The invention of lasers in the early sixties triggered the development of the rich field of nonlinear optics. Similarly, the development of lasers with ultrahigh intensities, that is, when the light electric field is larger than the attraction between electrons and nuclei, has boosted extreme nonlinear optics to a relevant and promising discipline in physics. Besides its technological potentialities, strong field physics is also challenging at a fundamental level, leading to the reconsideration of the basic processes of light-matter interactions. Also, the complexity of the exact solutions of the nonperturbative equations has encouraged the development of simple approaches based in semiclassical concepts that offer invaluable insight into the basic processes involved. In this sense, Bohmian trajectories offer an interesting extension of the semiclassical treatment, since their description is purely quantum and , yet, they retain the intuitiveness of a classical description. In this chapter we study the interaction of a hydrogen atom with short and intense laser pulses. By first using a simplified one-dimensional model, we show how Bohmian trajectories can be used in the calculation of the above-threshold ionization (ATI) and harmonic generation spectra. We also present a full three-dimensional (3D) model to study the interaction of an atom with beams bearing orbital angular momentum (OAM) and use the trajectories to gain physical insight into the absorption of angular momentum.
The invention of lasers in the early sixties triggered the development of the rich field of nonlinear optics. Similarly, the development of lasers with ultrahigh intensities, that is, when the light electric field is larger than the attraction between electrons and nuclei, has boosted extreme nonlinear optics to a relevant and promising discipline in physics. Besides its technological potentialities, strong field physics is also challenging at a fundamental level, leading to the reconsideration of the basic processes of light-matter interactions. Also, the complexity of the exact solutions of the nonperturbative equations has encouraged the development of simple approaches based in semiclassical concepts that offer invaluable insight into the basic processes involved. In this sense, Bohmian trajectories offer an interesting extension of the semiclassical treatment, since their description is purely quantum and , yet, they retain the intuitiveness of a classical description. In this chapter we study the interaction of a hydrogen atom with short and intense laser pulses. By first using a simplified one-dimensional model, we show how Bohmian trajectories can be used in the calculation of the above-threshold ionization (ATI) and harmonic generation spectra. We also present a full three-dimensional (3D) model to study the interaction of an atom with beams bearing orbital angular momentum (OAM) and use the trajectories to gain physical insight into the absorption of angular momentum.
In this paper, Bohmian mechanics is applied to intense laser–atom physics. The motion of an atomic electron in an intense laser field is obtained from the Bohm–Newton equation. We find that the quantum potential that dominates the quantum effect of a physical system becomes negligible as the electron is driven far from the parent ion by the intense laser field, i.e. the behavior of the electron smoothly tends towards classical soon after the electron is ionized. Our numerical calculations present direct positive evidence for semiclassical trajectory methods in intense laser–atom physics where the motion of the ionized electron is treated by classical mechanics, while quantum mechanics is needed before the ionization.
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.
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.
Intense laser-matter interactions are at the center of interest in research and technology since the development of high-power lasers.They have been widely used for fundamental studies in atomic, molecular, and optical physics, and they are at the core of attosecond physics and ultrafast optoelectronics.Although the majority of these studies have been successfully described using classical electromagnetic fields, recent investigations based on fully quantized approaches have shown that intense laser-atom interactions can be used for the generation of controllable high-photon-number entangled coherent states and coherent state superpositions.In this tutorial, we provide a comprehensive fully quantized description of intense laseratom interactions.We elaborate on the processes of high-harmonic generation, above-threshold ionization, and we discuss new phenomena that cannot be revealed within the context of semiclassical theories.We provide the description for conditioning the light field on different electronic processes, and their consequences for quantum state engineering of light.Finally, we discuss the extension of the approach to more complex materials, and the impact to quantum technologies for a new photonic platform composed of the symbiosis of attosecond physics and quantum information science.
Recent realization of an intense quantum light, namely bright squeezed vacuum, opened a new perspective on quantum light-matter interaction. Several theoretical works have appeared based on coherent state expansions of quantum state of light to investigate non-classical driving of high-harmonic generation in atomic gases and solids, or free-electron dynamics, but their predictions surprisingly coincide with what one could expect from essentially classical interpretations of the light statistics. A deeper theoretical insight into the underlying physics is necessary for understanding of observed experimental findings and predicting emerging effects relying on this new configuration. Here we present a theoretical framework to describe tunneling driven by quantum light, where the properties of such light are captured by a statistical ensemble of classical fields via a hydrodynamic, also referred to as Bohmian, formulation. Generalizing the quasiclassical theory of non-adiabatic tunneling driven by classical light, a single tunneling event is described by a bundle of tunneling solutions, each driven by a classical field corresponding to one realization in the ensemble. Quantum statistics of light are thus imprinted on the measured current. Fully quantum description of light via the Bohmian trajectories of its field provides a perfect fit to the description of the electron (under-) above-barrier dynamics in terms of (complex quasiclassical) real classical trajectories, resulting in a consistent and elegant theoretical approach. To illustrate this, we consider BSV-induced electron transport from the tip to the surface in the tunneling microscope configuration demonstrating the transition from the multiphoton to the direct tunneling regime.
Chapter 12 introduces light–matter interaction at the atomic scale and at interaction energies less than, or comparable to, the chemical bond. The classical electrodynamics treatment for fields is retained, but a very simple quantum atomic structure with electric dipole transitions among atomic and molecular internal states is introduced. The correspondence between classical and quantal electron orbital angular momentum states in atoms is developed in detail for the hydrogen atom, and the difference between quantised orbital states and real, space-directed orbitals is explained. A wave mechanical quantum representation brings out the analogies between classical light waves, quantum matter waves, classical dipole radiation, and atomic radiative emission. The intrinsic electron spin, that has no classical analogue, is introduced and discussed. The chapter ends with a discussion of the rigid rotor, harmonic oscillator model to interpret rotational and vibrational diatomic molecular spectra. Finally rovibronic states complete the picture with the introduction of diatomic molecular electronic transitions.