Electronic Double-Quantum Coherences and Their Impact on Ultrafast Spectroscopy: The Example of β-Carotene

Double-quantum spectroscopy of dense atomic vapors: Interplay between Doppler and self-broadenings

In this article, we present a simulation study of the linear and nonlinear spectroscopy of dense atomic vapors. Motivated by recent experiments, we focus on double quantum spectroscopy, which directly probes dipole-dipole interactions. By explicitly including thermal velocity, we show that temperature has an important impact on the self-broadening mechanisms of the linear and nonlinear spectra. We also provide analytical expressions for the response functions in the short time limit using the two-body approximation, which shows that double quantum spectroscopy for atomic vapors directly probes the transition amplitude of the electronic excitation between two atoms. We also propose an expression for the double quantum spectrum that includes the effect of Doppler broadening, and we discuss the effect of density on the spectrum. We show that when Doppler broadening is negligible compared to self-broadening, the double quantum spectrum scales with the atomic density, while when Doppler broadening dominates, it scales as the square of the density.

Time-Frequency Signatures of Electronic Coherence of Colloidal CdSe Quantum Dot Dimer Assemblies Probed at Room Temperature by Two-Dimensional Electronic Spectroscopy

Electronic coherence signatures can be directly identified in the time-frequency maps measured in two-dimensional electronic spectroscopy (2DES). Here, we demonstrate the theory and discuss the advantages of this approach via the detailed application to the fast-femtosecond beatings of a wide variety of electronic coherences in ensemble dimers of quantum dots (QDs), assembled from QDs of 3 nm in diameter, with 8% size dispersion in diameter. The observed and computed results can be consistently characterized directly in the time-frequency domain by probing the polarization in the 2DES setup. The experimental and computed time-frequency maps are found in very good agreement, and several electronic coherences are characterized at room temperature in solution, before the extensive dephasing due to the size dispersion begins. As compared to the frequency-frequency maps that are commonly used in 2DES, the time-frequency maps allow exploiting electronic coherences without additional post-processing and with fewer 2DES measurements. Towards quantum technology applications, we also report on the modeling of the time-frequency photocurrent response of these electronic coherences, which paves the way to integrating QD devices with classical architectures, thereby enhancing the quantum advantage of such technologies for parallel information processing at room temperature.

Pulse overlap artifacts and double quantum coherence spectroscopy

The double quantum coherence (DQC) signal in nonlinear spectroscopy gives information about the many-body correlation effects not easily available by other methods. The signal is short-lived, consequently, a significant part of it is generated during the pulse overlap. Since the signal is at two times the laser frequency, one may intuitively expect that the pulse overlap-related artifacts are filtered out by the Fourier transform. Here, we show that this is not the case. We perform explicit calculations of phase-modulated two-pulse experiments of a two-level system where the DQC is impossible. Still, we obtain a significant signal at the modulation frequency, which corresponds to the DQC, while the Fourier transform over the pulse delay shows a double frequency. We repeat the calculations with a three-level system where the true DQC signal occurs. We conclude that with realistic dephasing times, the pulse-overlap artifact can be significantly stronger than the DQC signal. Our results call for great care when analyzing such experiments. As a rule of thumb, we recommend that only delays larger than 1.5 times the pulse length should be used.

Exploring electronic energy level structure and excited electronic states of β-carotene using DFT

Carotenoids are a class of natural pigments that play a fundamental role in photosynthesis and optoelectronics. However, the complexity of their energy level structure and electronic states has prevented a clear interpretation of their photophysics and photochemistry. The mediating nonradiative decay of the bright S₂ state to the dark S₁ state of carotenoids involves a population of bridging intermediate state. Herein, time-dependent DFT was used to study the energy level and electronic excitation process of β-carotene. A π-π* transition and π electron delocalization of electron excitation could be inferred based on the difference in the electron cloud distribution of the HOMO and LUMO orbitals. Through the electronic transition contribution in the UV-vis spectra and the electron density difference between the ground state and the excited state, the electronic energy level structure and possible dark state were analyzed. On this basis, the electronic excitation process of β-carotene was theoretically studied by combining electron-hole analysis and transition density matrix (TDM). There was a charge transfer from the β-ionone ring to the long-chain in the (S₀) → (S₂), (S₀) → (S₄) and (S₀) → (S₅).

