Multidimensional high-harmonic echo spectroscopy: Resolving coherent electron dynamics in the EUV regime.

We theoretically propose a multidimensional high-harmonic echo spectroscopy technique which utilizes strong optical fields to resolve coherent electron dynamics spanning an energy range of multiple electronvolts. Using our recently developed semi-perturbative approach, we can describe the coherent valence electron dynamics driven by a sequence of phase-matched and well-separated short few-cycle strong infrared laser pulses. The recombination of tunnel-ionized electrons by each pulse coherently populates the valence states of a molecule, which allows for a direct observation of its dynamics via the high harmonic echo signal. The broad bandwidth of the effective dipole between valence states originated from the strong-field excitation results in nontrivial ultra-delayed partial rephasing echo, which is not observed in standard two-dimensional optical spectroscopic techniques in a two-level molecular systems. We demonstrate the results of simulations for the anionic molecular system and show that the ultrafast valence electron dynamics can be well captured with femtosecond resolution.

Multidimensional four-wave mixing signals detected by quantum squeezed light.

Four-wave mixing (FWM) of optical fields has been extensively used in quantum information processing, sensing, and memories. It also forms a basis for nonlinear spectroscopies such as transient grating, stimulated Raman, and photon echo where phase matching is used to select desired components of the third-order response of matter. Here we report an experimental study of the two-dimensional quantum noise intensity difference spectra of a pair of squeezed beams generated by FWM in hot Rb vapor. The measurement reveals details of the [Formula: see text] susceptibility dressed by the strong pump field which induces an AC Stark shift, with higher spectral resolution compared to classical measurements of probe and conjugate beam intensities. We demonstrate how quantum correlations of squeezed light can be utilized as a spectroscopic tool which unlike their classical counterparts are robust to external noise.

Impact of nuclear quantum effects on the structural inhomogeneity of liquid water.

The 2D Raman-terahertz (THz) response of liquid water is studied in dependence of temperature and isotope substitution ([Formula: see text]O, [Formula: see text]O, and [Formula: see text]O). In either case, a very short-lived (i.e., between 75 and 95 fs) echo is observed that reports on the inhomogeneity of the low-frequency intermolecular modes and hence, on the heterogeneity of the hydrogen bond networks of water. The echo lifetime slows down by about 20% when cooling the liquid from room temperature to the freezing point. Furthermore, the echo lifetime of [Formula: see text]O is [Formula: see text] slower than that of [Formula: see text]O, and both can be mapped on each other by introducing an effective temperature shift of [Formula: see text] K. In contrast, the temperature-dependent echo lifetimes of [Formula: see text]O and [Formula: see text]O are the same within error. [Formula: see text]O and [Formula: see text]O have identical masses, yet [Formula: see text]O is much closer to [Formula: see text]O in terms of nuclear quantum effects. It is, therefore, concluded that the echo is a measure of the structural inhomogeneity of liquid water induced by nuclear quantum effects.

Imaging electron-density fluctuations by multidimensional X-ray photon-coincidence diffraction.

The ultrafast spontaneous electron-density fluctuation dynamics in molecules is studied theoretically by off-resonant multiple X-ray diffraction events. The time- and wavevector-resolved photon-coincidence signals give an image of electron-density fluctuations expressed through the four-point correlation function of the charge density in momentum space. A Fourier transform of the signal provides a real-space image of the multipoint charge-density correlation functions, which reveal snapshots of the evolving electron density in between the diffraction events. The proposed technique is illustrated by ab initio simulations of the momentum- and real-space inelastic scattering signals from a linear cyanotetracetylene molecule.

Temperature as an Extra Dimension in Multidimensional Protein NMR Spectroscopy.

