Atoms subject to intense laser fields are capable of absorbing many more photons than the minimum number needed to ionize. This leads to two striking nonlinear phenomena, above-threshold ionization, and high-order harmonic generation. We have used time-dependent methods to calculate both these processes nonperturbatively for realistic, three-dimensional atoms. This allows us to clarify the relationships between photon and electron emission rates in the strong field regime.
Atoms subject to intense laser fields are capable of absorbing many more photons than the minimum number needed to ionize. This leads to two striking nonlinear phenomena, above-threshold ionization, and high-order harmonic generation. We have used time-dependent methods to calculate both these processes nonperturbatively for realistic, three-dimensional atoms. This allows us to clarify the relationships between photon and electron emission rates in the strong field regime.
The non linear interaction between an intense laser radiation and atoms leads to ionization through the absorption of N photons from the laser radiation via laser-induced virtual states. The multiphoton ionization rate varies as a function of the laser intensity I as IN. We discuss the two most important effects which govern multiphoton ionization processes : resonance effects and laser-coherence effects. In a moderate laser intensity range (107 - 109 W cm-2) corresponding to the two, three or four-photon ionization of atoms, resonance effects play a dominant role while the photon statistics of the laser radiation are relatively unimportant. On the contrary, in the very high intensity range (1012 - 1013 W cm-2) required to observe large Nth - order ionization processes, coherence effects play a dominant role through N! enhancement in the N-photon ionization rate, while resonance effects are completely damped due to the high laser intensity. We conclude by reviewing the possible applications of multiphoton absorption processes in other fields.
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.
We formulate a quantum theory of photon emission during strong-laser-field-induced ionization and show that such photons can be emitted in a single-step process. The probability of this process is many orders of magnitude higher than that of the well-known high-order harmonic generation, which is a three-step process. We analyzed photon emission for various wavelengths and intensities of the laser field and found that the probability of photon emission is maximal for energies near 5 eV and that it can be shifted to higher energies for higher intensity. For a bichromatic linearly polarized laser field the photon emission rate can be controlled with the relative phase between the field components and can be one order of magnitude higher than in the monochromatic case. For circular laser polarization the rate of photon emission is lower than for the linear one and it depends on the emitted photon direction (it is much lower if the emitted photon polarization is perpendicular to the laser-field polarization plane). For the counterrotating bicircular field the rate is much higher than for the corotating bicircular field, monochromatic circularly and linearly polarized fields, and bichromatic linearly polarized field. The rate is the highest for orthogonally polarized two-color field for the relative phase $\ensuremath{\pi}/2$.
When matter is exposed to strong fields, electrons are ionized and a number of processes such as high harmonic generation (HHG), above threshold ionization (ATI), non-sequential ionization happen. These processes are usually investigated semiclassically, i.e. matter is treated by quantum mechanics, and radiation is treated classically. In particular HHG which is the generation of ultrashort coherent extreme ultraviolet (XUV) pulses, has enabled a wealth of novel ultrashort spectroscopic methods in atomic, molecular, and condensed matter physics. Further, ionization has applications in micro-machining. Strong field physics continues to have numerous open questions. As an illustration, the mechanisms underlying dominant HHG pathways in solids remain insufficiently understood. It is not clear which mechanism dominates HHG in various materials. Possible pathways are the interband and intraband contributions. Furthermore, many of these processes in strong field physics have been described by single active electron (SAE) approximation. This approach relies on the assumption that the interaction between a single electron and the intense laser field dominates all other interactions. However, this is clearly not the case especially in solids where interactions with the lattice and other electrons can be important. In addition, quantum optical aspects of strong field physics have generated increasing interest, yet they remain partially explored. This chapter involves treating electromagnetic fields using the formalism of second quantization. Quantum optical properties, such as squeezing, entanglement and the negativity of the Wigner function, are of fundamental importance for the field of quantum information and quantum computation. The central theme of my thesis is the development of quantum optical and statistical theoretical frameworks for describing intense laser field processes such as ionization and HHG in atomic and molecular gases and in solids. The second chapter focuses on gaining a detailed understanding of the mathematical steps involved in the Keldysh theory of ionization to establish a solid theoretical foundation. Through this analysis we identified an additional factor of two compared to Keldysh’s original derivation of atomic ionization rates. The third chapter addresses the inadequately