Pulse overlap ambiguities in multiple quantum coherence spectroscopy

Coherent two-dimensional electronic spectroscopy probes ultrafast dynamics using femtosecond pulses. In the case where the time scale of the studied dynamics become comparable to the pulse duration, pulse overlap effects may compromise the experimental data. Here, we perform one-dimensional coherence scans and study pulse overlap effects in clean two-level systems. We find parasitic multiple-quantum coherences as a consequence of the arbitrary time ordering during the temporal pulse overlap. Surprisingly, the coherence lifetimes exceed the pulse coherence time by a factor of 1.85. These findings have important implications for the interpretation of higher-order coherent two-dimensional and related spectroscopy experiments.

Solvent-Dependent Characterization of Fucoxanthin through 2D Electronic Spectroscopy Reveals New Details on the Intramolecular Charge-Transfer State Dynamics

The electronic state manifolds of carotenoids and their relaxation dynamics are the object of intense investigation because most of the subtle details regulating their photophysics are still unknown. In order to contribute to this quest, here, we present a solvent-dependent 2D Electronic Spectroscopy (2DES) characterization of fucoxanthin, a carbonyl carotenoid involved in the light-harvesting process of brown algae. The 2DES technique allows probing its ultrafast relaxation dynamics in the first 1000 fs after photoexcitation with a 10 fs time resolution. The obtained results help shed light on the dynamics of the first electronic state manifold and, in particular, on an intramolecular charge-transfer state (ICT), whose photophysical properties are particularly elusive given its (almost) dark nature.

Molecular Coherent Three-Quantum Two-Dimensional Fluorescence Spectroscopy

We introduce molecular coherent three-quantum (3Q) two-dimensional (2D) fluorescence spectroscopy with phase cycling via shot-to-shot pulse shaping at a 1 kHz repetition rate. This allows us to acquire simultaneously, within a single scan, three fourth-order and six sixth-order signals correlating various one-quantum, two-quantum, and 3Q coherences. We demonstrate the approach on the dye molecule rhodamine 700 and reproduce all nine 2D data sets, including their absolute signal strengths, with simulations using a single, consistent set of model parameters. We observe a linear concentration dependence of all nonlinear signals, evidencing the absence of cascades and many-particle signals of noninteracting molecules. The single-beam, background-free implementation allows direct comparability between various nonlinear signal types and provides information about multiple excited states. Apart from molecules, the method is expected to be applicable to supramolecular systems, polymers, and solid-state materials with the prospect of revealing signatures of bi- and triexcitonic states.

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.

Fluorescence-Detected Two-Quantum and One-Quantum-Two-Quantum 2D Electronic Spectroscopy

We demonstrate two-quantum (2Q) coherent two-dimensional (2D) electronic spectroscopy using a shot-to-shot-modulated pulse shaper and fluorescence detection. Broadband collinear excitation is realized with the supercontinuum output of an argon-filled hollow-core fiber, enabling us to excite multiple transitions simultaneously in the visible range. The 2Q contribution is extracted via a three-pulse sequence with 16-fold phase cycling and simulated employing cresyl violet as a model system. Furthermore, we report the first experimental realization of one-quantum-two-quantum (1Q-2Q) 2D spectroscopy, offering less congested spectra as compared with the 2Q implementation. We avoid scattering artifacts and nonresonant solvent contributions by using fluorescence as the observable. This allows us to extract quantitative information about doubly excited states that agree with literature expectations. The high sensitivity and background-free nature of fluorescence detection allow for a general applicability of this method to many other systems.

Carotenoid-to-bacteriochlorophyll energy transfer through vibronic coupling in LH2 from Phaeosprillum molischianum

The peripheral light-harvesting antenna complex (LH2) of purple photosynthetic bacteria is an ideal testing ground for models of structure-function relationships due to its well-determined molecular structure and ultrafast energy deactivation. It has been the target for numerous studies in both theory and ultrafast spectroscopy; nevertheless, certain aspects of the convoluted relaxation network of LH2 lack a satisfactory explanation by conventional theories. For example, the initial carotenoid-to-bacteriochlorophyll energy transfer step necessary on visible light excitation was long considered to follow the Förster mechanism, even though transfer times as short as 40 femtoseconds (fs) have been observed. Such transfer times are hard to accommodate by Förster theory, as the moderate coupling strengths found in LH2 suggest much slower transfer within this framework. In this study, we investigate LH2 from Phaeospirillum (Ph.) molischianum in two types of transient absorption experiments-with narrowband pump and white-light probe resulting in 100 fs time resolution, and with degenerate broadband 10 fs pump and probe pulses. With regard to the split Q_x band in this system, we show that vibronically mediated transfer explains both the ultrafast carotenoid-to-B850 transfer, and the almost complete lack of transfer to B800. These results are beyond Förster theory, which predicts an almost equal partition between the two channels.

