Persistent Inter-Excitonic Quantum Coherence in CdSe Quantum Dots

Constructing Dynamical Symmetries for Quantum Computing: Applications to Coherent Dynamics in Coupled Quantum Dots

Dynamical symmetries, time-dependent operators that almost commute with the Hamiltonian, extend the role of ordinary symmetries. Motivated by progress in quantum technologies, we illustrate a practical algebraic approach to computing such time-dependent operators. Explicitly we expand them as a linear combination of time-independent operators with time-dependent coefficients. There are possible applications to the dynamics of systems of coupled coherent two-state systems, such as qubits, pumped by optical excitation and other addressing inputs. Thereby, the interaction of the system with the excitation is bilinear in the coherence between the two states and in the strength of the time-dependent excitation. The total Hamiltonian is a sum of such bilinear terms and of terms linear in the populations. The terms in the Hamiltonian form a basis for Lie algebra, which can be represented as coupled individual two-state systems, each using the population and the coherence between two states. Using the factorization approach of Wei and Norman, we construct a unitary quantum mechanical evolution operator that is a factored contribution of individual two-state systems. By that one can accurately propagate both the wave function and the density matrix with special relevance to quantum computing based on qubit architecture. Explicit examples are derived for the electronic dynamics in coupled semi-conducting nanoparticles that can be used as hardware for quantum technologies.

Quantum-State Renormalization in Semiconductor Nanoparticles

A single photoexcited electron-hole pair within a polar semiconductor nanocrystal (SNC) alters the charge screening and shielding within it. Perturbations of the crystal lattice and of the valence and conduction bands result, and the quantum-confinement states in a SNC shift uniquely with a dependence on the states occupied by the carriers. This shifting is termed quantum-state renormalization (QSR). This Perspective highlights QSR in semiconductor quantum wires and dots identified in time-resolved transient absorption and two-dimensional electronic spectroscopy experiments. Beyond the interest in understanding the principles of QSR and energy-coupling mechanisms, we pose the contributions of QSR in time-resolved spectroscopy data must be accounted for to accurately identify the time scales for intraband relaxation of the carriers within SNCs.

Unraveling the excitonics of light emission from metal-halide perovskite quantum dots

Metal halide semicondictor perovskites have been under intense investigation for their promise in light absorptive applications like photovoltaics. They have more recently experienced interest for their promise in light emissive applications. A key aspect of perovskites is their glassy, ionic lattice that exhibits dynamical disorder. One possible result of this dynamical disorder is their strong coupling between electronic and lattice degrees of freedom which may confer remarkable properties for light emission such as defect tolerance. How does the system, comprised of excitons, couple to the bath, comprised of lattice modes? How does this system-bath interaction give rise to novel light emissive properties and how do these properties give insight into the nature of these materials? We review recent work from this group in which time-resolved photoluminescence spectroscopy is used to reveal such insights. Based upon a fast time resolution of 3 ps, energy resolution, and temperature dependence, a wide variety of insights are gleaned. These insights include: lattice contributions to the emission linewidths, multiexciton formation, hot carrier cooling, excitonic fine structure, single dot superradiance, and a breakdown of the Condon approximation, all due to complex structural dynamics in these materials.

Exciton-photocarrier interference in mixed lead-halide-perovskite nanocrystals

The use of semiconductor nanocrystals in scalable quantum technologies requires characterization of the exciton coherence dynamics in an ensemble of electronically isolated crystals in which system-bath interactions are nevertheless strong. In this communication, we identify signatures of Fano-like interference between excitons and photocarriers in the coherent two-dimensional photoluminescence excitation spectral lineshapes of mixed lead-halide perovskite nanocrystals in dilute solution. Specifically, by tuning the femtosecond-pulse spectrum, we show such interference in an intermediate coupling regime, which is evident in the coherent lineshape when simultaneously exciting the exciton and the free-carrier band at higher energy. We conclude that this interference is an intrinsic effect that will be consequential in the quantum dynamics of the system and will thus dictate decoherence dynamics, with consequences in their application in quantum technologies.

