band, leading to the so-called "Mahan excitons." The binding energy of Mahan excitons is expected to be greatly reduced and any quantum coherence destroyed as a result of the screening and electron-electron interactions. Surprisingly, we observe strong quantum coherence between the heavy hole and light hole excitons. Such correlations are revealed by the dominating cross-diagonal peaks in both one-quantum and two-quantum two-dimensional Fourier transform spectra. Theoretical simulations based on the optical Bloch equations where many-body effects are included phenomenologically reproduce well the experimental spectra. Time-dependent density functional theory calculations provide insight into the underlying physics and attribute the observed strong quantum coherence to a significantly reduced screening length and collective excitations of the many-electron system.

Two-dimensional vibrational-electronic spectroscopy

Two-dimensional vibrational-electronic (2D VE) spectroscopy is a femtosecond Fourier transform (FT) third-order nonlinear technique that creates a link between existing 2D FT spectroscopies in the vibrational and electronic regions of the spectrum. 2D VE spectroscopy enables a direct measurement of infrared (IR) and electronic dipole moment cross terms by utilizing mid-IR pump and optical probe fields that are resonant with vibrational and electronic transitions, respectively, in a sample of interest. We detail this newly developed 2D VE spectroscopy experiment and outline the information contained in a 2D VE spectrum. We then use this technique and its single-pump counterpart (1D VE) to probe the vibrational-electronic couplings between high frequency cyanide stretching vibrations (νCN) and either a ligand-to-metal charge transfer transition ([Fe(III)(CN)6](3-) dissolved in formamide) or a metal-to-metal charge transfer (MMCT) transition ([(CN)5Fe(II)CNRu(III)(NH3)5](-) dissolved in formamide). The 2D VE spectra of both molecules reveal peaks resulting from coupled high- and low-frequency vibrational modes to the charge transfer transition. The time-evolving amplitudes and positions of the peaks in the 2D VE spectra report on coherent and incoherent vibrational energy transfer dynamics among the coupled vibrational modes and the charge transfer transition. The selectivity of 2D VE spectroscopy to vibronic processes is evidenced from the selective coupling of specific νCN modes to the MMCT transition in the mixed valence complex. The lineshapes in 2D VE spectra report on the correlation of the frequency fluctuations between the coupled vibrational and electronic frequencies in the mixed valence complex which has a time scale of 1 ps. The details and results of this study confirm the versatility of 2D VE spectroscopy and its applicability to probe how vibrations modulate charge and energy transfer in a wide range of complex molecular, material, and biological systems.

Exploring two-dimensional electron gases with two-dimensional Fourier transform spectroscopy

The dephasing of the Fermi edge singularity excitations in two modulation doped single quantum wells of 12 nm and 18 nm thickness and in-well carrier concentration of ∼4 × 10(11) cm(-2) was carefully measured using spectrally resolved four-wave mixing (FWM) and two-dimensional Fourier transform (2DFT) spectroscopy. Although the absorption at the Fermi edge is broad at this doping level, the spectrally resolved FWM shows narrow resonances. Two peaks are observed separated by the heavy hole/light hole energy splitting. Temperature dependent "rephasing" (S1) 2DFT spectra show a rapid linear increase of the homogeneous linewidth with temperature. The dephasing rate increases faster with temperature in the narrower 12 nm quantum well, likely due to an increased carrier-phonon scattering rate. The S1 2DFT spectra were measured using co-linear, cross-linear, and co-circular polarizations. Distinct 2DFT lineshapes were observed for co-linear and cross-linear polarizations, suggesting the existence of polarization dependent contributions. The "two-quantum coherence" (S3) 2DFT spectra for the 12 nm quantum well show a single peak for both co-linear and co-circular polarizations.

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.

Continuously tunable optical multidimensional Fourier-transform spectrometer

A multidimensional optical nonlinear spectrometer (MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. The MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delays between them while maintaining phase stability. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy. The present work reports on overcoming some important limitations on the original design of the MONSTR apparatus. One important advantage of the MONSTR is the fact that it is a closed platform, which provides the high stability. Once the optical alignment is performed, it is desirable to maintain the alignment over long periods of time. The previous design of the MONSTR was limited to a narrow spectral range defined by the optical coating of the beam splitters. In order to achieve tunability over a broad spectral range the internal optics needed to be changed. By using broadband coated and wedged beam splitters and compensator plates, combined with modifications of the beam paths, continuous tunability can be achieved from 520 nm to 1100 nm without changing any optics or performing alignment of the internal components of the MONSTR. Furthermore, in order to achieve continuous tunability in the spectral region between 520 nm and 720 nm, crucially important for studies on numerous biological molecules, a single longitudinal mode laser at 488.5 nm was identified and used as a metrology laser. The shorter wavelength of the metrology laser as compared to the usual HeNe laser has also increased the phase stability of the system. Finally, in order to perform experiments in the reflection geometry, a simple method to achieve active phase stabilization between the signal and the reference beams has been developed.

