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Physical Review A

Interpretation of optical three-dimensional coherent spectroscopy

Michael Titze, Hebin Li

Published Sep 12, 2017• 28 citations
Publisher

Abstract

As an extension to powerful two-dimensional coherent spectroscopy, optical three-dimensional (3D) coherent spectroscopy has been experimentally implemented and found beneficial in studying various systems in physics and chemistry. A critical challenge is how to interpret 3D spectra and extract useful quantitative information, given the richness and complexity of 3D data. Here, we demonstrate how the information of a system's optical response is manifested in 3D spectra by theoretical simulations of a few representative examples including a homogeneous three-level V system, an inhomogeneous three-level V system, and an inhomogeneous three-level ladder system. These examples show that important parameters of the system can be extracted from the spectral pattern, peak positions, amplitudes, and line shapes. The method developed here can be used to analyze 3D spectra of more sophisticated systems which might be a generalization or combination of the three examples, contributing to develop a general approach for the interpretation of 3D spectra.

DOI
10.1103/physreva.96.032508

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As an extension to powerful two-dimensional coherent spectroscopy, optical three-dimensional (3D) coherent spectroscopy has been experimentally implemented and found beneficial in studying various systems in physics and chemistry. A critical challenge is how to interpret 3D spectra and extract useful quantitative information, given the richness and complexity of 3D data. Here, we demonstrate how the information of a system's optical response is manifested in 3D spectra by theoretical simulations of a few representative examples including a homogeneous three-level V system, an inhomogeneous three-level V system, and an inhomogeneous three-level ladder system. These examples show that important parameters of the system can be extracted from the spectral pattern, peak positions, amplitudes, and line shapes. The method developed here can be used to analyze 3D spectra of more sophisticated systems which might be a generalization or combination of the three examples, contributing to develop a general approach for the interpretation of 3D spectra.
Optical multidimensional coherent spectroscopy is a powerful tool for studying structure and dynamics in complex systems, such as semiconductors. In optical two-dimensional coherent spectroscopy (2DCS), where the spectrum is presented in a two-dimensional (2D) plane with two frequency axes, an important advantage is the ability to isolate quantum pathways by unfolding a one-dimensional spectrum onto a 2D plane. For many systems, however, the quantum pathways are only partially separated in a 2D spectrum. In order to completely isolate the quantum pathways, we extend 2DCS into a third dimension to generate three-dimensional (3D) spectra in which the spectrum is further unfolded. A 3D spectrum provides complete and well-isolated information of the third-order optical response of the system. The information can be used to fully characterize the quantum pathways and to determine the system’s Hamiltonian. Quantitative knowledge of the Hamiltonian enables prediction and control of quantum processes. For instance, such information is essential for deterministic control and improved performance of coherent control schemes.
Double-quantum two-dimensional (2D) coherent spectroscopy (MDCS) is a powerful optical method that is used to study the optical properties of atomic and complex molecular systems and semiconductor materials. Double-quantum 2D spectra and particularly the peak line shapes on the spectra can also provide information about many-body interactions. We model 2D spectra by solving the optical Bloch equations and show the effects of correlation between coupled resonances, which also explains the discrepancies between the experimental results reported by multiple groups.
Predicting and controlling quantum mechanical phenomena require knowledge of the system Hamiltonian. A detailed understanding of the quantum pathways used to construct the Hamiltonian is essential for deterministic control and improved performance of coherent control schemes. In complex systems, parameters characterizing the pathways, especially those associated with inter-particle interactions and coupling to the environment, can only be identified experimentally. Quantitative insight can be obtained provided the quantum pathways are isolated and independently analysed. Here we demonstrate this possibility in an atomic vapour using optical three-dimensional Fourier-transform spectroscopy. By unfolding the system's nonlinear response onto three frequency dimensions, three-dimensional spectra unambiguously reveal transition energies, relaxation rates and dipole moments of each pathway. The results demonstrate the unique capacity of this technique as a powerful tool for resolving the complex nature of quantum systems. This experiment is a critical step in the pursuit of complete experimental characterization of a system's Hamiltonian.
Abstract This tutorial provides a joint theoretical and experimental overview of heterodyne wave mixing spectroscopy, focusing mainly on four-wave mixing (FWM). This powerful and versatile time-resolved nonlinear optical spectroscopy technique enables the investigation of individual localized single photon emitters, as well as microscopy of extended samples, e.g. two-dimensional transition metal dichalcogenides. Starting with the fundamental theory of optically driven two-level systems, we motivate the utility of wave mixing spectroscopy via a discussion on homogeneous and inhomogeneous linewidths which can be independently measured using FWM. We then provide a detailed overview of the heterodyne wave mixing setup operated by one of the authors (JK) at Institut Néel in Grenoble, supported by theoretical modeling of the signal detection process. Throughout the paper we elaborate on important benefits of heterodyne wave mixing spectroscopy, e.g. background-free detection, measurement of the full signal field including amplitude and phase, and investigation of coupling mechanisms in few-level systems. Within the context of the latter point we discuss the significance of two-dimensional FWM spectra. This tutorial is dedicated to students, young researchers, as well as experts in the field of nonlinear spectroscopy in general and FWM in particular. It explains the fundamental concepts and building blocks required to operate a heterodyne wave mixing experiment both from the experimental and theoretical side. This joint approach is helpful for theoreticians who want to accurately and quantitatively model wave mixing signals, as well as for experimentalists who aim to interpret their recorded data.
Multidimensional coherent spectroscopy (MDCS) has been established in quantum chemistry as a powerful tool for studying the nonlinear response and nonequilibrium dynamics of molecular systems. More recently, the technique has also been applied to correlated electron materials, where the interplay of localized and itinerant states makes the interpretation of the spectra more challenging. Here we use the Keldysh contour representation of effective models and nonequilibrium dynamical mean field theory to systematically study the MDCS signals of prototypical correlated lattice systems. By analyzing the current induced by sequences of ultrashort laser pulses we demonstrate the usefulness of MDCS as a diagnostic tool for excitation pathways and coherent processes in correlated solids. We also show that this technique allows to extract detailed information on the nature and evolution of photo-excited nonequilibrium states.