Abstract An introduction to multidimensional coherent spectroscopy (MDCS) is provided in this chapter. We start out by introducing MDCS in qualitative terms, as an extension of transient absorption spectroscopy. We proceed to discuss the meaning and utility of coherent spectroscopy more generally. We go on to discuss the specifics of MDCS as a specific form of coherent spectroscopy. Pulse sequences involved in generating MDCS plots are introduced. Finally, we discuss density matrix perturbation theory and double-sided Feynman diagrams, and the role of this formalism in simulating and interpreting MDCS.
Coherent multidimensional spectroscopy enables detailed investigations of vibronic effects in molecular and solid-state systems. We present explicit analytical expressions for multidimensional nonlinear response functions in the presence of Herzberg-Teller (non-Condon) coupling, within the displaced harmonic oscillator model. The formulation applies to electronic systems with an arbitrary number N of electronic states and to response functions of arbitrary order M in the light-matter interaction. We show that Herzberg-Teller coupling introduces additional oscillatory factors in the time-domain response functions, leading, upon Fourier transformation, to replicas of the Franck-Condon multidimensional spectra shifted by integer multiples of the vibrational frequencies. The present results provide a general analytical framework for the interpretation of non-Condon effects in coherent multidimensional spectroscopies. A Python code that implements the present approach and simulates multidimensional spectra for N-level systems is available on GitHub.
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.
Multidimensional spectroscopy has become an established tool for disentangling microscopic processes that remain unresolved in conventional linear spectroscopy. Its extension to the terahertz regime now enables analogous questions to be addressed for low-energy collective excitations in quantum materials and synthetic many-body systems. Unlike isolated few-level systems, however, these collective modes generally cannot be described within the standard framework of nonlinear spectroscopy based on a few-level description. Their response is instead governed by their extended nature, interplay of interactions, fluctuations, disorder, dissipation, and coupling to additional degrees of freedom. This thesis develops a theoretical framework for computing and interpreting multidimensional nonlinear spectroscopy in quantum many-body systems. Using real-time nonequilibrium field theory, we formulate nonlinear susceptibilities diagrammatically in terms of propagators, interaction vertices, and self-energies, with particular emphasis on the third-order susceptibility relevant to infrared-active collective excitations. This approach places the established concepts and capabilities of multidimensional spectroscopy within a systematic many-body field-theoretical framework. Furthermore, this formulation makes it possible to move beyond the established probing capabilities, extending multidimensional spectroscopy beyond few-level descriptions and revealing new signatures and functionalities specific to interacting many-body systems. At the same time, it provides a controlled framework for constructing approximations that preserve the underlying symmetries and conservation laws of the system while remaining amenable to both analytical and numerical calculations. By incorporating quantum and thermal fluctuations within the random-phase approximation, we demonstrate that two-dimensional spectra can reveal the growth of fluctuations, identify field-theoretical bound states, and characterize their coupling to many-body continua. We further develop a diagrammatic description of rephasing in extended bosonic systems in the presence of static disorder. We identify the disorder vertex corrections responsible for echo formation and show how echo spectroscopy separates disorder-induced broadening from intrinsic relaxation. This framework is extended to coupled modes and strongly interacting regimes, where interactions can either enhance or suppress rephasing. A further result is the identification of a nonrephasing four-wave-mixing signal that is critically enhanced near a phase transition, in contrast to simpler nonlinear protocols like third-harmonic generation. We apply this framework to electromagnons in NiI
2, Josephson plasmons in La
2−xSr
xCuO
4, and the low-energy collective excitations in coupled one-dimensional Bose-Einstein condensates. Across these systems, we show how multidimensional spectroscopy can disentangle disorder from intrinsic relaxation, reveal the effects of interactions and fluctuations, identify coupling between collective modes and continua, and extract microscopic information that remains obscured in conventional spectroscopy. Taken together, the results of this thesis provide a diagrammatic framework for calculating and interpreting multidimensional nonlinear spectroscopic signals in many-body systems, while establishing this technique as a selective probe of collective dynamics across a broad range of quantum materials and synthetic platforms.
A method for monitoring the time development of the coherent components in a multilevel system using an observable which can measure only the relative populations in the levels is presented. Using standard density matrix formulation, expressions are obtained for the conventional and this new ’’probe’’ pulse method. For several of the more common coherence experiments, optically detected magnetic resonance of molecular excited triplet states is used to illustrate the principles. The effect of coherent averaging of relaxation terms in the spin Hamiltonian is discussed and specifically applied to excited triplet states in zero field. Finally, experimental results of coherence measurements are presented along with a detailed description of the apparatus and methods used.