3D Spectroscopy of Vibrational Coherences in Quantum Dots: Theory

Vibrational coherences in half-broadband 2D electronic spectroscopy: Spectral filtering to identify excited state displacements

Vibrational coherences in ultrafast pump-probe (PP) and 2D electronic spectroscopy (2DES) provide insights into the excited state dynamics of molecules. Femtosecond coherence spectra and 2D beat maps yield information about displacements of excited state surfaces for key vibrational modes. Half-broadband 2DES uses a PP configuration with a white light continuum probe to extend the detection range and resolve vibrational coherences in the excited state absorption (ESA). However, the interpretation of these spectra is difficult as they are strongly dependent on the spectrum of the pump laser and the relative displacement of the excited states along the vibrational coordinates. We demonstrate the impact of these convoluting factors for a model based upon cresyl violet. A careful consideration of the position of the pump spectrum can be a powerful tool in resolving the ESA coherences to gain insights into excited state displacements. This paper also highlights the need for caution in considering the spectral window of the pulse when interpreting these spectra.

Theory of 2D electronic spectroscopy of water soluble chlorophyll-binding protein (WSCP): Signatures of Chl b derivate

We investigate how electronic excitations and subsequent dissipative dynamics in the water soluble chlorophyll-binding protein (WSCP) are connected to features in two-dimensional (2D) electronic spectra, thereby comparing results from our theoretical approach with experimental data from the literature. Our calculations rely on third-order response functions, which we derived from a second-order cumulant expansion of the dissipative dynamics involving the partial ordering prescription, assuming a fast vibrational relaxation in the potential energy surfaces of excitons. Depending on whether the WSCP complex containing a tetrameric arrangement of pigments composed of two dimers with weak excitonic coupling between them binds the chlorophyll variant Chl a or Chl b, the resulting linear absorption and circular dichroism spectra and particularly the 2D spectra exhibit substantial differences in line shapes. These differences between Chl a WSCP and Chl b WSCP cannot be explained by the slightly modified excitonic couplings within the two variants. In the case of Chl a WSCP, the assumption of equivalent dimer subunits facilitates a reproduction of substantial features from the experiment by the calculations. In contrast, for Chl b WSCP, we have to assume that the sample, in addition to Chl b dimers, contains a small but distinct fraction of chemically modified Chl b pigments. The existence of such Chl b derivates has been proposed by Pieper et al. [J. Phys. Chem. B 115, 4042 (2011)] based on low-temperature absorption and hole-burning spectroscopy. Here, we provide independent evidence.

Non-Hermitian Hamiltonians for linear and nonlinear optical response: A model for plexcitons

In polaritons, the properties of matter are modified by mixing the molecular transitions with light modes inside a cavity. Resultant hybrid light-matter states exhibit energy level shifts, are delocalized over many molecular units, and have a different excited-state potential energy landscape, which leads to modified exciton dynamics. Previously, non-Hermitian Hamiltonians have been derived to describe the excited states of molecules coupled to surface plasmons (i.e., plexcitons), and these operators have been successfully used in the description of linear and third order optical response. In this article, we rigorously derive non-Hermitian Hamiltonians in the response function formalism of nonlinear spectroscopy by means of Feshbach operators and apply them to explore spectroscopic signatures of plexcitons. In particular, we analyze the optical response below and above the exceptional point that arises for matching transition energies for plasmon and molecular components and study their decomposition using double-sided Feynman diagrams. We find a clear distinction between interference and Rabi splitting in linear spectroscopy and a qualitative change in the symmetry of the line shape of the nonlinear signal when crossing the exceptional point. This change corresponds to one in the symmetry of the eigenvalues of the Hamiltonian. Our work presents an approach for simulating the optical response of sublevels within an electronic system and opens new applications of nonlinear spectroscopy to examine the different regimes of the spectrum of non-Hermitian Hamiltonians.