NMR spectroscopy is a particularly informative method for studying protein structures and dynamics in solution; however, it is also one of the most time-consuming. Modern approaches to biomolecular NMR spectroscopy are based on lengthy multidimensional experiments, the duration of which grows exponentially with the number of dimensions. The experimental time may even be several days in the case of 3D and 4D spectra. Moreover, the experiment often has to be repeated under several different conditions, for example, to measure the temperature-dependent effects in a spectrum (temperature coefficients (TCs)). Herein, a new approach that involves joint sampling of indirect evolution times and temperature is proposed. This allows TCs to be measured through 3D spectra in even less time than that needed to acquire a single spectrum by using the conventional approach. Two signal processing methods that are complementary, in terms of sensitivity and resolution, 1) dividing data into overlapping subsets followed by compressed sensing reconstruction, and 2) treating the complete data set with a variant of the Radon transform, are proposed. The temperature-swept 3D HNCO spectra of two intrinsically disordered proteins, osteopontin and CD44 cytoplasmic tail, show that this new approach makes it possible to determine TCs and their non-linearities effectively. Non-linearities, which indicate the presence of a compact state, are particularly interesting. The complete package of data acquisition and processing software for this new approach are provided.

Multidimensional photon correlation spectroscopy of cavity polaritons.

The strong coupling of atoms and molecules to radiation field modes in optical cavities creates dressed matter/field states known as polaritons with controllable dynamical and energy transfer properties. We propose a multidimensional optical spectroscopy technique for monitoring polariton dynamics. The response of a two-level atom to the time-dependent coupling to a single-cavity mode is monitored through time-and-frequency-resolved single-photon coincidence measurements of spontaneous emission. Polariton population and coherence dynamics and its variation with cavity photon number and controlled by gating parameters are predicted by solving the Jaynes-Cummings model.

Primary processes in the bacterial reaction center probed by two-dimensional electronic spectroscopy.

In the initial steps of photosynthesis, reaction centers convert solar energy to stable charge-separated states with near-unity quantum efficiency. The reaction center from purple bacteria remains an important model system for probing the structure-function relationship and understanding mechanisms of photosynthetic charge separation. Here we perform 2D electronic spectroscopy (2DES) on bacterial reaction centers (BRCs) from two mutants of the purple bacterium Rhodobacter capsulatus, spanning the Q y absorption bands of the BRC. We analyze the 2DES data using a multiexcitation global-fitting approach that employs a common set of basis spectra for all excitation frequencies, incorporating inputs from the linear absorption spectrum and the BRC structure. We extract the exciton energies, resolving the previously hidden upper exciton state of the special pair. We show that the time-dependent 2DES data are well-represented by a two-step sequential reaction scheme in which charge separation proceeds from the excited state of the special pair (P*) to P+HA- via the intermediate P+BA- When inhomogeneous broadening and Stark shifts of the B* band are taken into account we can adequately describe the 2DES data without the need to introduce a second charge-separation pathway originating from the excited state of the monomeric bacteriochlorophyll BA*.

Mass-correlated rotational Raman spectra with high resolution, broad bandwidth, and absolute frequency accuracy.

We present mass-correlated rotational alignment spectroscopy, based on the optical excitation of a coherent rotational quantum wave and the observation of temporal wave interferences in a mass spectrometer. Combined electronic and opto-mechanical delays increased the observation time and energy resolution by an order of magnitude compared with preceding time-domain measurements. Rotational transition frequencies were referenced to an external clock for accurate absolute frequency measurements. Rotational Raman spectra for six naturally occurring carbon disulfide isotopologues were resolved with 3 MHz resolution over a spectral range of 500 GHz. Rotational constants were determined with single-kilohertz accuracy, competitive with state-of-the-art frequency domain measurements.

Coherent two-dimensional terahertz-terahertz-Raman spectroscopy.