Two-Dimensional Electronic Spectroscopy Reveals Dynamics within the Bright Fine Structure of CdSe Quantum Dots

Semiconductor quantum dots are characterized by a discrete excitonic structure featuring coarse as well as fine structure. The lowest fine structure states have splittings into bright-dark states which are now well confirmed by single dot spectroscopy. In contrast, the splitting of the lowest coarse exciton into bright-bright fine structure states has not been observed nor the dynamics between these states. Here, we use the unique combination of time and energy resolution of two-dimensional electronic spectroscopy to directly observe the fine structure splittings into a bright-bright doublet. These splittings are strongly size dependent, with population relaxation on the <100 fs time scale.

Nucleation-mediated growth of chiral 3D organic-inorganic perovskite single crystals

Although their zero- to two-dimensional counterparts are well known, three-dimensional chiral hybrid organic-inorganic perovskite single crystals have remained difficult because they contain no chiral components and their crystal phases belong to centrosymmetric achiral point groups. Here we report a general approach to grow single-crystalline 3D lead halide perovskites with chiroptical activity. Taking MAPbBr3 (MA, methylammonium) perovskite as a representative example, whereas achiral MAPbBr3 crystallized from precursors in solution by inverse temperature crystallization method, the addition of micro- or nanoparticles as nucleating agents promoted the formation of chiral crystals under a near equilibrium state. Experimental characterization supported by calculations showed that the chirality of the 3D APbX3 (where A is an ammonium ion and X is Cl, Br or mixed Cl-Br or Br-I) perovskites arises from chiral patterns of the A-site cations and their interaction with the [PbX6]4- octahedra in the perovskite structure. The chiral structure obeys the lowest-energy principle and thereby thermodynamically stable. The chiral 3D hybrid organic-inorganic perovskites served in a circularly polarized light photodetector prototype successfully.

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.

A quantum information processing machine for computing by observables

A quantum machine that accepts an input and processes it in parallel is described. The logic variables of the machine are not wavefunctions (qubits) but observables (i.e., operators) and its operation is described in the Heisenberg picture. The active core is a solid-state assembly of small nanosized colloidal quantum dots (QDs) or dimers of dots. The size dispersion of the QDs that causes fluctuations in their discrete electronic energies is a limiting factor. The input to the machine is provided by a train of very brief laser pulses, at least four in number. The coherent band width of each ultrashort pulse needs to span at least several and preferably all the single electron excited states of the dots. The spectrum of the QD assembly is measured as a function of the time delays between the input laser pulses. The dependence of the spectrum on the time delays can be Fourier transformed to a frequency spectrum. This spectrum of a finite range in time is made up of discrete pixels. These are the visible, raw, basic logic variables. The spectrum is analyzed to determine a possibly smaller number of principal components. A Lie-algebraic point of view is used to explore the use of the machine to emulate the dynamics of other quantum systems. An explicit example demonstrates the considerable quantum advantage of our scheme.

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.

Ultrafast Coherent Delocalization Revealed in Multilayer QDs under a Chiral Potential

In recent years, it was found that current passing through chiral molecules exhibits spin preference, an effect known as Chiral Induced Spin Selectivity (CISS). The effect also enables the reduction of scattering and therefore enhances delocalization. As a result, the delocalization of an exciton generated in the dots is not symmetric and relates to the electronic and hole excited spins. In this work utilizing fast spectroscopy on hybrid multilayered QDs with a chiral polypeptide linker system, we probed the interdot chiral coupling on a short time scale. Surprisingly, we found strong coherent coupling and delocalization despite having long 4-nm chiral linkers. We ascribe the results to asymmetric delocalization that is controlled by the electron spin. The effect is not measured when using shorter nonchiral linkers. As the system mimics light-harvesting antennas, the results may shed light on a mechanism of fast and efficient energy transfer in these systems.

