Effects of finite laser pulse width on two-dimensional electronic spectroscopy

Simulation of the Pump-Probe Spectra and Excitation Energy Relaxation of the B850 Band of the LH2 Complex in Purple Bacteria

Ultrafast spectroscopic techniques have been vital in studying excitation energy transfer (EET) in photosynthetic light harvesting complexes. In this paper, we simulate the pump-probe spectra of the B850 band of the light harvesting complex 2 (LH2) of purple bacteria, by using the hierarchical equation of motion method and the optical response function approach. The ground state bleach, stimulated emission, and excited state absorption components of the pump-probe spectra are analyzed in detail. The laser pulse-induced population dynamics are also simulated to help understand the main features of the pump-probe spectra and the EET process. It is shown that the excitation energy relaxation is an ultrafast process with multiple time scales. The first 40 fs of the pump-probe spectra is dominated by the relaxation of the k = ±1 states to both the k = 0 and higher energy states. Dynamics on a longer time scale around 200 fs reflects the relaxation of higher energy states to the k = 0 state.

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.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Time-dependent simulation of photocurrent-detected two-dimensional spectroscopy of open systems

A new time-domain simulation protocol of two-dimensional electronic spectra with photocurrent detection is presented. Time-dependent density functional theory for open systems at finite temperature is applied to evaluate the photocurrent response to four laser pulses, and a non-perturbative phase-matching approach is implemented to extract the fourth-order photocurrent signal with a desired phase-matching condition. Simulations for an open three-level model indicates that transition dipoles interact resonantly with the incident pulses and that different sample-electrode couplings may be identified by appearance of different peaks/valleys in photocurrent spectra from different electrodes. Moreover, qualitative reproduction of experimental spectra of a PbS quantum dot photocell [Karki et al., Nat. Commun. 5(1), 5869 (2014)] reveals the stimulated electron dynamics.

A quantum Langevin equation approach for two-dimensional electronic spectra of coupled vibrational and electronic dynamics

We present an efficient method to simulate two-dimensional (2D) electronic spectra of condensed-phase systems with an emphasis on treating quantum nuclear wave packet dynamics explicitly. To this end, we combine a quantum Langevin equation (QLE) approach for dissipation and a perturbative scheme to calculate three-pulse photon-echo polarizations based on wave packet dynamics under the influence of external fields. The proposed dynamical approach provides a consistent description of nuclear quantum dynamics, pulse-overlap effects, and vibrational relaxation, enabling simulations of 2D electronic spectra with explicit and non-perturbative treatment of coupled electronic-nuclear dynamics. We apply the method to simulate 2D electronic spectra of a displaced-oscillator model in the condensed phase and discuss the spectral and temporal evolutions of 2D signals. Our results show that the proposed QLE approach is capable of describing vibrational relaxation, decoherence, and vibrational coherence transfer, as well as their manifestations in spectroscopic signals. Furthermore, vibrational quantum beats specific for excited-state vs ground-state nuclear wave packet dynamics can also be identified. We anticipate that this method will provide a useful tool to conduct theoretical studies of 2D spectroscopy for strong vibronically coupled systems and to elucidate intricate vibronic couplings in complex molecular systems.

Two-dimensional spectroscopy beyond the perturbative limit: The influence of finite pulses and detection modes

Ultra-fast and multi-dimensional spectroscopy gives a powerful looking glass into the dynamics of molecular systems. In particular, two-dimensional electronic spectroscopy (2DES) provides a probe of coherence and the flow of energy within quantum systems, which is not possible with more conventional techniques. While heterodyne-detected (HD) 2DES is increasingly common, more recently fluorescence-detected (FD) 2DES offers new opportunities, including single-molecule experiments. However, in both techniques, it can be difficult to unambiguously identify the pathways that dominate the signal. Therefore, the use of numerically modeling of 2DES is vitally important, which, in turn, requires approximating the pulsing scheme to some degree. Here, we employ non-perturbative time evolution to investigate the effects of finite pulse width and amplitude on 2DES signals. In doing so, we identify key differences in the response of HD and FD detection schemes, as well as the regions of parameter space where the signal is obscured by unwanted artifacts in either technique. Mapping out parameter space in this way provides a guide to choosing experimental conditions and also shows in which limits the usual theoretical approximations work well and in which limits more sophisticated approaches are required.