Effects of tunable excitation in carotenoids explained by the vibrational energy relaxation approach

Carotenoids are fundamental building blocks of natural light harvesters with convoluted and ultrafast energy deactivation networks. In order to disentangle such complex relaxation dynamics, several studies focused on transient absorption measurements and their dependence on the pump wavelength. However, such findings are inconclusive and sometimes contradictory. In this study, we compare internal conversion dynamics in [Formula: see text]-carotene, pumped at the first, second, and third vibronic progression peak. Instead of employing data fitting algorithms based on global analysis of the transient absorption spectra, we apply a fully quantum mechanical model to treat the high-frequency symmetric carbon-carbon (C=C and C-C) stretching modes explicitly. This model successfully describes observed population dynamics as well as spectral line shapes in their time-dependence and allows us to reach two conclusions: Firstly, the broadening of the induced absorption upon excess excitation is an effect of vibrational cooling in the first excited state ([Formula: see text]). Secondly, the internal conversion rate between the second excited state ([Formula: see text]) and [Formula: see text] crucially depends on the relative curve displacement. The latter point serves as a new perspective on solvent- and excitation wavelength-dependent experiments and lifts contradictions between several studies found in literature.

A Unified Picture of S* in Carotenoids

In π-conjugated chain molecules such as carotenoids, coupling between electronic and vibrational degrees of freedom is of central importance. It governs both dynamic and static properties, such as the time scales of excited state relaxation as well as absorption spectra. In this work, we treat vibronic dynamics in carotenoids on four electronic states (|S0⟩, |S1⟩, |S2⟩, and |Sn⟩) in a physically rigorous framework. This model explains all features previously associated with the intensely debated S* state. Besides successfully fitting transient absorption data of a zeaxanthin homologue, this model also accounts for previous results from global target analysis and chain length-dependent studies. Additionally, we are able to incorporate findings from pump-deplete-probe experiments, which were incompatible to any pre-existing model. Thus, we present the first comprehensive and unified interpretation of S*-related features, explaining them by vibronic transitions on either S1, S0, or both, depending on the chain length of the investigated carotenoid.

Vibronic coupling explains the ultrafast carotenoid-to-bacteriochlorophyll energy transfer in natural and artificial light harvesters

The initial energy transfer steps in photosynthesis occur on ultrafast timescales. We analyze the carotenoid to bacteriochlorophyll energy transfer in LH2 Marichromatium purpuratum as well as in an artificial light-harvesting dyad system by using transient grating and two-dimensional electronic spectroscopy with 10 fs time resolution. We find that Förster-type models reproduce the experimentally observed 60 fs transfer times, but overestimate coupling constants, which lead to a disagreement with both linear absorption and electronic 2D-spectra. We show that a vibronic model, which treats carotenoid vibrations on both electronic ground and excited states as part of the system's Hamiltonian, reproduces all measured quantities. Importantly, the vibronic model presented here can explain the fast energy transfer rates with only moderate coupling constants, which are in agreement with structure based calculations. Counterintuitively, the vibrational levels on the carotenoid electronic ground state play the central role in the excited state population transfer to bacteriochlorophyll; resonance between the donor-acceptor energy gap and the vibrational ground state energies is the physical basis of the ultrafast energy transfer rates in these systems.