We present 2D terahertz-terahertz-Raman (2D TTR) spectroscopy, the first technique, to our knowledge, to interrogate a liquid with multiple pulses of terahertz (THz) light. This hybrid approach isolates nonlinear signatures in isotropic media, and is sensitive to the coupling and anharmonicity of thermally activated THz modes that play a central role in liquid-phase chemistry. Specifically, by varying the timing between two intense THz pulses, we control the orientational alignment of molecules in a liquid, and nonlinearly excite vibrational coherences. A comparison of experimental and simulated 2D TTR spectra of bromoform (CHBr3), carbon tetrachloride (CCl4), and dibromodichloromethane (CBr2Cl2) shows previously unobserved off-diagonal anharmonic coupling between thermally populated vibrational modes.

Excitation transfer and trapping kinetics in plant photosystem I probed by two-dimensional electronic spectroscopy.

Photosystem I is a robust and highly efficient biological solar engine. Its capacity to utilize virtually every absorbed photon's energy in a photochemical reaction generates great interest in the kinetics and mechanisms of excitation energy transfer and charge separation. In this work, we have employed room-temperature coherent two-dimensional electronic spectroscopy and time-resolved fluorescence spectroscopy to follow exciton equilibration and excitation trapping in intact Photosystem I complexes as well as core complexes isolated from Pisum sativum. We performed two-dimensional electronic spectroscopy measurements with low excitation pulse energies to record excited-state kinetics free from singlet-singlet annihilation. Global lifetime analysis resolved energy transfer and trapping lifetimes closely matches the time-correlated single-photon counting data. Exciton energy equilibration in the core antenna occurred on a timescale of 0.5 ps. We further observed spectral equilibration component in the core complex with a 3-4 ps lifetime between the bulk Chl states and a state absorbing at 700 nm. Trapping in the core complex occurred with a 20 ps lifetime, which in the supercomplex split into two lifetimes, 16 ps and 67-75 ps. The experimental data could be modelled with two alternative models resulting in equally good fits-a transfer-to-trap-limited model and a trap-limited model. However, the former model is only possible if the 3-4 ps component is ascribed to equilibration with a "red" core antenna pool absorbing at 700 nm. Conversely, if these low-energy states are identified with the P700 reaction centre, the transfer-to-trap-model is ruled out in favour of a trap-limited model.

ASAP: An automatic sequential assignment program for congested multidimensional solid state NMR spectra.

Accurate signal assignments can be challenging for congested solid-state NMR (ssNMR) spectra. We describe an automatic sequential assignment program (ASAP) to partially overcome this challenge. ASAP takes three input files: the residue type assignments (RTAs) determined from the better-resolved NCACX spectrum, the full peak list of the NCOCX spectrum, and the protein sequence. It integrates our auto-residue type assignment strategy (ARTIST) with the Monte Carlo simulated annealing (MCSA) algorithm to overcome the hurdle for accurate signal assignments caused by incomplete side-chain resonances and spectral congestion. Combined, ASAP demonstrates robust performance and accelerates signal assignments of large proteins (>200 residues) that lack crystalline order.

Investigation on concentration detection of turbid solution based on hemisphere sample cell and multidimensional spectroscopy.

The study developed a hemisphere sample cell and constructed a multidimensional spectroscopy acquisition system to enhance the accuracy of detecting turbid solution with scattering properties. The system simultaneously captures absorption and scattering information from the tested samples. Monte Carlo simulation was employed to model the transmission light intensity distribution data from sample cells of various shapes. It was found that the hemisphere sample cell increases the dimensionality of transmission light intensity information and enables the acquisition of more scattering-related data. Furthermore, 46 samples of intralipid-20% solution with varying concentrations were examined. Models were constructed using partial least squares (PLS) regression with one-dimensional and two-dimensional light intensity distribution data. The results indicate that the model using two-dimensional light intensity distribution data significantly outperforms the model using one-dimensional data, reducing the root mean square error by 39.96% and increasing the correlation coefficient by 0.332%. Experimental results demonstrate that the multidimensional spectroscopic modeling method employing the hemisphere sample cell can significantly enhance the accuracy and speed of detecting chemical composition concentrations in turbid solution.

