Optical two-dimensional fourier transform spectroscopy of semiconductor quantum wells

Higher-Order Multidimensional and Pump-Probe Spectroscopies

Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.

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

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

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

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

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

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

Deciphering hot- and multi-exciton dynamics in core-shell QDs by 2D electronic spectroscopies

2D electronic spectroscopy maps acquired in different configurations unveil intraband hot carrier cooling and interband multi-exciton recombination dynamics.

Although the harnessing of multiple and hot excitons is a prerequisite for many of the groundbreaking applications of semiconductor quantum dots (QDs), the characterization of their dynamics through conventional spectroscopic techniques is cumbersome. Here, we show how a careful analysis of 2DES maps acquired in different configurations (BOXCARS and pump–probe geometry) allows the tracking and visualization of intraband Auger relaxation mechanisms, driving the hot carrier cooling, and interband bi- and tri-exciton recombination dynamics. The results obtained on archetypal core–shell CdSe/ZnS QDs suggest that, given the global analysis of the resulting datasets, 2D electronic spectroscopy techniques can successfully and efficiently dispel the intertwined dynamics of fast and ultrafast recombination processes in nanomaterials. Hence, we propose this analysis scheme to be used in future research on novel quantum confined systems.

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

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

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.

Ultrabroadband 2D electronic spectroscopy with high-speed, shot-to-shot detection

Two-dimensional electronic spectroscopy (2DES) is an incisive tool for disentangling excited state energies and dynamics in the condensed phase by directly mapping out the correlation between excitation and emission frequencies as a function of time. Despite its enhanced frequency resolution, the spectral window of detection is limited to the laser bandwidth, which has often hindered the visualization of full electronic energy relaxation pathways spread over the entire visible region. Here, we describe a high-sensitivity, ultrabroadband 2DES apparatus. We report a new combination of a simple and robust setup for increased spectral bandwidth and shot-to-shot detection. We utilize 8-fs supercontinuum pulses generated by gas filamentation spanning the entire visible region (450 - 800 nm), which allows for a simultaneous interrogation of electronic transitions over a 200-nm bandwidth, and an all-reflective interferometric delay system with angled nanopositioner stages achieves interferometric precision in coherence time control without introducing wavelength-dependent dispersion to the ultrabroadband spectrum. To address deterioration of detection sensitivity due to the inherent instability of ultrabroadband sources, we introduce a 5-kHz shot-to-shot, dual chopping acquisition scheme by combining a high-speed line-scan camera and two optical choppers to remove scatter contributions from the signal. Comparison of 2D spectra acquired by shot-to-shot detection and averaged detection shows a 15-fold improvement in the signal-to-noise ratio. This is the first direct quantification of detection sensitivity on a filamentation-based ultrabroadband 2DES apparatus.

Multidimensional x-ray spectroscopy of valence and core excitations in cysteine

Several nonlinear spectroscopy experiments which employ broadband x-ray pulses to probe the coupling between localized core and delocalized valence excitation are simulated for the amino acid cysteine at the K-edges of oxygen and nitrogen and the K- and L-edges of sulfur. We focus on two-dimensional (2D) and 3D signals generated by two- and three-pulse stimulated x-ray Raman spectroscopy (SXRS) with frequency-dispersed probe. We show how the four-pulse x-ray signals [Formula: see text] and [Formula: see text] can give new 3D insight into the SXRS signals. The coupling between valence- and core-excited states can be visualized in three-dimensional plots, revealing the origin of the polarizability that controls the simpler pump-probe SXRS signals.

Enhanced-Resolution Single-Shot 2DFT Spectroscopy by Spatial Spectral Interferometry

We demonstrate use of spatial interference for the complete electric field reconstruction of two-dimensional (2D) coherent spectroscopic signals generated through four-wave mixing (4WM) in a single laser shot. Until now, the amplitude and phase characterization of 4WM signals has relied primarily on Fourier transform spectral interferometry (FTSI), which limits the measurement's sensitivity and resolution. We show that spatial spectral interferometry (SSI) is a generalized approach to 4WM signal detection that eliminates these inherent limitations of FTSI without introducing additional experimental complexity. SSI is used to measure the 2D photon echo spectra of two systems with dramatically different line widths, the coupled D line transitions in rubidium vapor and the energy-transfer dynamics in the light-harvesting protein LH2.