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

The Coulomb correlations between photoexcited charged particles in materials such as photosynthetic complexes, conjugated polymer systems, J-aggregates, and bulk or nanostructured semiconductors produce a hierarchy of collective electronic excitations, for example, excitons, and biexcitons, which may be harnessed for applications in quantum optics, light-harvesting, or quantum information technologies. These excitations represent correlations among successively greater numbers of electrons and holes, and their associated multiple-quantum coherences could reveal detailed information about complex many-body interactions and dynamics. However, unlike single-quantum coherences involving excitons, multiple-quantum coherences do not radiate; consequently, they have largely eluded direct observation and characterization. In this Account, we present a novel optical technique, two-quantum, two-dimensional Fourier transform optical spectroscopy (2Q 2D FTOPT), which allows direct observation of the dynamics of multiple exciton states that reflect the correlations of their constituent electrons and holes. The approach is based on closely analogous methods in NMR, in which multiple phase-coherent fields are used to drive successive transitions such that multiple-quantum coherences can be accessed and probed. In 2Q 2D FTOPT, a spatiotemporal femtosecond pulse-shaping technique has been used to overcome the challenge of control over multiple, noncollinear, phase-coherent optical fields in experimental geometries used to isolate selected signal contributions through wavevector matching. We present results from a prototype GaAs quantum well system, which reveal distinct coherences of biexcitons that are formed from two identical excitons or from two excitons that have holes in different spin sublevels ("heavy-hole" and "light-hole" excitons). The biexciton binding energies and dephasing dynamics are determined, and changes in the dephasing rates as a function of the excitation density are observed, revealing still higher order correlations due to exciton-biexciton interactions. Two-quantum coherences due to four-particle correlations that do not involve bound biexciton states but that influence the exciton properties are also observed and characterized. The 2Q 2D FTOPT technique allows many-body interactions that cannot be treated with a mean-field approximation to be studied in detail; the pulse-shaping approach simplifies greatly what would have otherwise been daunting measurements. This spectroscopic tool might soon offer insight into specific applications, for example, in detailing the interactions that affect how electronic energy moves within the strata of organic photovoltaic cells.

Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells

Coherent light-matter interactions of direct-gap semiconductor nanostructures provide a great test system for fundamental research into quantum electronics and many-body physics. The understanding gained from studying these interactions can facilitate the design of optoelectronic devices. Recently, we have used optical two-dimensional Fourier-transform spectroscopy to explore coherent light-matter interactions in semiconductor quantum wells. Using three laser pulses to generate a four-wave-mixing signal, we acquire spectra by tracking the phase of the signal with respect to two time axes and then Fourier transforming them. In this Account, we show several two-dimensional projections and demonstrate techniques to isolate different contributions to the coherent response of semiconductors. The low-temperature spectrum of semiconductor quantum wells is dominated by excitons, which are electron-hole pairs bound through Coulombic interactions. Excitons are sensitive to their electronic and structural environment, which influences their optical resonance energies and line widths. In near perfect quantum wells, a small fluctuation of the quantum well thickness leads to spatial localization of the center-of-mass wave function of the excitons and inhomogeneous broadening of the optical resonance. The inhomogeneous broadening often masks the homogeneous line widths associated with the scattering of the excitons. In addition to forming excitons, Coulombic correlations also form excitonic molecules, called biexcitons. Therefore, the coherent response of the quantum wells encompasses the intra-action and interaction of both excitons and biexcitons in the presence of inhomogeneous broadening. Transient four-wave-mixing studies combined with microscopic theories have determined that many-body interactions dominate the strong coherent response from quantum wells. Although the numerous competing interactions cannot be easily separated in either the spectral or temporal domains, they can be separated using two-dimensional Fourier transform spectroscopy. The most common two-dimensional Fourier spectra are S(I)(omega(tau),T,omega(t)) in which the second time period is held fixed. The result is a spectrum that unfolds congested one-dimensional spectra, separates excitonic pathways, and shows which excitons are coherently coupled. This method also separates the biexciton contributions and isolates the homogeneous and inhomogeneous line widths. For semiconductor excitons, the line shape in the real part of the spectrum is sensitive to the many-body interactions, which we can suppress by exploiting polarization selection rules. In an alternative two-dimensional projection, S(I)(tau,omega(Tau),omega(t)), the nonradiative Raman coherent interactions are isolated. Finally, we show S(III)(tau,omega(Tau),omega(t)) spectra that isolate the two-quantum coherences associated with the biexciton. These spectra reveal previously unobserved many-body correlations.