Coherent vibrational dynamics of Au144(SR)60 nanoclusters

The coherent vibrational dynamics of gold nanoclusters (NCs) provides important information on the coupling between vibrations and electrons as well as their mechanical properties, which is critical for understanding the evolution from a metallic state to a molecular state with diminishing size. Coherent vibrations have been widely explored in small-sized atomically precise gold NCs, while it remains a challenge to observe them in large-sized gold NCs. In this work, we report the coherent vibrational dynamics of atomically precise Au144(SR)60 NCs via temperature-dependent femtosecond transient absorption (TA) spectroscopy. The population dynamics of Au144(SR)60 consists of three relaxation processes: internal conversion, core-shell charge transfer and relaxation to the ground state. After removing the population dynamics from the TA kinetics, fast Fourier transform analysis on the residual oscillation reveals distinct vibrational modes at 1.5 THz (50 cm-1) and 2 THz (67 cm-1), which arise from the wavepacket motions along the ground-state and excited-state potential energy surfaces (PES), respectively. These results are helpful for understanding the physical properties of gold nanostructures with a threshold size that lies in between those of molecular-like NCs and metallic-state nanoparticles.

Coherent Two-Dimensional and Broadband Electronic Spectroscopies

Over the past few decades, coherent broadband spectroscopy has been widely used to improve our understanding of ultrafast processes (e.g., photoinduced electron transfer, proton transfer, and proton-coupled electron transfer reactions) at femtosecond resolution. The advances in femtosecond laser technology along with the development of nonlinear multidimensional spectroscopy enabled further insights into ultrafast energy transfer and carrier relaxation processes in complex biological and material systems. New discoveries and interpretations have led to improved design principles for optimizing the photophysical properties of various artificial systems. In this review, we first provide a detailed theoretical framework of both coherent broadband and two-dimensional electronic spectroscopy (2DES). We then discuss a selection of experimental approaches and considerations of 2DES along with best practices for data processing and analysis. Finally, we review several examples where coherent broadband and 2DES were employed to reveal mechanisms of photoinitiated ultrafast processes in molecular, biological, and material systems. We end the review with a brief perspective on the future of the experimental techniques themselves and their potential to answer an even greater range of scientific questions.

OPA-driven hollow-core fiber as a tunable, broadband source for coherent multidimensional spectroscopy

Despite the impressive abilities of coherent multi-dimensional spectroscopy (CMDS), its' implementation is limited due to the complexity of continuum generation and required phase stability between the pump pulse pair. In light of this, we have implemented a system producing sub-10 fs pulses with tunable central wavelength. Using a commercial OPA to drive a hollow-core fiber, the system is extremely simple. Output pulse energies lie in the 40-80 μJ range, more than sufficient for transmission through the pulse shaping optics and beam splitters necessary for CMDS. Power fluctuations are minimal, mode quality is excellent, and spectral phase is well behaved at the output. To demonstrate the strength of this source, we measure the two-dimensional spectrum of CdSe quantum dots over a range of population times and find clean signals and clear phonon vibrations. This combination of OPA and hollow-core fiber provides a substantial extension to the capabilities of CMDS.

Enhanced Exciton Quantum Coherence in Single CsPbBr3 Perovskite Quantum Dots using Femtosecond Two-Photon Near-Field Scanning Optical Microscopy

Cesium-halide perovskite quantum dots (QDs) have gained tremendous interest as quantum emitters in quantum information processing applications due to their optical and photophysical properties. However, engineering excitonic states in quantum dots requires a deep knowledge of the coherent dynamics of their excitons at a single-particle level. Here, we use femtosecond time-resolved two-photon near-field scanning optical microscopy (NSOM) to reveal coherences involving a single cesium lead bromide perovskite QD (CsPbBr₃) at room temperature. We show that, compared to other nonperovskite nanoparticles, the electronic coherence on a single perovskite QD has a relatively long lifetime of ca. 150 fs, whereas CdSe QDs have exciton coherence times shorter than 75 fs at room temperature. One possible explanation for the longer coherence time observed for the CsPbBr₃ perovskite system is related to the exciton fine structure of these perovskite QDs compared to other nanoparticles. These perovskite QDs exhibit interesting optical properties that differ from those of the traditional QDs including bright triplet exciton states. In fact, due to the small amplitude of the energy gap fluctuations of dipole-allowed triplet states in perovskite QDs, the coherent superposition could be preserved for longer times. Furthermore, single-particle excitation approach implemented in this work allows us to remove effects of heterogeneity that are usually present in ensemble averaging experiments at room temperature. The realization of quantum-mechanical phase-coherence of a charge carrier that can operate at room temperature is an issue of great importance for the potential application of coherent electronic phenomena in electronic and optoelectronic devices. These interesting findings provide further evidence of the great potential of these perovskite QDs as candidates for quantum computing and information processing applications.