Excitation-Dependence of Excited-State Dynamics and Vibrational Relaxation of Lutein Explored by Multiplex Transient Grating

Multiplex transient grating (MTG) spectroscopy was applied to lutein in ethanol to investigate the excitation-energy dependence of the excited-state dynamics and vibrational relaxation. The transient spectra obtained upon low (480 nm) and high-energy (380 nm) excitation both recorded a strong excited-state absorption (ESA) of S₁ → S _n as well as a broad band in the blue wavelength that was previously proposed as the S* state. By means of Gaussian decomposition and global fitting of the ESA band, a long-time component assigned to the triplet state was derived from the kinetic trace of 480 nm excitation. Moreover, the MTG signal with a resolution of 110 fs displayed the short-time quantum beat signal. In order to unveil the vibrational coherence in the excited-state decay, the linear and non-linear simulations of the steady spectrum and dynamic signals were presented in which at least three fundamental modes standing for C-C stretching (ν₁), C=C stretching (ν₂), and O-H valence vibrations (ν₃) were considered to analyze the experimental signals. It was identified that the vibrational coherence between ν₁ and ν₃ or ν₂ and ν₃ was responsible for quantum beat that may be associated with the triplet state. We concluded that upon low- or high-energy excitation into the S₂ state, the photo-isomerization of the molecule and structural recovery on the time-scale of vibrational cooling are the key factors to form a mixed conformation in the hot-S₁ state that is the precursor of a long life-time triplet.

Beating signals in CdSe quantum dots measured by low-temperature 2D spectroscopy

Advances in ultrafast spectroscopy can provide access to dynamics involving nontrivial quantum correlations and their evolutions. In coherent 2D spectroscopy, the oscillatory time dependence of a signal is a signature of such quantum dynamics. Here we study such beating signals in electronic coherent 2D spectroscopy of CdSe quantum dots (CdSe QDs) at 77 K. The beating signals are analyzed in terms of their positive and negative Fourier components. We conclude that the beatings originate from coherent LO-phonons of CdSe QDs. No evidence for the quantum dot size dependence of the LO-phonon frequency was identified.

Excited States and Their Dynamics in CdSe Quantum Dots Studied by Two-Color 2D Spectroscopy

Quantum dots (QDs) form a promising family of nanomaterials for various applications in optoelectronics. Understanding the details of the excited-state dynamics in QDs is vital for optimizing their function. We apply two-color 2D electronic spectroscopy to investigate CdSe QDs at 77 K within a broad spectral range. Analysis of the electronic dynamics during the population time allows us to identify the details of the excitation pathways. The initially excited high-energy electrons relax with the time constant of 100 fs. Simultaneously, the states at the band edge rise within 700 fs. Remarkably, the excited-state absorption is rising with a very similar time constant of 700 fs. This makes us reconsider the earlier interpretation of the excited-state absorption as the signature of a long-lived trap state. Instead, we propose that this signal originates from the excitation of the electrons that have arrived in the conduction-band edge.

Exciton-phonon coupling strength in single-layer MoSe2 at room temperature

Single-layer transition metal dichalcogenides are at the center of an ever increasing research effort both in terms of fundamental physics and applications. Exciton–phonon coupling plays a key role in determining the (opto)electronic properties of these materials. However, the exciton–phonon coupling strength has not been measured at room temperature. Here, we use two-dimensional micro-spectroscopy to determine exciton–phonon coupling of single-layer MoSe₂. We detect beating signals as a function of waiting time induced by the coupling between A excitons and A′₁ optical phonons. Analysis of beating maps combined with simulations provides the exciton–phonon coupling. We get a Huang–Rhys factor ~1, larger than in most other inorganic semiconductor nanostructures. Our technique offers a unique tool to measure exciton–phonon coupling also in other heterogeneous semiconducting systems, with a spatial resolution ~260 nm, and provides design-relevant parameters for the development of optoelectronic devices.

The exciton–phonon coupling (EXPC) affects the opto-electronic properties of atomically thin semiconductors. Here, the authors develop two-dimensional micro-spectroscopy to determine the EXPC of monolayer MoSe₂.

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.

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.

