Wavelet analysis of molecular dynamics: Efficient extraction of time-frequency information in ultrafast optical processes

Dynamics of diverse coherences in primary charge separation of bacterial reaction center at 77 K revealed by wavelet analysis

To uncover the mechanism behind the high photo-electronic conversion efficiency in natural photosynthetic complexes it is essential to trace the dynamics of electronic and vibrational quantum coherences. Here we apply wavelet analysis to two-dimensional electronic spectroscopy data for three purple bacterial reaction centers with mutations that produce drastically different rates of primary charge separation. From the frequency distribution and dynamic evolution features of the quantum beating, electronic coherence with a dephasing lifetime of ~50 fs, vibronic coherence with a lifetime of ~150 fs and vibrational/vibronic coherences with a lifetime of 450 fs are distinguished. We find that they are responsible for, or couple to, different specific steps during the primary charge separation process, i.e., intradimer charge transfer inside the special bacteriochlorophyll pair followed by its relaxation and stabilization of the charge-transfer state. The results enlighten our understanding of how quantum coherences participate in, and contribute to, a biological electron transfer reaction.

Signatures of exciton dynamics and interaction in coherently and fluorescence-detected four- and six-wave-mixing two-dimensional electronic spectroscopy

Two-dimensional electronic spectroscopy (2DES) can be realized in increasing nonlinear orders of interaction with the electric field, bringing new information about single- and multi-particle properties and dynamics. Furthermore, signals can be detected both coherently (C-2DES) and by fluorescence (F-2DES), with fundamental and practical differences. We directly compare the simultaneous measurements of four- and six-wave mixing C-2DES and F-2DES on an excitonic heterodimer of squaraine molecules. Spectral features are described in increasing orders of nonlinearity by an explicit excitonic model. We demonstrate that the four-wave-mixing spectra are sensitive to one-exciton energies, their delocalization and dynamics, while the six-wave-mixing spectra include information on bi-exciton and higher excited states including the state energies, electronic coupling, and exciton-exciton annihilation. We focus on the possibility to extract the dynamics arising from exciton-exciton interaction directly from the six-wave-mixing spectra. To this end, in analogy to previously demonstrated fifth-order coherently detected exciton-exciton-interaction 2DES (EEI2D spectroscopy), we introduce a sixth-order fluorescence-detected EEI2D spectroscopy variant.

Room-Temperature Ferroelectric LiNb6Ba5Ti4O30 Spinel Phase in a Nanocomposite Thin Film Form for Nonlinear Photonics

Tetragonal tungsten bronze (TTB) materials are one of the most promising classes of materials for ferroelectric and nonlinear optical devices, owing to their very unique noncentrosymmetric crystal structure. In this work, a new TTB phase of LiNb₆Ba₅Ti₄O₃₀ (LNBTO) has been discovered and studied. A small amount of a secondary phase, LiTiO₂ (LTO), has been incorporated as nanopillars that are vertically embedded in the LNBTO matrix. The new multifunctional nanocomposite thin film presents exotic highly anisotropic microstructure and properties, e.g., strong ferroelectricity, high optical transparency, anisotropic dielectric function, and strong optical nonlinearity evidenced by the second harmonic generation results. An optical waveguide structure based on the stacks of α-Si on SiO₂/LNBTO-LTO has been fabricated, exhibiting low optical dispersion with an optimized evanescent field staying in the LNBTO-LTO active layer. This work highlights the combination of new TTB material designs and vertically aligned nanocomposite structures for further enhanced anisotropic and nonlinear properties.

Optimization and selection of time-frequency transforms for wave-packet analysis in ultrafast spectroscopy

The analysis of quantum beats in time-resolved spectroscopic signals is becoming a task of primary importance because it is now clear that they bring crucial information about chemical reactivity, transport, and relaxation processes. Here we describe how to exploit the wide family of time-frequency transform methodologies to obtain information not only about the frequency but also about the dynamics of the oscillating components contributing to the overall beating signal. Several linear and bilinear transforms have been considered, and a general and easy procedure to judge in a non-arbitrary way the performances of different transforms has been outlined.

