Stochastic Liouville equations for coherent multidimensional spectroscopy of excitons

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.

Correlated spectral fluctuations quantified by line shape analysis of fifth-order two-dimensional electronic spectra

Correlated spectral fluctuations were suggested to coordinate excitation transport inside natural light harvesting complexes. We demonstrate the capacities of 2D line shapes from fifth-order coherent electronic signals (R5-2D) to report on such fluctuations in molecular aggregates and present a stochastic approach to fluctuations in correlated site and bi-exciton binding energies in the optical dynamics of Frenkel excitons. The model is applied to R5-2D line shapes of a homodimer, and we show that the peak tilt dynamics are a measure for site energy disorder, inter-site correlation, and the strength of bi-exciton binding energy fluctuations.

Anharmonic Molecular Motion Drives Resonance Energy Transfer in peri-Arylene Dyads

Spectral and dynamical properties of molecular donor-acceptor systems strongly depend on the steric arrangement of the constituents with exciton coupling J as a key control parameter. In the present work we study two peri-arylene based dyads with orthogonal and parallel transition dipoles for donor and acceptor moieties, respectively. We show that the anharmonic multi-well character of the orthogonal dyad's intramolecular potential explains findings from both stationary and time-resolved absorption experiments. While for a parallel dyad, standard quantum chemical estimates of J at 0 K are in good agreement with experimental observations, J becomes vanishingly small for the orthogonal dyad, in contrast to its ultrafast experimental transfer times. This discrepancy is not resolved even by accounting for harmonic fluctuations along normal coordinates. We resolve this problem by supplementing quantum chemical approaches with dynamical sampling of fluctuating geometries. In contrast to the moderate Gaussian fluctuations of J for the parallel dyad, fluctuations for the orthogonal dyad are found to follow non-Gaussian statistics leading to significantly higher effective J in good agreement with experimental observations. In effort to apply a unified framework for treating the dynamics of optical coherence and excitonic populations of both dyads, we employ a vibronic approach treating electronic and selected vibrational degrees on an equal footing. This vibronic model is used to model absorption and fluorescence spectra as well as donor-acceptor transport dynamics and covers the more traditional categories of Förster and Redfield transport as limiting cases.

Polariton-Assisted Cooperativity of Molecules in Microcavities Monitored by Two-Dimensional Infrared Spectroscopy

Molecular polaritons created by the strong coupling between matter and field in microcavities enable the control of molecular dynamical processes and optical response. Multidimensional infrared spectroscopy is proposed for monitoring the polariton-assisted cooperative properties. The response of molecules to local fluctuations is incorporated and the full dynamics is monitored through the time- and frequency-resolved multidimensional signal. The cooperativity against solvent-induced disorder and its connection to the localization of the vibrational excitations are predicted. New insights are provided for recent 2DIR experiments on vibrational polaritons.

Center Line Slope Analysis in Two-Dimensional Electronic Spectroscopy

Center line slope (CLS) analysis in 2D infrared spectroscopy has been extensively used to extract frequency–frequency correlation functions of vibrational transitions. We apply this concept to 2D electronic spectroscopy, where CLS is a measure of electronic gap fluctuations. The two domains, infrared and electronic, possess differences: In the infrared, the frequency fluctuations are classical, often slow and Gaussian. In contrast, electronic spectra are subject to fast spectral diffusion and affected by underdamped vibrational wavepackets in addition to Stokes shift. All these effects result in non-Gaussian peak profiles. Here, we extend CLS-analysis beyond Gaussian line shapes and test the developed methodology on a solvated molecule, zinc phthalocyanine. We find that CLS facilitates the interpretation of 2D electronic spectra by reducing their complexity to one dimension. In this way, CLS provides a highly sensitive measure of model parameters describing electronic–vibrational and electronic–solvent interaction.

Stochastic Liouville equations for femtosecond stimulated Raman spectroscopy

Electron and vibrational dynamics of molecules are commonly studied by subjecting them to two interactions with a fast actinic pulse that prepares them in a nonstationary state and after a variable delay period T, probing them with a Raman process induced by a combination of a broadband and a narrowband pulse. This technique, known as femtosecond stimulated Raman spectroscopy (FSRS), can effectively probe time resolved vibrational resonances. We show how FSRS signals can be modeled and interpreted using the stochastic Liouville equations (SLE), originally developed for NMR lineshapes. The SLE provide a convenient simulation protocol that can describe complex dynamics caused by coupling to collective bath coordinates at much lower cost than a full dynamical simulation. The origin of the dispersive features that appear when there is no separation of timescales between vibrational variations and the dephasing time is clarified.

Quantum process tomography quantifies coherence transfer dynamics in vibrational exciton

Quantum coherence has been a subject of great interest in many scientific disciplines. However, detailed characterization of the quantum coherence in molecular systems, especially its transfer and relaxation mechanisms, still remains a major challenge. The difficulties arise in part because the spectroscopic signatures of the coherence transfer are typically overwhelmed by other excitation-relaxation processes. We use quantum process tomography (QPT) via two-dimensional infrared spectroscopy to quantify the rate of the elusive coherence transfer between two vibrational exciton states. QPT retrieves the dynamics of the dissipative quantum system directly from the experimental observables. It thus serves as an experimental alternative to theoretical models of the system-bath interaction and can be used to validate these theories. Our results for coupled carbonyl groups of a diketone molecule in chloroform, used as a benchmark system, reveal the nonsecular nature of the interaction between the exciton and the Markovian bath and open the door for the systematic studies of the dissipative quantum systems dynamics in detail.

Novel coherent two-dimensional optical spectroscopy probes of chirality exchange and fluctuations in molecules

We demonstrate how stochastic transitions between molecular configurations with opposite senses of chirality may be probed by 2D optical signals with specific pulse polarization configurations. The third-order optical response of molecular dimers (such as biphenyls) with dynamical axial chirality is calculated to order of k(2) in the wavevector of light. Spectroscopic signatures of equilibrium chirality fluctuations are predicted for three dynamical models (Ornstein-Uhlenbeck, two-state jump, and diffusion in double well) of the dihedral angle that controls the chirality.

Exciton coherence length fluctuations in chromophore aggregates probed by multidimensional optical spectroscopy

The coherent third order optical response of molecular aggregates with fluctuating frequencies, couplings, and transition dipole moments is studied. We derived stochastic nonlinear exciton equations (SNEEs) by combining the quasiparticle picture of excitons with the path integral over stochastic bath paths described by the stochastic Liouville equations. Coherent two-dimensional (2D) spectra are calculated for a tetramer model system whose transition dipole orientations undergo two-state stochastic jumps on an arbitrary timescale. Correspondence between domains of ordered dipoles, which determine the exciton coherence length and the absorption peaks, is established. Signatures of domain coherence length fluctuations are observed in the cross peak dynamics of the 2D spectra in specific pulse polarization configurations.