Two-dimensional electronic spectroscopy reveals liquid-like lineshape dynamics in CsPbI3 perovskite nanocrystals

Lead-halide perovskites have attracted tremendous attention, initially for their performance in thin film photovoltaics, and more recently for a variety of remarkable optical properties. Defect tolerance through polaron formation within the ionic lattice is a key aspect of these materials. Polaron formation arises from the dynamical coupling of atomic fluctuations to electronic states. Measuring the properties of these fluctuations is therefore essential in light of potential optoelectronic applications. Here we apply two-dimensional electronic spectroscopy (2DES) to probe the timescale and amplitude of the electronic gap correlations in CsPbI₃ perovskite nanocrystals via homogeneous lineshape dynamics. The 2DES data reveal irreversible, diffusive dynamics that are qualitatively inconsistent with the coherent dynamics in covalent solids such as CdSe quantum dots. In contrast, these dynamics are consistent with liquid-like structural dynamics on the 100 femtosecond timescale. These dynamics are assigned to the optical signature of polaron formation, the conceptual solid-state analogue of solvation.

Lead-halide perovskites have promising optoelectronic properties, determined by interplay of electronic and structural properties. Here the authors probe CsPbI₃ nanocrystals by two-dimensional electronic spectroscopy, showing liquid-like structural dynamics signature of polaron formation.

Double-crossed polarization transient grating for distinction and characterization of coherences

Coherent phenomena have been widely suggested to play a role in efficient photosynthetic light harvesting and charge separation processes. To substantiate these ideas, separation of intramolecular vibrational coherences from purely electronic or mixed vibronic coherences is essential. To this end, polarization-controlled two-dimensional electronic spectroscopy has been shown to provide an effective selectivity. We show that analogous discrimination can be achieved in a transient grating experiment by employing the double-crossed polarization scheme. This is demonstrated in a study of bacterial reaction centers. Significantly faster acquisition times of these experiments make longer population time scans feasible, thereby achieving improved frequency resolution and allowing for accurate extraction of coherence frequencies and dephasing times. These parameters are crucial for the discussion on relevance of the measured coherences to energy or electron transfer phenomena.

Characterization of Vibrational Coherence in Monomeric Bacteriochlorophyll a by Two-Dimensional Electronic Spectroscopy

Bacteriochlorophyll a (BChla) is the most abundant pigment found in the Bacterial Reaction Center (BRC) and light-harvesting proteins of photosynthetic purple and green bacteria. Recent two-dimensional electronic spectroscopy (2DES) studies of photosynthetic pigment-protein complexes including the BRC and the Fenna-Matthews-Olson (FMO) complex have shown oscillatory signals, or coherences, whose physical origin has been hotly debated. To better understand the observations of coherence in larger photosynthetic systems, it is important to carefully characterize the spectroscopic signatures of the monomeric pigments. Prior spectroscopic studies of BChla have differed significantly in their observations, with some studies reporting little to no coherence. Here we present evidence of strong coherences in monomeric BChla in isopropanol using 2DES at 77 K. We resolve many modes with frequencies that correspond well with known vibrational modes. We confirm their vibrational origin by comparing the 2D spectroscopic signatures with expectations based on a purely vibrational model.

Identification and characterization of diverse coherences in the Fenna-Matthews-Olson complex

The idea that excitonic (electronic) coherences are of fundamental importance to natural photosynthesis gained popularity when slowly dephasing quantum beats (QBs) were observed in the two-dimensional electronic spectra of the Fenna-Matthews-Olson (FMO) complex at 77 K. These were assigned to superpositions of excitonic states, a controversial interpretation, as the strong chromophore-environment interactions in the complex suggest fast dephasing. Although it has been pointed out that vibrational motion produces similar spectral signatures, a concrete assignment of these oscillatory signals to distinct physical processes is still lacking. Here we revisit the coherence dynamics of the FMO complex using polarization-controlled two-dimensional electronic spectroscopy, supported by theoretical modelling. We show that the long-lived QBs are exclusively vibrational in origin, whereas the dephasing of the electronic coherences is completed within 240 fs even at 77 K. We further find that specific vibrational coherences are produced via vibronically coupled excited states. The presence of such states suggests that vibronic coupling is relevant for photosynthetic energy transfer.

