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

Coherence in Chemistry: Foundations and Frontiers

Coherence refers to correlations in waves. Because matter has a wave-particle nature, it is unsurprising that coherence has deep connections with the most contemporary issues in chemistry research (e.g., energy harvesting, femtosecond spectroscopy, molecular qubits and more). But what does the word "coherence" really mean in the context of molecules and other quantum systems? We provide a review of key concepts, definitions, and methodologies, surrounding coherence phenomena in chemistry, and we describe how the terms "coherence" and "quantum coherence" refer to many different phenomena in chemistry. Moreover, we show how these notions are related to the concept of an interference pattern. Coherence phenomena are indeed complex, and ambiguous definitions may spawn confusion. By describing the many definitions and contexts for coherence in the molecular sciences, we aim to enhance understanding and communication in this broad and active area of chemistry.

Two-dimensional coherent electronic spectrometer with switchable multi-color configurations

Broadband implementation of two-dimensional electronic spectroscopy (2DES) is a desirable goal for numerous research groups, yet achieving it presents considerable challenges. An effective strategy to mitigate these challenges is the utilization of two-color approaches, effectively broadening the spectral bandwidth accessible with 2DES. Here, we present a simple approach to include multi-color configurations based on adjustable mirror mounts. This enables seamless toggling between single-color, two-color, and transient 2DES within the same spectroscopic apparatus, which is benchmarked on two common laser dyes, Rhodamine 6G and Nile blue. Upon mixing the dyes, single-color 2DES shows overlapping signals, whereas a high selectivity toward Nile blue responses is maintained in two-color and transient 2DES, owing to the fully resonant excitation that is spectrally shifted relative to the detection window. This method is readily implemented in other setups with similar experimental layouts and can be used as a simple solution to overcome existing bandwidth limitations. With the inclusion of transient 2DES, additional insights into excited-state processes can be gained due to its increased sensitivity toward excited-state coherences.

Higher-Order Multidimensional and Pump-Probe Spectroscopies

Transient absorption and coherent two-dimensional spectroscopy are widely established methods for the investigation of ultrafast dynamics in quantum systems. Conventionally, they are interpreted in the framework of perturbation theory at the third order of interaction. Here, we discuss the potential of higher-(than-third-)order pump-probe and multidimensional spectroscopy to provide insight into excited multiparticle states and their dynamics. We focus on recent developments from our group. In particular, we demonstrate how phase cycling can be used in fluorescence-detected two-dimensional spectroscopy to isolate higher-order spectra that provide information about highly excited states such as the correlation of multiexciton states. We discuss coherently detected fifth-order 2D spectroscopy and its power to track exciton diffusion. Finally, we show how to extract higher-order signals even from ordinary pump-probe experiments, providing annihilation-free signals at high excitation densities and insight into multiexciton interactions.

Unifying Nonlinear Response and Incoherent Mixing in Action-2D Electronic Spectroscopy

Action-detection has expanded the scope and applicability of 2D electronic spectroscopy, while posing new challenges for the unambiguous interpretation of spectral features. In this context, identifying the origin of cross-peaks at early waiting times is not trivial, and incoherent mixing is often invoked as an unwanted contribution masking the nonlinear signal. In this work, we elaborate on the relation between the nonlinear response and the incoherent mixing contribution by analyzing the action signal in terms of one- and two-particle observables. Considering a weakly interacting molecular dimer, we show how cross-peaks at early waiting times, reflecting exciton-exciton annihilation dynamics, can be equivalently interpreted as arising from incoherent mixing. This equivalence, on the one hand, highlights the information content of spectral features related to incoherent mixing and, on the other hand, provides an efficient numerical scheme to simulate the action response of weakly interacting systems.

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.

Theory of two-dimensional spectroscopy with intense laser fields

Two-dimensional vibrational and electronic spectroscopic observables of isotropically oriented molecular samples in solution are sensitive to laser field intensities and polarization. The third-order response function formalism predicts a signal that grows linearly with the field strength of each laser pulse, thus lacking a way of accounting for non-trivial intensity-dependent effects, such as saturation and finite bleaching. An analytical expression to describe the orientational part of the molecular response, which, in the weak-field limit, becomes equivalent to a four-point correlation function, is presented. Such an expression is evaluated for Liouville-space pathways accounting for diagonal and cross peaks for all-parallel and cross-polarized pulse sequences, in both the weak- and strong-field conditions, via truncation of a Taylor series expansion at different orders. The results obtained in the strong-field conditions suggest how a careful analysis of two-dimensional spectroscopic experimental data should include laser pulse intensity considerations when determining molecular internal coordinates.