Fluorescence-Detected Pump-Probe Spectroscopy

We introduce a new approach to transient spectroscopy, fluorescence-detected pump-probe (F-PP) spectroscopy, that overcomes several limitations of traditional PP. F-PP suppresses excited-state absorption, provides background-free detection, removes artifacts resulting from pump-pulse scattering, from non-resonant solvent response, or from coherent pulse overlap, and allows unique extraction of excited-state dynamics under certain conditions. Despite incoherent detection, time resolution of F-PP is given by the duration of the laser pulses, independent of the fluorescence lifetime. We describe the working principle of F-PP and provide its theoretical description. Then we illustrate specific features of F-PP by direct comparison with PP, theoretically and experimentally. For this purpose, we investigate, with both techniques, a molecular squaraine heterodimer, core-shell CdSe/ZnS quantum dots, and fluorescent protein mCherry. F-PP is broadly applicable to chemical systems in various environments and in different spectral regimes.

2D Electronic Spectroscopic Techniques for Quantum Technology Applications

2D electronic spectroscopy (2DES) techniques have gained particular interest given their capability of following ultrafast coherent and noncoherent processes in real-time. Although the fame of 2DES is still majorly linked to the investigation of energy and charge transport in biological light-harvesting complexes, 2DES is now starting to be recognized as a particularly valuable tool for studying transport processes in artificial nanomaterials and nanodevices. Particularly meaningful is the possibility of assessing coherent mechanisms active in the transport of excitation energy in these materials toward possible quantum technology applications. The diverse nature of these new target samples poses significant challenges and calls for a critical rethinking of the technique and its different realizations. With the confluence of promising new applications and rapidly developing technical capabilities, the enormous potential of 2DES techniques to impact the field of nanosystems, quantum technologies, and quantum devices is here delineated.

Observing Multiexciton Correlations in Colloidal Semiconductor Quantum Dots via Multiple-Quantum Two-Dimensional Fluorescence Spectroscopy

Correlations between excitons, that is, electron-hole pairs, have a great impact on the optoelectronic properties of semiconductor quantum dots and thus are relevant for applications such as lasers and photovoltaics. Upon multiphoton excitation, these correlations lead to the formation of multiexciton states. It is challenging to observe these states spectroscopically, especially higher multiexciton states, because of their short lifetimes and nonradiative decay. Moreover, solvent contributions in experiments with coherent signal detection may complicate the analysis. Here we employ multiple-quantum two-dimensional (2D) fluorescence spectroscopy on colloidal CdSe_1-xS_x/ZnS alloyed core/shell quantum dots. We selectively map the electronic structure of multiexcitons and their correlations by using two- and three-quantum 2D spectroscopy, conducted in a simultaneous measurement. Our experiments reveal the characteristics of biexcitons and triexcitons such as transition dipole moments, binding energies, and correlated transition energy fluctuations. We determine the binding energies of the first six biexciton states by simulating the two-quantum 2D spectrum. By analyzing the line shape of the three-quantum 2D spectrum, we find strong correlations between biexciton and triexciton states. Our method contributes to a more comprehensive understanding of multiexcitonic species in quantum dots and other semiconductor nanostructures.