Multidimensional Electronic Spectroscopy of Photochemical Reactions

Coherent multidimensional electronic spectroscopy can be employed to unravel various channels in molecular chemical reactions. This approach is thus not limited to analysis of energy transfer or charge transfer (i.e. processes from photophysics), but can also be employed in situations where the investigated system undergoes permanent structural changes (i.e. in photochemistry). Photochemical model reactions are discussed by using the example of merocyanine/spiropyran-based molecular switches, which show a rich variety of reaction channels, in particular ring opening and ring closing, cis-trans isomerization, coherent vibrational wave-packet motion, radical ion formation, and population relaxation. Using pump-probe, pump-repump-probe, coherent two-dimensional and three-dimensional, triggered-exchange 2D, and quantum-control spectroscopy, we gain intuitive pictures on which product emerges from which reactant and which reactive molecular modes are associated.

Excited state electronic landscape of mPlum revealed by two-dimensional double quantum coherence spectroscopy

Red fluorescent proteins (RFPs) are widely used probes for monitoring subcellular processes with extremely high spatial and temporal precision. In this work, we employed spectrally resolved transient absorption (SRTA) and two-dimensional double quantum coherence (2D2Q) spectroscopy to investigate the excited state electronic structure of mPlum, a well-known RFP. The SRTA spectra reveal the presence of excited state absorption features at both the low- and high-energy sides of the dominant ground state bleach contribution. The 2D2Q spectra measured at several excitation wavelengths reveal a peak pattern consistent with the presence of more than three electronic states (i.e., ground, excited, and doubly excited). Numerical modeling of this response suggests that the features are consistent with a 1-1-2 electronic structure. The two closely spaced (∼1500 cm(-1)) levels in the double quantum manifold appear at opposite anharmonicities relative to twice the energy of the lowest energy transition. These observations explain the excited state absorption contributions observed in spectrally resolved transient grating and transient absorption measurements and demonstrate the utility of multidimensional spectroscopy in unraveling congested spectra relative to conventional one-dimensional methods.

Experimental implementations of two-dimensional fourier transform electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Vibronic energy relaxation approach highlighting deactivation pathways in carotenoids

Energy relaxation between two electronic states of a molecule is mediated by a set of relevant vibrational states.

Ultrafast intramolecular relaxation dynamics of Mg- and Zn-bacteriochlorophyll a

Ultrafast excited-state dynamics of the photosynthetic pigment (Mg-)bacteriochlorophyll a and its Zn-substituted form were investigated by steady-state absorption∕fluorescence and femtosecond pump-probe spectroscopic measurements. The obtained steady-state absorption and fluorescence spectra of bacteriochlorophyll a in solution showed that the central metal compound significantly affects the energy of the Qx state, but has almost no effect on the Qy state. Photo-induced absorption spectra were recorded upon excitation of Mg- and Zn-bacteriochlorophyll a into either their Qx or Qy state. By comparing the kinetic traces of transient absorption, ground-state beaching, and stimulated emission after excitation to the Qx or Qy state, we showed that the Qx state was substantially incorporated in the ultrafast excited-state dynamics of bacteriochlorophyll a. Based on these observations, the lifetime of the Qx state was determined to be 50 and 70 fs for Mg- and Zn-bacteriochlorophyll a, respectively, indicating that the lifetime was influenced by the central metal atom due to the change of the energy gap between the Qx and Qy states.

Pulse shaping based two-dimensional electronic spectroscopy in a background free geometry

We demonstrate a "drop-in" modification of the pulse-shaped pump-probe geometry two-dimensional Fourier transform spectrometer that significantly improves its performance by making the measurement background-free. The modification uses a hybrid diffractive optic/pulse-shaping approach that combines the advantages of background-free detection with the precise timing and phase-cycling capabilities enabled by pulse-shaping. In addition, we present a simple new method for accurate phasing of optically heterodyned two-dimensional spectra. We demonstrate the high quality of data obtainable with this approach by reporting two-dimensional Fourier transform electronic spectra of chlorophyll a in glycerol/water at 77 K.

On the photophysics of carotenoids: a multireference DFT study of peridinin

We present a quantum-mechanical investigation of the photophysics of a specific carotenoid, peridinin, which is present in light-harvesting complexes. The fundamental role played by the geometry in determining the position and character of its low-lying singlet electronic states is investigated using a multireference DFT approach in combination with a continuum solvation model. The main photophysical properties of peridinin appear to be governed by the lowest two singlet excited states, as no evidence points to an intermediate S* state and the energies of the upper excited states are too high to allow their population with excitation in the visible range. These two excited states (S1, 2(1)A(g)(-) and S2, 1(1)B(u)(+)) are highly connected through the conjugation path here characterized by the value of the bond length alternation (BLA). The S1 and S2 states present distinct natures for small BLA values, whereas for larger ones they become more similar in terms of both brightness and dipolar character and their energies become closer. The geometrical issue is thus of fundamental importance for a correct interpretation of the spectroscopic signatures of peridinin.