Coherent multidimensional optical spectra measured using incoherent light

Four-wave mixing measurements can reveal spectral and dynamics information that is hidden in linear spectra by the interactions among light-absorbing molecules and with their environment. Coherent multidimensional optical spectroscopy is an important variant of four-wave mixing because it resolves a map of interactions and correlations between absorption bands. Previous coherent multidimensional optical spectroscopy measurements have used femtosecond pulses with great success, and it may seem that femtosecond pulses are necessary for such measurements. Here we present coherent two-dimensional electronic spectra measured using incoherent light. The spectra of model molecular systems using broadband spectrally incoherent light are similar but not identical to those expected from measurements using femtosecond pulses. Specifically, the spectra show particular sensitivity to long-lived intermediates such as photoisomers. The results will motivate the design of similar experiments in spectral ranges where femtosecond pulses are difficult to produce.

Designs for molecular circuits that use electronic coherence

The mounting evidence of recent years regarding long-lived coherent dynamics of electronic excitations in several light-harvesting antenna proteins suggests the possibility of realizing and exploiting light-initiated quantum dynamics in synthetic molecular devices based on electronic energy transfer. Inspired by the field of molecular logic, we focus this discussion on the prospect of using quantum coherence to control the direction of energy flow in a molecular circuit. As a prototype system we consider a circuit consisting of three chromophores that deliver energy to two trap chromophores. Our aim is to control to which trap the energy is more likely to be delivered. This is achieved by switching one of the circuit chromophores ON and OFF from the system, such that the direction of energy flow substantially changes from the ON and OFF states of the circuit. We find that quantum coherence can allow a significant ability to direct energy transfer in the circuit. However, when realistic levels of noise are added, quantum coherence only slightly improves the ability to direct electronic energy in comparison to a classical hopping mechanism.

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.

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 superposition states in CdSe nanocrystals measured using broadband two-dimensional electronic spectroscopy

Coherent superpositions among eigenstates are of interest in fields as diverse as photosynthesis and quantum computation. In this report, we used two-dimensional electronic spectroscopy (2D ES) to measure the decoherence time of a superposition of the two lowest-energy excitons in colloidal CdSe nanocrystals (cubic phase) in solution at room temperature. In the electron-hole representation, the quantum coherence is, remarkably, a twelve-particle correlation. By comparing the measured 2D ES to simulations, we also explored the effects of inhomogeneous broadening and examined the spectroscopic signatures of biexcitons.

Resonance lineshapes in two-dimensional Fourier transform spectroscopy

We derive an analytical form for resonance lineshapes in two-dimensional (2D) Fourier transform spectroscopy. Our starting point is the solution of the optical Bloch equations for a two-level system in the 2D time domain. Application of the projection-slice theorem of 2D Fourier transforms reveals the form of diagonal and cross-diagonal slices in the 2D frequency data for arbitrary inhomogeneity. The results are applied in quantitative measurements of homogeneous and inhomogeneous broadening of multiple resonances in experimental data.

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.

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.

Instantaneous mapping of coherently coupled electronic transitions and energy transfers in a photosynthetic complex using angle-resolved coherent optical wave-mixing

Understanding the role of coherent electronic motion is expected to resolve general questions of importance in macromolecular energy transfer. We demonstrate a novel nonlinear optical method, angle-resolved coherent wave mixing, that separates out coherently coupled electronic transitions and energy transfers in an instantaneous two-dimensional mapping. Angular resolution of the signal is achieved by using millimeter laser beam waists at the sample and by signal relay to the far field; for this we use a high energy, ultrabroadband hollow fiber laser source. We reveal quantum electronic beating with a time-ordered selection of transition energies in a photosynthetic complex.