Stochastically Realized Observables for Excitonic Molecular Aggregates

We show that a stochastic approach enables calculations of the optical properties of large 2-dimensional and nanotubular excitonic molecular aggregates. Previous studies of such systems relied on numerically diagonalizing the dense and disordered Frenkel Hamiltonian, which scales approximately as O(N3) for N dye molecules. Our approach scales much more efficiently as O(Nlog(N)), enabling quick study of systems with a million of coupled molecules on the micrometer size scale. We calculate several important experimental observables, including the optical absorption spectrum and density of states, and develop a stochastic formalism for the participation ratio. Quantitative agreement with traditional matrix diagonalization methods is demonstrated for both small- and intermediate-size systems. The stochastic methodology enables the study of the effects of spatial-correlation in site energies on the optical signatures of large 2D aggregates. Our results demonstrate that stochastic methods present a path forward for screening structural parameters and validating experiments and theoretical predictions in large excitonic aggregates.

Massively parallel classical logic via coherent dynamics of an ensemble of quantum systems with dispersion in size

Quantum parallelism can be implemented on a classical ensemble of discrete level quantum systems. The nanosystems are not quite identical, and the ensemble represents their individual variability. An underlying Lie algebraic theory is developed using the closure of the algebra to demonstrate the parallel information processing at the level of the ensemble. The ensemble is addressed by a sequence of laser pulses. In the Heisenberg picture of quantum dynamics the coherence between the N levels of a given quantum system can be handled as an observable. Thereby there are N ² logic variables per N level system. This is how massive parallelism is achieved in that there are N ² potential outputs for a quantum system of N levels. The use of an ensemble allows simultaneous reading of such outputs. Due to size dispersion the expectation values of the observables can differ somewhat from system to system. We show that for a moderate variability of the systems one can average the N ² expectation values over the ensemble while retaining closure and parallelism. This allows directly propagating in time the ensemble averaged values of the observables. Results of simulations of electronic excitonic dynamics in an ensemble of quantum dot (QD) dimers are presented. The QD size and interdot distance in the dimer are used to parametrize the Hamiltonian. The dimer N levels include local and charge transfer excitons within each dimer. The well-studied physics of semiconducting QDs suggests that the dimer coherences can be probed at room temperature.

Atomic fluctuations in electronic materials revealed by dephasing

The microscopic origin and timescale of the fluctuations of the energies of electronic states has a significant impact on the properties of interest of electronic materials, with implication in fields ranging from photovoltaic devices to quantum information processing. Spectroscopic investigations of coherent dynamics provide a direct measurement of electronic fluctuations. Modern multidimensional spectroscopy techniques allow the mapping of coherent processes along multiple time or frequency axes and thus allow unprecedented discrimination between different sources of electronic dephasing. Exploiting modern abilities in coherence mapping in both amplitude and phase, we unravel dissipative processes of electronic coherences in the model system of CdSe quantum dots (QDs). The method allows the assignment of the nature of the observed coherence as vibrational or electronic. The expected coherence maps are obtained for the coherent longitudinal optical (LO) phonon, which serves as an internal standard and confirms the sensitivity of the technique. Fast dephasing is observed between the first two exciton states, despite their shared electron state and common environment. This result is contrary to predictions of the standard effective mass model for these materials, in which the exciton levels are strongly correlated through a common size dependence. In contrast, the experiment is in agreement with ab initio molecular dynamics of a single QD. Electronic dephasing in these materials is thus dominated by the realistic electronic structure arising from fluctuations at the atomic level rather than static size distribution. The analysis of electronic dephasing thereby uniquely enables the study of electronic fluctuations in complex materials.

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.

Coherent Exciton Dynamics in Ensembles of Size-Dispersed CdSe Quantum Dot Dimers Probed via Ultrafast Spectroscopy: A Quantum Computational Study

Interdot coherent excitonic dynamics in nanometric colloidal CdSe quantum dots (QD) dimers lead to interdot charge migration and energy transfer. We show by electronic quantum dynamical simulations that the interdot coherent response to ultrashort fs laser pulses can be characterized by pump-probe transient absorption spectroscopy in spite of the inevitable inherent size dispersion of colloidal QDs. The latter, leading to a broadening of the excitonic bands, induce accidental resonances that actually increase the efficiency of the interdot coupling. The optical electronic response is computed by solving the time-dependent Schrodinger equation including the interaction with the oscillating electric field of the pulses for an ensemble of dimers that differ by their size. The excitonic Hamiltonian of each dimer is parameterized by the QD size and interdot distance, using an effective mass approximation. Local and charge transfer excitons are included in the dimer basis set. By tailoring the QD size, the excitonic bands can be tuned to overlap and thus favor interdot coupling. Computed pump-probe transient absorption maps averaged over the ensemble show that the coherence of excitons in QD dimers that lead to interdot charge migration can survive size disorder and could be observed in fs pump-probe, four-wave mixing, or covariance spectroscopy.