Precise phasing of 2D-electronic spectra in a fully non-collinear phase-matching geometry

We report an experimental design for two-dimensional electronic spectroscopy (2D-ES) that avoids the need to measure notoriously weak pump-probe spectra. Retaining a fully non-collinear folded boxcar geometry, the described layout replaces pump-probe with heterodyned transient grating (het-TG). The absorptive component of the het-TG signal is measured directly, following a straightforward optimization routine. The use of het-TG achieves an improvement in signal to noise ratio by almost two orders of magnitude. As a result, 2D-ES-signals down to 0.5% can be clearly resolved.

Explaining the temperature dependence of spirilloxanthin's S* signal by an inhomogeneous ground state model

We investigate the nature of the S* excited state in carotenoids by performing a series of pump–probe experiments with sub-20 fs time resolution on spirilloxanthin in a polymethyl-methacrylate matrix varying the sample temperature. Following photoexcitation, we observe sub-200 fs internal conversion of the bright S₂ state into the lower-lying S₁ and S* states, which in turn relax to the ground state on a picosecond time scale. Upon cooling down the sample to 77 K, we observe a systematic decrease of the S*/S₁ ratio. This result can be explained by assuming two thermally populated ground state isomers. The higher lying one generates the S* state, which can then be effectively frozen out by cooling. These findings are supported by quantum chemical modeling and provide strong evidence for the existence and importance of ground state isomers in the photophysics of carotenoids.

Broadband 2D Electronic Spectroscopy Reveals a Carotenoid Dark State in Purple Bacteria

Although the energy transfer processes in natural light-harvesting systems have been intensively studied for the past 60 years, certain details of the underlying mechanisms remain controversial. We performed broadband two-dimensional (2D) electronic spectroscopy measurements on light-harvesting proteins from purple bacteria and isolated carotenoids in order to characterize in more detail the excited-state manifold of carotenoids, which channel energy to bacteriochlorophyll molecules. The data revealed a well-resolved signal consistent with a previously postulated carotenoid dark state, the presence of which was confirmed by global kinetic analysis. The results point to this state’s role in mediating energy flow from carotenoid to bacteriochlorophyll.

Coherent nonlinear optical studies of elementary processes in biological complexes: diagrammatic techniques based on the wave function versus the density matrix

Two types of diagrammatic approaches for the design and simulation of nonlinear optical experiments (closed-time path loops based on the wave function and double-sided Feynman diagrams for the density matrix) are presented and compared. We give guidelines for the assignment of relevant pathways and provide rules for the interpretation of existing nonlinear experiments in carotenoids.

Two-dimensional double-quantum spectra reveal collective resonances in an atomic vapor

We report the observation of double-quantum coherence signals in a gas of potassium atoms at twice the frequency of the one-quantum coherences. Since a single atom does not have a state at the corresponding energy, this observation must be attributed to a collective resonance involving multiple atoms. These resonances are induced by weak interatomic dipole-dipole interactions, which means that the atoms cannot be treated in isolation, even at a low density of 10(12)  cm(-3).

High frequency vibrational modulations in two-dimensional electronic spectra and their resemblance to electronic coherence signatures

In this work we analyze how nuclear coherences modulate diagonal and off-diagonal peaks in two-dimensional electronic spectroscopy. 2D electronic spectra of pinacyanol chloride are measured with 8 fs pulses, which allows coherent excitation of the 1300 cm(-1) vibrational mode. The 2D spectrum reveals both diagonal and off-diagonal peaks related to the vibrational mode. On early time scales, up to 30 fs, coherent dynamics give rise to oscillations in the amplitudes, positions, and shapes of the peaks in the 2D spectrum. We find an anticorrelation between the amplitude and the diagonal width of the two diagonal peaks. The measured data are reproduced with a model incorporating a high frequency mode coupled to an electronic two-level-system. Our results show that these anticorrelated oscillations occur for vibrational wavepackets and not exclusively for electronic coherences as has been assumed previously.