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.
Abstract Optical multidimensional coherent spectroscopy provides information about the structure and excitation dynamics in a broad range of material systems. This book focuses on systems of interest in physics, including atomic vapors, semiconductor nanostructures and two-dimensional materials. An introduction to ultrafast spectroscopy and the fundamental concepts of multidimensional coherent spectroscopy applies to all material systems. Relevant experimental implementations, including phase-stabilized crossed-beams, frequency-tagged fully-collinear, three-dimensional and frequency-comb based methods. The use of the method to study atomic vapors, semiconductor quantum wells, semiconductor quantum dots and two-dimensional materials are described in separate chapters. The final chapters survey the use of the method in some other areas and speculate on future directions.
The fast dynamics of molecular polaritonics is scrutinized theoretically through the implementation of two-dimensional spectroscopy protocols. We derive conceptually simple and computationally efficient formulas to calculate two-dimensional spectra for molecules, each of them modeled as a system of two electronic states including vibrational relaxation, immersed in an optical cavity, thus coupled to quantized radiation. Cavity photon losses and molecular relaxation are incorporated into the Hamiltonian dynamics to form an open quantum system that is solved through a master equation. In the collective case, the relaxation dynamics into dark states is revealed to be the crucial factor to explain the asymmetries in both the diagonal and cross peaks of two-dimensional spectra for long waiting times between excitation and detection, a feature shown by recent experiments. Our theoretical method provides a deeper insight in those processes that yield relevant signals in multidimensional molecular spectroscopy.
We present a fully quantum theory of time-resolved transient absorption spectroscopy, providing a general framework for describing the linear response of a nonequilibrium target to quantum probe fields beyond the semiclassical approximation. We elucidate how quantum correlations between probe-field frequency modes couple to coherences in the target and derive a simple expression for computing the resulting spectroscopic signals. We identify conditions under which quantum light can modify transient absorption spectra beyond the limits achievable with classical fields. Our work establishes a theoretical foundation for exploiting quantum light in ultrafast spectroscopy and suggests new routes for resolving dynamics in matter on timescales shorter than the duration of the probe pulse.
Spectroscopy based on individual-photon-level light sources brings new variables to both spectroscopy and imaging. We refer to this approach as quantum-light spectroscopy (QLS). The photon statistics of different types of photon sources and photon entanglements are briefly described. We then illustrate the potential of QLS by means of some current experimental examples including time-resolved spectroscopy performed with single photons and quantum-enhanced optical imaging, showing how all the methods rely on correlations between entangled photons in the pair. We then ask: how might physical chemists exploit QLSs to expose new physical insights? For example, can we address fundamental questions in interactions between light and molecules or materials that are very difficult to address with classical light sources? Does QLS open up techniques to study highly congested spectra with higher combined spectral and temporal resolution than is possible with classical light? The concept of QLS also opens the potential study of fundamental questions such as what initial excited states are produced by individual photon absorption? We also point out the experimental challenges in extending QLS to more complex spectroscopies, such as multidimensional spectroscopies. We conclude with a brief selection of recent theoretical proposals to extend the capabilities of the QLS.
Abstract This tutorial outlines the theory of nonlinear spectroscopy with quantum light, and in particular with entangled photons. To this end, we briefly review molecular quantum electrodynamics, and discuss the approximations involved. Then we outline the perturbation theory underlying nonlinear spectroscopy. In contrast to the conventional semiclassical theory, our derivation starts from Glauber's photon counting formalism, and naturally includes the semiclassical theory as a special case. Finally, we review previous work, which we sort into work depending on the unusual features of quantum noise, and work relying upon quantum correlations in entangled photons. This work naturally draws from both quantum optics and chemical physics. Even though it is impossible to provide a comprehensive overview of both fields in one tutorial, this text aims to be self-contained. We refer to specialised reviews, where we cannot provide details. We do not attempt to provide an exhaustive review of all the literature, but rather focus on specific examples intended to elucidate the underlying physics, and merely cite the remaining publications.