Steric Interactions Impact Vibronic and Vibrational Coherences in Perylenediimide Cyclophanes

Designing molecular systems that exploit vibronic coherence to improve light harvesting efficiencies relies on understanding how interchromophoric interactions, such as van der Waals forces and dipolar coupling, influence these coherences in multichromophoric arrays. However, disentangling these interactions requires studies of molecular systems with tunable structural relationships. Here, we use a combination of two-dimensional electronic spectroscopy and femtosecond stimulated Raman spectroscopy to investigate the role of steric hindrance between chromophores in driving changes to vibronic and vibrational coherences in a series of substituted perylenediimide (PDI) cyclophane dimers. We report significant differences in the frequency power spectra from the cyclophane dimers versus the corresponding monomer reference. We attribute these differences to distortion of the PDI cores from steric interactions between the substituents. These results highlight the importance of considering structural changes when rationalizing vibronic coupling in multichromophoric systems.

Ligand-Enhanced Energy Transport in Nanocrystal Solids Viewed with Two-Dimensional Electronic Spectroscopy

We examine CdSe NCs functionalized with the exciton-delocalizing ligand phenyldithiocarbamate (PDTC) using two-dimensional electronic spectroscopy (2DES). PDTC forms hybrid molecular orbitals with CdSe's valence band that relax hole spatial confinement and create potential for enhanced exciton migration in NC solids. We find PDTC broadens the intrinsic line width of individual NCs in solution by ∼30 meV, which we ascribe to modulation of NC band edge states by ligand motion. In PDTC-exchanged solids, photoexcited excitons are mobile and rapidly move to low-energy NC sites over ∼30 ps. We also find placing excitons into high-energy states can accelerate their rate of migration by over an order of magnitude, which we attribute to enhanced spatial delocalization of these states that improves inter-NC wave function overlap. Our work demonstrates that NC surface ligands can actively facilitate inter-NC energy transfer and highlights principles to consider when designing ligands for this application.

Non-Markovian Exciton-Phonon Interactions in Core-Shell Colloidal Quantum Dots at Femtosecond Timescales

We perform two-dimensional coherent spectroscopy on CdSe/CdZnS core-shell colloidal quantum dots at cryogenic temperatures. In the two-dimensional spectra, sidebands due to electronic coupling with CdSe lattice LO-phonon modes are observed to have evolutions deviating from the exponential dephasing expected from Markovian spectral diffusion, which is instantaneous and memoryless. Comparison to simulations provides evidence that LO-phonon coupling induces energy-gap fluctuations on the finite timescales of nuclear motion. The femtosecond resolution of our technique probes exciton dynamics directly on the timescales of phonon coupling in nanocrystals.

Multi-dimensional coherent spectroscopy of CdSe colloidal quantum dots at cryogenic temperatures

One-quantum and zero-quantum multi-dimensional coherent spectroscopy are used to study CdSe colloidal quantum dots at cryogenic temperatures. Each technique reveals unique aspects of the electron-phonon coupling dynamics in the material.

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.