A versatile ultrastable platform for optical multidimensional Fourier-transform spectroscopy

The JILA multidimensional optical nonlinear spectrometer (JILA-MONSTR) is a robust, ultrastable platform consisting of nested and folded Michelson interferometers that can be actively phase stabilized. This platform generates a square of identical laser pulses that can be adjusted to have arbitrary time delay between them while maintaining phase stability. The JILA-MONSTR provides output pulses for nonlinear excitation of materials and phase-stabilized reference pulses for heterodyne detection of the induced signal. This arrangement is ideal for performing coherent optical experiments, such as multidimensional Fourier-transform spectroscopy, which records the phase of the nonlinear signal as a function of the time delay between several of the excitation pulses. The resulting multidimensional spectrum is obtained from a Fourier transform. This spectrum can resolve, separate, and isolate coherent contributions to the light-matter interactions associated with electronic excitation at optical frequencies. To show the versatility of the JILA-MONSTR, several demonstrations of two-dimensional Fourier-transform spectroscopy are presented, including an example of a phase-cycling scheme that reduces noise. Also shown is a spectrum that accesses two-quantum coherences, where all excitation pulses require phase locking for detection of the signal.

Isolating excitonic Raman coherence in semiconductors using two-dimensional correlation spectroscopy

We present the experimental and simulation results of two-dimensional optical coherent correlation spectroscopy signals along the phase-matching direction k(I) = -k(1) + k(2) + k(3) projected on the two-dimensional (2D) (Omega(3),Omega(2)) plane corresponding to the second and third delay periods. Overlapping Raman coherences in the conventional (Omega(3),Omega(1)) 2D projection may now be clearly resolved. The linewidths of the heavy-hole (HH) and light-hole (LH) excitonic Raman coherence peaks are obtained. Further insights on the higher-order (beyond time-dependent Hartree-Fock) correlation effects among mixed (HH and LH) two excitons can be gained by using a cocircular pulse polarization configuration.

Polarization-dependent optical 2D Fourier transform spectroscopy of semiconductors

Optical 2D Fourier transform spectroscopy (2DFTS) provides insight into the many-body interactions in direct gap semiconductors by separating the contributions to the coherent nonlinear optical response. We demonstrate these features of optical 2DFTS by studying the heavy-hole and light-hole excitonic resonances in a gallium arsenide quantum well at low temperature. Varying the polarization of the incident beams exploits selection rules to achieve further separation. Calculations using a full many-body theory agree well with experimental results and unambiguously demonstrate the dominance of many-body physics.

Coherently Controlled Ultrafast Four-Wave Mixing Spectroscopy

A novel approach to coherent nonlinear optical spectroscopy based on two-dimensional femtosecond pulse shaping is introduced. Multiple phase-stable output beams are created and overlapped at the sample in a phase-matched boxcars geometry via two-dimensional femtosecond pulse shaping. The pulse timing, shape, phase, and spectral content within all beams may be specified, yielding an unprecedented level of control over the interacting fields in nonlinear spectroscopic experiments. Heterodyne detection and phase cycling of the nonlinear signal are easily implemented due to the excellent phase stability among all output beams. This approach combines the waveform generation capabilities of magnetic resonance spectroscopy with the wavevector specification and phase matching of nonlinear optical spectroscopy, yielding the control capabilities and signal selectivity of both. Results on four prototype systems are used to illustrate some of the novel possibilities of this method.

Analysis of cross peaks in two-dimensional electronic photon-echo spectroscopy for simple models with vibrations and dissipation

The recently developed efficient method for the calculation of four-wave mixing signals [M. F. Gelin et al., J. Chem. Phys. 123, 164112 (2005)] is employed for the calculation of two-dimensional electronic photon-echo spectra. The effect of the explicit treatment of vibrations coupled to the electronic transitions is systematically analyzed. The impact of pulse durations, optical dephasing, and temperature on the spectra is investigated. The study aims at an understanding of the mechanisms which may give rise to cross peaks in the two-dimensional electronic spectra and at clarifying the conditions of their detection.

Many-body interactions in semiconductors probed by optical two-dimensional fourier transform spectroscopy

We study many-body interactions between excitons in semiconductors by applying the powerful technique of optical two-dimensional Fourier transform spectroscopy. A two-dimensional spectrum correlates the phase (frequency) evolution of the nonlinear polarization field during the initial evolution and the final detection period. A single two-dimensional spectrum can identify couplings between resonances, separate quantum mechanical pathways, and distinguish among microscopic many-body interactions.