Mechanistic insight into internal conversion process within Q-bands of chlorophyll a

The non-radiative relaxation of the excitation energy from higher energy states to the lowest energy state in chlorophylls is a crucial preliminary step for the process of photosynthesis. Despite the continuous theoretical and experimental efforts to clarify the ultrafast dynamics of this process, it still represents the object of an intense investigation because the ultrafast timescale and the congestion of the involved states makes its characterization particularly challenging. Here we exploit 2D electronic spectroscopy and recently developed data analysis tools to provide more detailed insights into the mechanism of internal conversion within the Q-bands of chlorophyll a. The measurements confirmed the timescale of the overall internal conversion rate (170 fs) and captured the presence of a previously unidentified ultrafast (40 fs) intermediate step, involving vibronic levels of the lowest excited state.

Quantum coherence as a witness of vibronically hot energy transfer in bacterial reaction center

Photosynthetic proteins have evolved over billions of years so as to undergo optimal energy transfer to the sites of charge separation. On the basis of spectroscopically detected quantum coherences, it has been suggested that this energy transfer is partially wavelike. This conclusion depends critically on the assignment of the coherences to the evolution of excitonic superpositions. We demonstrate that, for a bacterial reaction center protein, long-lived coherent spectroscopic oscillations, which bear canonical signatures of excitonic superpositions, are essentially vibrational excited-state coherences shifted to the ground state of the chromophores. We show that the appearance of these coherences arises from a release of electronic energy during energy transfer. Our results establish how energy migrates on vibrationally hot chromophores in the reaction center, and they call for a reexamination of claims of quantum energy transfer in photosynthesis.

Discrimination of Diverse Coherences Allows Identification of Electronic Transitions of a Molecular Nanoring

The role of quantum coherence in photochemical functions of molecular systems such as photosynthetic complexes is a broadly debated topic. Coexistence and intermixing of electronic and vibrational coherences has been proposed to be responsible for the observed long-lived coherences and high energy transfer efficiency. However, clear experimental evidence of coherences with different origins operating at the same time has been elusive. In this work, multidimensional spectra obtained from a six-porphyrin nanoring system are analyzed in detail with support from theoretical modeling. We uncover a great diversity of separable electronic, vibrational, and mixed coherences and show their cooperation in shaping the spectroscopic response. The results permit direct assignment of electronic and vibronic states and characterization of the excitation dynamics. The clear disentanglement of coherences in molecules with extended π-conjugation opens up new avenues for exploring coherent phenomena and understanding their importance for the function of complex systems.

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.

Role of coherent vibrations in energy transfer and conversion in photosynthetic pigment-protein complexes

Oscillatory features of two-dimensional spectra of photosynthetic pigment-protein complexes during few picoseconds after electronic excitations of chlorophylls in various pigment-proteins were recently related to the coherent nuclear vibrations. It has been also speculated that the vibrations may assist the excitonic energy transfer and charge separation, hence contributing to energy transport and energy conversion efficiency. Here, we consider three theoretical approaches usually used for characterization of the excitation dynamics and charge separation, namely Redfield, Förster, and Marcus model descriptions, regarding this question. We show that two out of the three mechanisms require explicit resonances of excitonic splittings and the nuclear vibration frequencies. However, the third one related to the electron transfer is in principle off resonant.

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.

Persistent Inter-Excitonic Quantum Coherence in CdSe Quantum Dots

The creation and manipulation of quantum superpositions is a fundamental goal for the development of materials with novel optoelectronic properties. In this letter, we report persistent (~80 fs lifetime) quantum coherence between the 1S and 1P excitonic states in zinc-blende colloidal CdSe quantum dots at room temperature, measured using Two-Dimensional Electronic Spectroscopy. We demonstrate that this quantum coherence manifests as an intradot phenomenon, the frequency of which depends on the size of the dot excited within the ensemble of QDs. We model the lifetime of the coherence and demonstrate that correlated interexcitonic fluctuations preserve relative phase between excitonic states. These observations suggest an avenue for engineering long-lived interexcitonic quantum coherence in colloidal quantum dots.