Ferritin and neuromelanin "quantum dot" array structures in dopamine neurons of the substantia nigra pars compacta and norepinephrine neurons of the locus coeruleus

In this review, the author shows that ferritin has documented quantum dot material properties that have been reported in numerous independent studies, and can enable quantum mechanical electron transport over substantial distances. In addition, neuromelanin is a pi-conjugated polymer, and quantum dot/pi-conjugated polymer combinations have been reported in numerous independent studies to facilitate electron transport for solar photovoltaic and other applications. Both ferritin and neuromelanin are present in large quantities in the dopamine neurons of the substantia nigra pars compactaand the norepinephrine neurons of the locus coeruleus. The unique structure of subgroups of these neurons that have a large number of axon branches and synapses may have evolved to take advantage of this electron transport mechanism, if it is present, such as to coordinate conscious action, or for other purposes. Independent clinical and laboratory studies are also reviewed that corroborate this theory of coordinated action in these neuron groups. Research to validate the theory using charge transport measurements, materials characterization, existing fluorescent probe material and reaction time testing is proposed.

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.

Seeing Multiexcitons through Sample Inhomogeneity: Band-Edge Biexciton Structure in CdSe Nanocrystals Revealed by Two-Dimensional Electronic Spectroscopy

The electronic structure of multiexcitons significantly impacts the performance of nanostructures in lasing and light-emitting applications. However, these multiexcitons remain poorly understood due to their complexity arising from many-body physics. Standard transient-absorption and photoluminescence spectroscopies are unable to unambiguously distinguish effects of sample inhomogeneity from exciton-biexciton interactions. Here, we exploit the energy and time resolution of two-dimensional electronic spectroscopy to access the electronic structure of the band-edge biexciton in colloidal CdSe quantum dots. By removing effects of inhomogeneities, we show that the band-edge biexciton structure must consist of a discrete manifold of electronic states. Furthermore, the biexciton states within the manifold feature distinctive binding energies. Our findings have direct implications for optical gain thresholds and efficiency droop in light-emitting devices and provide experimental measures of many-body physics in nanostructures.

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.

Two-Dimensional Electronic Spectroscopy Unravels sub-100 fs Electron and Hole Relaxation Dynamics in Cd-Chalcogenide Nanostructures

We use two-dimensional electronic spectroscopy (2DES) to disentangle the separate electron and hole relaxation pathways and dynamics of CdTe nanorods on a sub-100 fs time scale. By simultaneously exciting and probing the first three excitonic transitions (S1, S2, and S3) and exploiting the unique combination of high temporal and spectral resolution of 2DES, we derive a complete picture for the state-selective carrier relaxation. We find that hot holes relax from the 1Σ_3/2 to the 1Σ_1/2 state (S2 → S1) with 30 ± 10 fs time constant, and the hot electrons relax from the Σ' to the Σ state (S3 → S1) with 50 ± 10 fs time constant. This observation would not have been possible with conventional transient absorption spectroscopy due to the spectral congestion of the transitions and the very fast relaxation time scales.

Probing Homogeneous Line Broadening in CdSe Nanocrystals Using Multidimensional Electronic Spectroscopy

The finite spectral line width of an ensemble of CdSe nanocrystals arises from size and shape inhomogeneity and the single-nanocrystal spectrum itself. This line width directly limits the performance of nanocrystal-based devices, yet most optical measurements cannot resolve the underlying contributions. We use two-dimensional electronic spectroscopy (2D ES) to measure the line width of the band-edge exciton of CdSe nanocrystals as a function of radii and surface chemistry. We find that the homogeneous width decreases for increasing nanocrystal radius and that surface chemistry plays a critical role in controlling this line width. To explore the hypothesis that unpassivated trap states serve to broaden the homogeneous line width and to explain its size-dependence, we use 3D ES to identify the spectral signatures of exciton-phonon coupling to optical and acoustic phonons. We find enhanced coupling to optical phonon modes for nanocrystals that lack electron-passivating ligands, suggesting that localized surface charges enhance exciton-phonon coupling via the Fröhlich interaction. Lastly, the data reveal that spectral diffusion contributes negligibly to the homogeneous line width on subnanosecond time scales.