Automatic Feynman diagram generation for nonlinear optical spectroscopies and application to fifth-order spectroscopy with pulse overlaps

Perturbative nonlinear optical spectroscopies are powerful methods to understand the dynamics of excitonic and other condensed phase systems. Feynman diagrams have long provided the essential tool to understand and interpret experimental spectra and to organize the calculation of spectra for model systems. When optical pulses are strictly time ordered, only a small number of diagrams contribute, but in many experiments, pulse-overlap effects are important for interpreting results. When pulses overlap, the number of contributing diagrams can increase rapidly, especially with higher order spectroscopies, and human error is especially likely when attempting to write down all the diagrams. We present an automated Diagram Generator (DG) that generates all the Feynman diagrams needed to calculate any nth-order spectroscopic signal. We characterize all perturbative nonlinear spectroscopies by their associated phase-discrimination condition as well as the time intervals where pulse amplitudes are nonzero. Although the DG can be used to automate impulsive calculations, its greatest strength lies in automating finite pulse calculations where pulse overlaps are important. We consider third-order transient absorption spectroscopy and fifth-order exciton-exciton interaction 2D (EEI2D) spectroscopy, which are described by six or seven diagrams in the impulsive limit, respectively, but 16 or 240 diagrams, respectively, when pulses overlap. The DG allows users to automatically include all relevant diagrams at a relatively low computational cost, since the extra diagrams are only generated for the inter-pulse delays where they are relevant. For EEI2D spectroscopy, we show the important effects of including the overlap diagrams.

Investigation of Laser Power Output and Its Effect on Raman Spectrum for Marine Metal Corrosion Cleaning

The relationship between the laser power output and its effect on Raman spectrum is investigated for a laser cleaning application of marine metal corrosion processing. First, an image feature based on a corrosion degree evaluation is implemented before cleaning. The image features include texture coarseness, texture entropy, texture intensity, texture contrast, the texture’s cluster degree, and texture homogeneity. To decrease the image feature dimension for a convenient application, the Analytic Hierarchy Process (AHP) method is used to estimate the weight of each feature. Then the linear weighted sum of image features can be computed to get only one evaluation result. Second, a series of laser power outputs are implemented for the cleaning application under a typical corrosion degree. Then the analysis results of Raman spectrum can be obtained. The analyzed spectrum results include the corrosion components and their contents. Lastly, the relationship between laser power output and Raman spectrum under a typical initial corrosion degree can be constructed. This research study can build the prediction result of the cleaning effect map for the workpiece and guide the secondary processing of metal surface cleaning.

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.

Correction of spectral distortion in two-dimensional electronic spectroscopy arising from the wedge-based delay line

Unlike the probe wavelength, which is spectrally resolved by monochromator, the excitation wavelength in two-dimensional electronic spectroscopy is retrieved by means of Fourier transform of the interference signal introduced by the coherence delay time between the first and second excitation laser pulses. Hence, the calibration of delay lines would determine its accuracy. In this work, we showed that an inaccurate calibration factor of wedge-based delay line would result in a global peak shift and asymmetric spectral twists along the excitation axis. Both theoretical analysis and experiments have shown that such spectral distortions can be corrected by an accurately predetermined calibration factor. The relative accuracy of calibration factor reaches 3 × 10^-5 in our setup. The dispersion effect of wedges also has been considered for the broadband excitation.

One- to Two-Exciton Transitions in Perylene Bisimide Dimer Revealed by Two-Dimensional Electronic Spectroscopy

The excited-state energy levels of molecular dimers and aggregates play a critical role in their photophysical behavior and an understanding of the photodynamics in such structures is important for developing applications such as photovoltaics and optoelectronic devices. Here, exciton transitions in two different covalently bound PBI dimers are studied by two-dimensional electronic spectroscopy (2DES), a powerful spectroscopic method, providing the most complete picture of vibronic transitions in molecular systems. The data are accurately reproduced using the equation of motion-phase matching approach. The unambiguous presence of one-exciton to two-exciton transitions are captured in our results and described in terms of a molecular exciton energy level scheme based on the Kasha model. Furthermore, the results are supported by comparative measurements with the PBI monomer and another dimer in which the interchromophore distance is increased.

Spectral Filtering as a Tool for Two-Dimensional Spectroscopy: A Theoretical Model

Two-dimensional optical spectroscopy is a powerful technique for the probing of coherent quantum superpositions. Recently, the finite width of the laser spectrum has been employed to selectively tune experiments for the study of particular coherences. This involves the exclusion of certain transition frequencies, which results in the elimination of specific Liouville pathways. The rigorous analysis of such experiments requires the use of ever more sophisticated theoretical models for the optical spectroscopy of electronic and vibronic systems. Here we develop a nonimpulsive and non-Markovian model, which combines an explicit definition of the laser spectrum, via the equation of motion-phase matching approach (EOM-PMA), with the hierarchical equations of motion (HEOM). This theoretical framework is capable of simulating the 2D spectroscopy of vibronic systems with low frequency modes, coupled to environments of intermediate and slower time scales. In order to demonstrate the spectral filtering of vibronic coherences, we examine the elimination of lower energy peaks from the 2D spectra of a zinc porphyrin monomer upon blue-shifting the laser spectrum. The filtering of Liouville pathways is revealed through the disappearance of peaks from the amplitude spectra for a coupled vibrational mode.

The origin of absorptive features in the two-dimensional electronic spectra of rhodopsin

A three-state three-mode model Hamiltonian reveals the origin of the absorptive features in the two-dimensional electronic spectra of rhodopsin.