For both, fundamental physics and novel applications, nonlinear effects are crucial.Powerful laser fields require to treat mobile electrons beyond linear response theory.Phenomena familiar from nonlinear optics are manifest in ultracold Rydberg systems, which have a high potential for advancing the understanding of many-body physics via quantum simulations and promote progress in quantum computation and -information.Various devices and plasmonics systems are based on thin, nearly two dimensional (2D) layers, such as quantum wells, graphene-like structures or transition metal dichalcogenides.We here derive an expression for nonlinear response functions in arbitrary order, and evaluate it explicitly in 2D for the quadratic and the cubic density response of non-interacting fermions.As correlations are of enhanced importance in low dimensions, we next incorporate screened interactions.This results in the generation of 2nd and 3rd harmonics of the collective modes (zero sound and plasmons), damped by multiple particle-hole continua.
For both, fundamental physics and novel applications, nonlinear effects are crucial.Powerful laser fields require to treat mobile electrons beyond linear response theory.Phenomena familiar from nonlinear optics are manifest in ultracold Rydberg systems, which have a high potential for advancing the understanding of many-body physics via quantum simulations and promote progress in quantum computation and -information.Various devices and plasmonics systems are based on thin, nearly two dimensional (2D) layers, such as quantum wells, graphene-like structures or transition metal dichalcogenides.We here derive an expression for nonlinear response functions in arbitrary order, and evaluate it explicitly in 2D for the quadratic and the cubic density response of non-interacting fermions.As correlations are of enhanced importance in low dimensions, we next incorporate screened interactions.This results in the generation of 2nd and 3rd harmonics of the collective modes (zero sound and plasmons), damped by multiple particle-hole continua.
Abstract Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic, quartic and quintic responses reveal a deep connection with the linear response. Careful analysis of the static long wavelength limit led us to conjecture a canonical non-interacting form that expresses arbitrary order nonlinear responses as the weighted sum of the linear responses evaluated at all multiple harmonics. This harmonic expansion is successfully validated against ab initio path integral Monte Carlo simulations.
Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. Particularly, we focus on the 1d interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities and demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition" term and its nonlinear oscillations is the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak and can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.
Nonlinear responses in crystalline solids are attracting a great deal of attention because of exciting phenomena, such as the bulk photovoltaic effect in noncentrosymmetric crystals and the third-harmonic generation related to Higgs modes in superconductors, and their potential applicability to electronic devices. Recently, nonlinear responses have also been studied in strongly correlated electron systems. Experimental evidence has revealed that correlations play a significant role in nonlinear responses. However, most theoretical calculations only consider excitonic effects or involve numerically demanding approaches, making interpreting the results challenging. In this paper, we adopt another approach, which is based on real-time evolution using the correlation expansion method. We focus in particular on the one-dimensional interacting Rice-Mele model. We analyze the impact of the density-density interaction on the linear and nonlinear conductivities, and we demonstrate that two-particle correlations beyond the mean-field level enhance second-order nonlinear responses, especially the second-harmonic generation, while the linear response is not strongly affected. Furthermore, by decomposing the current into a one-particle contribution and six two-particle contributions, we show that the ``biexciton transition'' term and its nonlinear oscillations are the most dominant two-particle contribution to the nonlinear response. In addition, we also show that the intercell charge-charge correlation is strongly enhanced when the system is driven with the frequency corresponding to the excitonic peak, and it can even exceed the intracell correlation. This implies the possibility of manipulating two-particle correlations with external fields.
This dissertation addresses both fundamental aspects of Coulomb correlations in semiconductor quantum wells and more practical aspects of theoretical analysis of semiconductor optoelectronic devices. After introducing the subject, we present and evaluate a state-of-the-art theory of the third order coherent optical response of a semiconductor quantum well based on the Dynamics Controlled Truncation (DCT) scheme. Already in the third order (the so-called chi (3)) regime, semiconductors exhibit a number of many-body Coulomb correlation effects. Their manifestation in various multi-pulse experimental configurations, customarily used in ultrafast semiconductor spectroscopy, has been an important component of this thesis. Coherent optical effects in a semiconductor 3-band system based on the heavy-hole, light-hole and conduction bands were investigated. The quantum beats in the time-integrated differential transmission signal were analyzed and compared with experimental data obtained at the University of Iowa. Fundamental differences from corresponding quantum beats in atomic 3-level systems were found. Also, the analysis of experimental data (obtained at the University of Arizona) of the coupled heavy-hole-light-hole optical Stark shift revealed evidence of intervalence band coherences, an analog of Raman coherences in atomic 3-levels systems. A scheme for realization of electromagnetically-induced transparency (EIT) based on the interference of excitonic and biexcitonic coherences was proposed. Corresponding experiments performed at the University of Oregon showed indeed a considerable coherent reduction of excitonic absorption. Furthermore, an extension of the chi(3) analysis revealed an energy renormalization of the biexciton, in good agreement with the corresponding experiment. A microscopic analysis of polarization dynamics in time-resolved four-wave mixing signals was performed, revealing interesting implications for the biexciton dephasing in addition to the significance of many-body correlations. In the case of four-wave mixing in semiconductor microcavities, our theoretical analysis in conjunction with experimental data obtained at the University of Tokyo gave us indications for a significant shortcoming of the second Born approximation (2nd BA) applied to two-exciton Coulomb correlations in a thin semiconductor quantum well, in agreement with the general knowledge of the qualitative failure of the 2nd BA in systems with short-range interaction in two dimensions. We also analyzed a novel all-optical switching technique based on the nonlinear polarization rotation. Apart from identifying the many-particle processes relevant for the switch operation in the chi(3) regime, we proposed ways to further optimize the switch.
We develop a systematic theory of multiparticle excitations in strongly interacting Fermi systems. Our work is the generalization of the time-honored work by Jackson, Feenberg, and Campbell for bosons, that provides, in its most advanced implementation, quantitative predictions for the dynamic structure function in the whole experimentally accessible energy/momentum regime. Our view is that the same physical effects, namely, fluctuations of the wave function at an atomic length scale are responsible for the correct energetics of the excitations in both Bose and Fermi fluids. Besides a comprehensive derivation of the fermion version of the theory and discussion of the approximations made, we present results for homogeneous 3He and electrons in three dimensions. We find indeed a significant lowering of the zero-sound mode in 3He and a broadening of the collective mode due to the coupling to two-particle--two-hole excitations in good agreement with experiments. The most visible effect in electronic systems is the appearance of a ``double-plasmon'' excitation.
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 NiI2, Josephson plasmons in La2−xSrxCuO4, 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.