Atomistic Analysis of Room Temperature Quantum Coherence in Two-Dimensional CdSe Nanostructures

Recent experiments on CdSe nanoplatelets synthesized with precisely controlled thickness that eliminates ensemble disorder have allowed accurate measurement of quantum coherence at room temperature. Matching exactly the CdSe cores of the experimentally studied particles and considering several defects, we establish the atomistic origins of the loss of coherence between heavy and light hole excitations in two-dimensional CdSe and CdSe/CdZnS core/shell structures. The coherence times obtained using molecular dynamics based on tight-binding density functional theory are in excellent agreement with the measured values. We show that a long coherence time is a consequence of both small fluctuations in the energy gap between the excited state pair, which is much less than thermal energy, and a slow decay of correlation between the energies of the two states. Anionic defects at the core/shell interface have little effect on the coherence lifetime, while cationic defects strongly perturb the electronic structure, destroying the experimentally observed coherence. By coupling to the same phonon modes, the heavy and light holes synchronize their energy fluctuations, facilitating long-lived coherence. We further demonstrate that the electronic excitations are localized close to the surface of these narrow nanoscale systems, and therefore, they couple most strongly to surface acoustic phonons. The established features of electron-phonon coupling and the influence of defects, surfaces, and core/shell interfaces provide important insights into quantum coherence in nanoscale materials in general.

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).

Detection of dark states in two-dimensional electronic photon-echo signals via ground-state coherence

Several recent experiments report on possibility of dark-state detection by means of so called beating maps of two-dimensional photon-echo spectroscopy [Ostroumov et al., Science 340, 52 (2013); Bakulin et al., Ultrafast Phenomena XIX (Springer International Publishing, 2015)]. The main idea of this detection scheme is to use coherence induced upon the laser excitation as a very sensitive probe. In this study, we investigate the performance of ground-state coherence in the detection of dark electronic states. For this purpose, we simulate beating maps of several models where the excited-state coherence can be hardly detected and is assumed not to contribute to the beating maps. The models represent strongly coupled electron-nuclear dynamics involving avoided crossings and conical intersections. In all the models, the initially populated optically accessible excited state decays to a lower-lying dark state within few hundreds femtoseconds. We address the role of Raman modes and of interstate-coupling nature. Our findings suggest that the presence of low-frequency Raman active modes significantly increases the chances for detection of dark states populated via avoided crossings, whereas conical intersections represent a more challenging task.

Observation of an Excitonic Quantum Coherence in CdSe Nanocrystals

Recent observations of excitonic coherences within photosynthetic complexes suggest that quantum coherences could enhance biological light harvesting efficiencies. Here, we employ optical pump-probe spectroscopy with few-femtosecond pulses to observe an excitonic quantum coherence in CdSe nanocrystals, a prototypical artificial light harvesting system. This coherence, which encodes the high-speed migration of charge over nanometer length scales, is also found to markedly alter the displacement amplitudes of phonons, signaling dynamics in the non-Born-Oppenheimer regime.

Exploring size and state dynamics in CdSe quantum dots using two-dimensional electronic spectroscopy

Development of optoelectronic technologies based on quantum dots depends on measuring, optimizing, and ultimately predicting charge carrier dynamics in the nanocrystal. In such systems, size inhomogeneity and the photoexcited population distribution among various excitonic states have distinct effects on electron and hole relaxation, which are difficult to distinguish spectroscopically. Two-dimensional electronic spectroscopy can help to untangle these effects by resolving excitation energy and subsequent nonlinear response in a single experiment. Using a filament-generated continuum as a pump and probe source, we collect two-dimensional spectra with sufficient spectral bandwidth to follow dynamics upon excitation of the lowest three optical transitions in a polydisperse ensemble of colloidal CdSe quantum dots. We first compare to prior transient absorption studies to confirm excitation-state-dependent dynamics such as increased surface-trapping upon excitation of hot electrons. Second, we demonstrate fast band-edge electron-hole pair solvation by ligand and phonon modes, as the ensemble relaxes to the photoluminescent state on a sub-picosecond time-scale. Third, we find that static disorder due to size polydispersity dominates the nonlinear response upon excitation into the hot electron manifold; this broadening mechanism stands in contrast to that of the band-edge exciton. Finally, we demonstrate excitation-energy dependent hot-carrier relaxation rates, and we describe how two-dimensional electronic spectroscopy can complement other transient nonlinear techniques.