Hierarchical Equations of Motion Simulation of Temperature-Dependent Two-Dimensional Electronic Spectroscopy of the Chlorophyll a Manifold in LHCII.

We simulated two-dimensional electronic spectra (2DES) of the chlorophyll a manifold of light-harvesting complex II (LHCII) at various temperatures (77, 110, 150, 190, 230, 273, and 293 K) using the hierarchical equations of the motion-phase matching approach. We confirm the main excitation energy transfer pathways assignments within the chlorophyll a manifold of LHCII measured in a recent work (J. Phys. Chem. B 2019, 123, 6765-6775). The calculated transfer rates are also in general agreement with the measured rates. We also provided theoretical confirmation for the experimental assignments, as uphill and downhill energy transfer processes, of 2D spectral features that were reported in recent experimental reports. These temperature-dependent features were also ascertained to follow the detailed-balance principle.

Insights into the mechanisms and dynamics of energy transfer in plant light-harvesting complexes from two-dimensional electronic spectroscopy.

During the past two decades, two-dimensional electronic spectroscopy (2DES) and related techniques have emerged as a potent experimental toolset to study the ultrafast elementary steps of photosynthesis. Apart from the highly engaging albeit controversial analysis of the role of quantum coherences in the photosynthetic processes, 2DES has been applied to resolve the dynamics and pathways of energy and electron transport in various light-harvesting antenna systems and reaction centres, providing unsurpassed level of detail. In this paper we discuss the main technical approaches and their applicability for solving specific problems in photosynthesis. We then recount applications of 2DES to study the exciton dynamics in plant and photosynthetic light-harvesting complexes, especially light-harvesting complex II (LHCII) and the fucoxanthin-chlorophyll proteins of diatoms, with emphasis on the types of unique information about such systems that 2DES is capable to deliver. This article is part of a Special Issue entitled Light harvesting, edited by Dr. Roberta Croce.

Multidimensional Vibrational Coherence Spectroscopy.

Multidimensional vibrational coherence spectroscopy has been part of laser spectroscopy since the 1990s and its role in several areas of science has continuously been increasing. In this contribution, after introducing the principals of vibrational coherence spectroscopy (VCS), we review the three most widespread experimental methods for multidimensional VCS (multi-VCS), namely femtosecond stimulated Raman spectroscopy, pump-impulsive vibrational spectroscopy, and pump-degenerate four wave-mixing. Focus is given to the generation and typical analysis of the respective signals in the time and spectral domains. Critical aspects of all multidimensional techniques are the challenges in the data interpretation due to the existence of several possible contributions to the observed signals or to optical interferences and how to overcome the corresponding difficulties by exploiting experimental parameters including higher-order nonlinear effects. We overview how multidimensional vibrational coherence spectroscopy can assist a chemist in understanding how molecular structural changes and eventually photochemical reactions take place. In order to illustrate the application of the techniques described in this chapter, two molecular systems are discussed in more detail in regard to the vibrational dynamics in the electronic excited states: (1) carotenoids as a non-reactive system and (2) stilbene derivatives as a reactive system.

Introduction to State-of-the-Art Multidimensional Time-Resolved Spectroscopy Methods.

The field of multidimensional laser spectroscopy comprises a variety of highly developed state-of-the-art methods, which exhibit broad prospects for applications in several areas of natural, material, and even medical sciences. This collection summarizes the main achievements from this area and gives basic introductory insight into what is currently possible with such methods. In the present introductory contribution, we briefly outline the general concept behind multidimensional laser spectroscopy, for instance by highlighting the often-employed analogy between multidimensional laser spectroscopy and NMR methods. Our initial introduction is followed by an overview of the most important and widely used multidimensional spectroscopies' classification. Special emphasis is placed on how the contributing spectral region defines a natural way of grouping the techniques in terms of their information content. On this basis, we introduce the most important graphical ways in which multidimensional data is generally visualized. This is done by comparing specifically temporal and spectra axes that make up each single multidimensional data plot. Several central experimental methods that are common to the various techniques reviewed in this collection are addressed in the perspective of recent developments and their impact on the field. These methods include, for example, heterodyne/homodyne detection, fast scanning, spatial light modulation, and sparse sampling methods. Importantly, we address the central and fundamental questions where multidimensional ultrafast spectroscopy can be used to help understanding chemical dynamics and intermolecular interactions. Finally, we briefly pinpoint what we believe are the main open questions and what will be the future directions for technical developments and promotion of scientific understanding that multidimensional spectroscopy can provide for chemistry, physics, and life sciences.