Coherence in carotenoid-to-chlorophyll energy transfer

The subtle details of the mechanism of energy flow from carotenoids to chlorophylls in biological light-harvesting complexes are still not fully understood, especially in the ultrafast regime. Here we focus on the antenna complex peridinin–chlorophyll a–protein (PCP), known for its remarkable efficiency of excitation energy transfer from carotenoids—peridinins—to chlorophylls. PCP solutions are studied by means of 2D electronic spectroscopy in different experimental conditions. Together with a global kinetic analysis and multiscale quantum chemical calculations, these data allow us to comprehensively address the contribution of the potential pathways of energy flow in PCP. These data support dominant energy transfer from peridinin S₂ to chlorophyll Q_y state via an ultrafast coherent mechanism. The coherent superposition of the two states is functional to drive population to the final acceptor state, adding an important piece of information in the quest for connections between coherent phenomena and biological functions.

Energy transfer from carotenoids to chlorophylls in light-harvesting is still not fully understood, especially in the ultrafast regime. Here, the authors investigate the coherent dynamics of this process in peridinin-chlorophyll a-protein complex via 2D electronic spectroscopy and quantum chemical calculations.

Exciton-vibrational resonance and dynamics of charge separation in the photosystem II reaction center

The dynamics of charge separation in the photosystem II reaction center (PSII-RC) in the presence of intramolecular vibrations with their frequency matching the energy gap between the exciton state acting as the primary electron donor and the first charge-transfer (CT) state are investigated. A reduced PSII-RC 4-state model explicitly including a CT state is analyzed within Redfield relaxation theory in the multidimensional exciton-vibrational (vibronic) basis. This model is used to study coherent energy/electron transfers and their spectral signatures obtained by two-dimensional electronic spectroscopy (2DES). Modeling of the time-resolved 2D frequency maps obtained by wavelet analysis reveals the origins of the coherences which produce the observed oscillating features in 2DES and allows comparing the lifetimes of the coherences. The results suggest faster excitonic decoherence as compared with longer-lived vibronic oscillations. The emerging picture of the dynamics unravels the role of resonant vibrations in sustaining the effective energy conversion in the PSII-RC. We demonstrate that the mixing of the exciton and CT states promoted by a resonant vibrational quantum allows faster penetration of excitation energy into the CT with subsequent dynamic localization at the bottom of the CT potential induced by the remaining non-resonant nuclear modes. The degree of vibration-assisted mixing and, correspondingly, the rate of primary charge separation, increases significantly in the case of electron-vibrational resonance. The observed features illustrate the principles of quantum design of the photosynthetic unit. These principles are connected with the phenomenon of coherent mixing within vibronic eigenstates, increasing the effectiveness of charge separation not only upon coherent and impulsive laser excitation utilized in the 2DES experiment, but also under natural conditions under non-coherent non-impulsive solar light illumination.

Quantum - coherent dynamics in photosynthetic charge separation revealed by wavelet analysis

Experimental/theoretical evidence for sustained vibration-assisted electronic (vibronic) coherence in the Photosystem II Reaction Center (PSII RC) indicates that photosynthetic solar-energy conversion might be optimized through the interplay of electronic and vibrational quantum dynamics. This evidence has been obtained by investigating the primary charge separation process in the PSII RC by two-dimensional electronic spectroscopy (2DES) and Redfield modeling of the experimental data. However, while conventional Fourier transform analysis of the 2DES data allows oscillatory signatures of vibronic coherence to be identified in the frequency domain in the form of static 2D frequency maps, the real-time evolution of the coherences is lost. Here we apply for the first time wavelet analysis to the PSII RC 2DES data to obtain time-resolved 2D frequency maps. These maps allow us to demonstrate that (i) coherence between the excitons initiating the two different charge separation pathways is active for more than 500 fs, and (ii) coherence between exciton and charge-transfer states, the reactant and product of the charge separation reaction, respectively; is active for at least 1 ps. These findings imply that the PSII RC employs coherence (i) to sample competing electron transfer pathways, and ii) to perform directed, ultrafast and efficient electron transfer.

