High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.
High-order harmonic generation is a highly nonlinear phenomenon in which ultraviolet photons are generated when an atom is subjected to a high-intensity infrared laser field. This process has been extensively studied, but most of the formulations employ a semiclassical approach in which the electron is treated quantum mechanically while the driving field is treated classically. Although some recent studies follow a quantum-optical approach, the existing descriptions do not offer much insight into the physical processes taking place, and are always limited to monochromatic driving fields. In this thesis, we construct a fully quantized framework for strong-field ionization and high-harmonic generation that allows for quantization of both the driving field and the ultraviolet emission. The presented formalism extends the Strong-Field Approximation theory to a quantum-optical framework, with which we can obtain an analytical expression for the electron and the driving field after the interaction.
High-order harmonics in the extreme-ultraviolet spectral range, resulting from the strong-field laser-atom interaction, have been used in a broad range of fascinating applications in all states of matter. In the majority of these studies the harmonic generation process is described using semi-classical theories which treat the electromagnetic field of the driving laser pulse classically without taking into account its quantum nature. In addition, for the measurement of the generated harmonics, all the experiments require diagnostics in the extreme-ultraviolet spectral region. Here by treating the driving laser field quantum mechanically we reveal the quantum-optical nature of the high-order harmonic generation process by measuring the photon number distribution of the infrared light exiting the harmonic generation medium. It is found that the high-order harmonics are imprinted in the photon number distribution of the infrared light and can be recorded without the need of a spectrometer in the extreme-ultraviolet.
The interaction of electrons with strong laser fields is usually treated with semiclassical theory, where the laser is represented by an external field. There are analytic solutions for the free electron wave functions, which incorporate the interaction with the laser field exactly, but the joint effect of the atomic binding potential presents an obstacle for the analysis. Moreover, the radiation is a dynamical system, the number of photons changes during the interactions. Thus, it is legitimate to ask how can one treat the high order processes nonperturbatively, in such a way that the electron-atom interaction and the quantized nature of radiation be simultaneously taken into account? An analytic method is proposed to answer this question in the framework of nonrelativistic quantum electrodynamics. As an application, a quantum optical generalization of the strong-field Kramers-Heisenberg formula is derived for describing high-harmonic generation. Our formalism is suitable to analyse, among various quantal effects, the possible role of arbitrary photon statistics of the incoming field. The present paper is dedicated to the memory of Prof. Dr. Fritz Ehlotzky, who had significantly contributed to the theory of strong-field phenomena over many decades.
We analytically describe the strong-field light-electron interaction using a quantized coherent laser state with arbitrary photon number. We obtain a light-electron wave function which is a closed-form solution of the time-dependent Schrödinger equation (TDSE). This wave function provides information about the quantum optical features of the interaction not accessible by semi-classical theories. With this approach we can reveal the quantum optical properties of high harmonic generation (HHG) process in gases by measuring the photon statistics of the transmitted infrared (IR) laser radiation. This work can lead to novel experiments in high-resolution spectroscopy in extreme-ultraviolet (XUV) and attosecond science without the need to measure the XUV light, while it can pave the way for the development of intense non-classical light sources.
The generation of higher-order harmonic radiation originating from the interaction of intense laser pulses with matter is typically described semiclassically: While the electronic structure and dynamics of matter is described quantum mechanically, the intense light field is described classically---and accordingly the generated harmonic radiation. However, pioneering experiments on quantum optical properties of high-order harmonic generation (HHG) in atomic gases from the group of P. Tzallas [I. Gonoskov et al., Sci. Rep. 6, 32821 (2016) and N. Tsatrafyllis et al., Nat. Commun. 8, 15170 (2017)], and theoretical investigations from the group of M. Lewenstein [M. Lewenstein et al., Nat. Phys. 17, 1104 (2021) and P. Stammer et al., Phys. Rev. Lett. 128, 123603 (2022)] have impressively demonstrated that light's quantum properties are observable in the strong-field realm. In this paper, we develop a quantum optical description of HHG in a bulk semiconductor originating from the nonlinear Bloch current. This mechanism of HHG, known as the intraband current, constitutes the major contribution to the emission spectrum for harmonic with energies of quanta roughly below the bandgap. Under certain approximations, employing a quantum description of both light and matter, we obtain analytical solutions, which allow us to analyze the classical and quantum optical characteristics of the fundamental mode of light and the harmonic modes. We find intricate but sufficiently mild modifications of the photon statistics of the fundamental mode and coherent displacements depending on the parameters of the driving laser field. Similar to high-harmonic generation in atoms, the fundamental and emitted harmonic field modes are entangled. Moreover, our analytical model predicts parameter ranges where these quantum optical properties will be most pronounced, allowing protocols for quantum information processing with high photon numbers over a large range of frequencies.
Quantum-optical descriptions of strong-field processes have attracted significant attention in recent years. Typically, the theoretical modeling has been conducted in the Schrödinger picture, where results are only obtainable under certain approximations, while, in contrast, the Heisenberg picture has remained relatively unexplored. In this work, we develop an accurately controlled perturbative expansion of the time-evolution operator in the Heisenberg picture and derive beyond-semiclassical corrections to the emitter dynamics due to the coupling to the quantized electromagnetic field, capturing effects of the quantum fluctuations present in the latter. We focus on high-order harmonic generation (HHG), where the approach is accurate in parameter regimes of current interest and it gives closed-form expressions for key observables. This formulation not only simplifies numerical calculations compared to the Schrödinger-picture approach but also provides a clear correspondence between nonclassical features of the emitted light and the underlying induced dynamics of the generating medium including quantum fluctuations. Moreover, the Heisenberg framework naturally yields scaling relations with the number of independent emitters, enabling us to assess whether nonclassical behavior should persist under typical experimental conditions involving large emitter ensembles. Interestingly, we find that the degree of squeezing increases with the number of emitters, whereas the photon statistics approaches a classical Poissonian distribution in the many-emitter limit. We also find that the beyond-semiclassical emitter dynamics significantly enhances the degree of squeezing of the emitted light. Our work advances the theoretical understanding of quantum-optical HHG and introduces an accessible and well-controlled framework to describe realistic experiments.
High-order harmonic generation (HHG) is a significant nonlinear phenomenon triggered by the interaction of intense laser fields with matter. As a high-quality coherent light source, it has found extensive applications in areas such as attosecond pulse generation and ultrafast spectroscopy. Recent studies have revealed the prevalent existence of nonclassical effects in high-harmonic radiation, including nonclassical photon statistics, intermodal correlations, and entanglement. It holds broad development prospects in directions including the generation of nonclassical states with high photon numbers, precise control of entanglement in solid-state systems, and integration with cavity quantum electrodynamics. This review systematically summarizes the research progress concerning the nonclassical effects in HHG. It begins with an overview of the semiclassical model and strong-field quantum theory, clarifying the differences in the quantum properties of harmonic fields when driven by coherent states versus nonclassical states. Subsequently, it focuses on various physical schemes for generating nonclassical optical field states, such as optical cat states and squeezed states, via this process. Research on strong-field HHG not only deepens our understanding of the fundamental nature of intense laser physics but also opens new avenues for the generation and application of quantum light sources in the extreme ultraviolet to X-ray spectral regions.