Quick, sensitive serial NMR experiments with Radon transform.

The Radon transform is a potentially powerful tool for processing the data from serial spectroscopic experiments. It makes it possible to decode the rate at which frequencies of spectral peaks shift under the effect of changing conditions, such as temperature, pH, or solvent. In this paper we show how it also improves speed and sensitivity, especially in multidimensional experiments. This is particularly important in the case of low-sensitivity techniques, such as NMR spectroscopy. As an example, we demonstrate how Radon transform processing allows serial measurements of 15N-HSQC spectra of unlabelled peptides that would otherwise be infeasible.

Revealing true coupling strengths in two-dimensional spectroscopy with sparsity-based signal recovery.

Two-dimensional (2D) spectroscopy is used to study the interactions between energy levels in both the field of optics and nuclear magnetic resonance (NMR). Conventionally, the strength of interaction between two levels is inferred from the value of their common off-diagonal peak in the 2D spectrum, which is termed the cross peak. However, stronger diagonal peaks often have long tails that extend into the locations of the cross peaks and alter their values. Here, we introduce a method for retrieving the true interaction strengths by using sparse signal recovery techniques and apply our method in 2D Raman spectroscopy experiments.

Two-Dimensional Resonance Raman Signatures of Vibronic Coherence Transfer in Chemical Reactions.

Two-dimensional resonance Raman (2DRR) spectroscopy has been developed for studies of photochemical reaction mechanisms and structural heterogeneity in condensed phase systems. 2DRR spectroscopy is motivated by knowledge of non-equilibrium effects that cannot be detected with traditional resonance Raman spectroscopy. For example, 2DRR spectra may reveal correlated distributions of reactant and product geometries in systems that undergo chemical reactions on the femtosecond time scale. Structural heterogeneity in an ensemble may also be reflected in the 2D spectroscopic line shapes of both reactive and non-reactive systems. In this chapter, these capabilities of 2DRR spectroscopy are discussed in the context of recent applications to the photodissociation reactions of triiodide. We show that signatures of "vibronic coherence transfer" in the photodissociation process can be targeted with particular 2DRR pulse sequences. Key differences between the signal generation mechanisms for 2DRR and off-resonant 2D Raman spectroscopy techniques are also addressed. Overall, recent experimental developments and applications of the 2DRR method suggest that it will be a valuable tool for elucidating ultrafast chemical reaction mechanisms.

Two-Color Nonlinear Spectroscopy for the Rapid Acquisition of Coherent Dynamics.

There has been considerable recent interest in the observation of coherent dynamics in photosynthetic systems by 2D electronic spectroscopy (2DES). In particular, coherences that persist during the "waiting time" in a 2DES experiment have been attributed to electronic, vibrational, and vibronic origins in various systems. The typical method for characterizing these coherent dynamics requires the acquisition of 2DES spectra as a function of waiting time, essentially a 3DES measurement. Such experiments require lengthy data acquisition times that degrade the signal-to-noise of the recorded coherent dynamics. We present a rapid and high signal-to-noise pulse-shaping-based approach for the characterization of coherent dynamics. Using chlorophyll a, we demonstrate that this method retains much of the information content of a 3DES measurement and provides insight into the physical origin of the coherent dynamics, distinguishing between ground and excited state coherences. It also enables high resolution determination of ground and excited state frequencies.