Global analysis of coherence and population dynamics in 2D electronic spectroscopy

2D electronic spectroscopy is a widely exploited tool to study excited state dynamics. A high density of information is enclosed in 2D spectra. A crucial challenge is to objectively disentangle all the features of the third order optical signal. We propose a global analysis method based on the variable projection algorithm, which is able to reproduce simultaneously coherence and population dynamics of rephasing and non-rephasing contributions. Test measures at room temperature on a standard dye are used to validate the procedure and to discuss the advantages of the proposed methodology with respect to the currently employed analysis procedures.

Slow Intramolecular Vibrational Relaxation Leads to Long-Lived Excited-State Wavepackets

Broadband optical pump and compressed white light continuum probe were used to measure the transient excited-state absorption, ground-state bleach, and stimulated emission signals of cresyl violet solution in methanol. Amplitude oscillations caused by wavepacket motion in the ground and excited electronic states were analyzed. It was found that vibrational coherences in the excited state persist for more than the experimental waiting time window of 6 ps, and the strongest mode had a dephasing time constant of 2.4 ps. We hypothesize the dephasing of the wavepacket in the excited state is predominantly caused by intramolecular vibrational relaxation (IVR). Slow IVR indicates weak mode-mode coupling and therefore weak anharmonicity of the potential of this vibration. Thus, the initially prepared vibrational wavepacket in the excited state is not significantly perturbed by nonadiabatic coupling to other electronic states, and hence the diabatic and adiabatic representations of the system are essentially identical within the Born-Oppenheimer approximation. The wavepacket therefore evolves with time in an almost harmonic potential, slowly dephased by IVR and the pure vibrational decoherence. The consistency in the position of node (phase change in the wavepacket) in the excited-state absorption and stimulated emission signals without undergoing any frequency shift until the wavepacket is completely dephased conforms to the absence of any reactive internal conversion.

Observing Vibrational Wavepackets during an Ultrafast Electron Transfer Reaction

Recent work has proposed that coherent effects impact ultrafast electron transfer reactions. Here we report studies using broadband pump-probe and two-dimensional electronic spectroscopy of intramolecular nuclear motion on the time scale of the electron transfer between oxazine 1 (Ox1) and dimethylaniline (DMA). We performed time-frequency analysis on the time domain data to assign signal amplitude modulations to ground or excited electronic states in the reactive system (Ox1 in DMA) relative to the control system (Ox1 in chloronaphthalene). It was found that our ability to detect vibrational coherence via the excited electronic state of Ox1 diminishes on the time scale that population is lost by electron transfer. However, the vibrational wavepacket is not damped by the electron transfer process and has been observed previously by detecting the Ox1 radical transient absorption. The analysis presented here indicates that the "addition" of an electron to the photoexcited electron acceptor does not significantly perturb the vibrational coherence, suggesting its presence as a spectator, consistent with the Born-Oppenheimer separation of electronic and nuclear degrees of freedom.

Exploring laser-driven quantum phenomena from a time-frequency analysis perspective: a comprehensive study

Time-frequency (TF) analysis is a powerful tool for exploring ultrafast dynamics in atoms and molecules. While some TF methods have demonstrated their usefulness and potential in several quantum systems, a systematic comparison among them is still lacking. To this end, we compare a series of classical and contemporary TF methods by taking hydrogen atom in a strong laser field as a benchmark. In addition, several TF methods such as Cohen class distribution other than the Wigner-Ville distribution, reassignment methods, and the empirical mode decomposition method are first introduced to exploration of ultrafast dynamics. Among these TF methods, the synchrosqueezing transform successfully illustrates the physical mechanisms in the multiphoton ionization regime and in the tunneling ionization regime. Furthermore, an empirical procedure to analyze an unknown complicated quantum system is provided, suggesting the versatility of TF analysis as a new viable venue for exploring quantum dynamics.

Time-frequency methods for coherent spectroscopy

Time-frequency decomposition techniques, borrowed from the signal-processing field, have been adapted and applied to the analysis of 2D oscillating signals. While the Fourier-analysis techniques available so far are able to interpret the information content of the oscillating signal only in terms of its frequency components, the time-frequency transforms (TFT) proposed in this work can instead provide simultaneously frequency and time resolution, unveiling the dynamics of the relevant beating components, and supplying a valuable help in their interpretation. In order to fully exploit the potentiality of this method, several TFTs have been tested in the analysis of sample 2D data. Possible artifacts and sources of misinterpretation have been identified and discussed.