understood mechanisms that govern dominant high harmonic generation (HHG) pathways in solids. One approach to clarify these mechanisms involves introducing real (resonant) and virtual processes. We developed the strong field adiabatic following (SFAF) formalism which is based on Dyson expansion using the von-Neumann equation of density matrix. Using SFAF a diagnostic method is obtained to separate virtual and resonant channels. Through this separation, and by comparing with experimental results, we identified the need to incorporate many-body effects. The fourth chapter explores the fact that a solid is a complex many body system in which the SAE approximation is very crude. The electron interacts with holes, other electrons, collective excitations such as plasmons, and phonons. Our work is based on the idea that all theses effects can be treated as a quantum statistical heat bath of bosonic harmonic oscillators. We apply this to our SFAF formalism. In the ionization case, this work has settled a long standing issue which is the fact that simple phenomenological approaches such as the relaxation time approximation 𝑇2 result in nonphysical enhancement of ionization. In chapter five, we have investigated ways to transfer quantum optical properties on the otherwise classical high harmonic radiation. The goal is to use HHG to scale quantum sources to smaller wavelengths. Quantum properties can be imprinted by perturbing HHG with a quantum field, such as bright squeezed vacuum (BSV). In this chapter, the theory of quantum sideband high harmonic generation (QSHHG) in atoms and solids is derived to find ways by which to transfer quantum properties from the perturbative BSV to the harmonic sideband. The theoretical framework is a quantum generalization of the semi-classical Lewenstein model of HHG. It gives closed-form solutions for the HHG and QSHHG wavefunctions. Knowing the wavefunction, we can identify the quantum properties of QSHHG. The additional photons absorbed and emitted from the quantum perturbation, here BSV, create entanglement between individual harmonic sidebands and between the harmonic sidebands and the BSV. We show how this entanglement can be used to create a variety of non-classical states commonly used in quantum information science, such as high-purity single-photon states, Schrödinger cat states, and photon-added squeezed vacuum states. Some of these non-Gaussian states with negative Wigner functions have been shown to provide a quantum computational advantage over their Gaussian counterparts. Additionally, they play a significant role in quantum metrology, enhancing precision measurements beyond classical limits. This chapter has opened a path to quantum engineering of HHG.
Recently we have demonstrated the quantum nature of light in strongly laser driven atoms, and we have shown how the process of high harmonic generation can be used for the creation of highly non-classical light states, in particular superpositions of two coherent states, i.e., optical Schr\{o}dinger states [M. Lewenstein et al., Generation of optical Schr\odinger cat states in intense laser-matter interactions, Nat. Phys., 17 1104-1108 (2021)]. Here, we investigate the quantum optical description of the interaction, incorporating many atoms and the back-action of the high harmonic generation or above threshold ionization processes on the coherent state of the driving laser field. We show how the conditioning on high harmonic generation and above threshold ionization can lead to non-classical light states, and we discuss the key parameters that can be used for controlling and characterizing the non-classical states obtained after high harmonic generation. The theoretical results have been experimentally confirmed by demonstrating how the obtained coherent state superposition changes from an optical to kitten state by changing the number of atoms participating in the high harmonic generation process. Additionally, we experimentally verify the applicability of the approach for generating high photon number non-classical light states. This is shown by demonstrating the generation of a 9--photon optical state which, to our knowledge, is the highest photon number optical state experimentally reported. Our findings anticipate the development of new methods that naturally lead to the creation of high photon number controllable coherent state superpositions, advancing investigations in quantum technology.
A general program has been developed to calculate multiphoton processes in atomic hydrogen to arbitrarily high order in perturbation theory. This program can be used to calculate quantities in intense field multiphoton processes, such as the generalized cross section of multiphoton absorption, the a.c. Stark effect (shift and the broadening of the level due to the field interaction), and the parameters in nonlinear optics such as the nonlinear index of refraction and the nonlinear susceptibility. Effective parametrization of high-order susceptibilities has been achieved over a wide range of frequencies, utilizing concepts from quantum defect theory to express the results of lengthy calculations in a compact form that also permits extrapolation across thresholds and resonance poles. Significant progress has been made in direct numerical solution of the time-dependent Schroedinger equation. In addition, contributions have been made in: understanding the role of spatial dimensionality in the solution of model systems (e.G., the one-dimensional delta-function potential); the development of a general R-matrix code for perturbative computations of multiphoton processes in many-electron atoms; and multiphoton ionization with two commensurate laser frequencies.