Interactions between light and matter is one way to study both particles whose small spatial sizes render them irresolvable to our eyes and events where the characteristic time scale is too short for conventional recording and measurement techniques. The advent of free electron lasers allow laser pulses of high intensity and small temporal duration such that ultra-fast dynamics in matter systems and resulting non-linear effects can be resolved experimentally. This thesis discusses some theories to mathematically model such light-matter interactions and presents results based both on analytical expressions—where such expressions are available— from the Schrödinger and the Dirac equations as well as numerical calculations. Some models presented are a semi-classical model where light is treated classically and the atomic system quantum-mechanically and a statistical model which describes the light as quantized to feature effects like spontaneous emission and thermal excitation. The main theme of the thesis is relativistic effects and scalings of interaction effects with nuclear charge Z. The results discussed in the work shows that the equivalent characteristics of the dynamics of highly ionized hydrogen-like atoms predicted by the Schrödinger equation fail when relativistic effects are taken into account. This is shown to be a result of the quantities such as energy and mean radial distance from the nucleus not being exactly proportional to powers of Z in Dirac’s description of quantum mechanics. Further, deviations occur due to the necessary detuning of the driving laser field when spin-orbit interactions (a relativistic effect) split states of non-zero orbital momentum. Also, it is shown that as the characteristic time scales of interactions and inherent effects such as spontaneous emission scale differently with Z, the characteristic dynamics are not invariant to atomic number and it is not possible to rescale quantities to make them so. This work provides a guide for future Free-electron laser experiments on highly charged ions at X-ray wave- lengths.
Interactions between light and matter is one way to study both particles whose small spatial sizes render them irresolvable to our eyes and events where the characteristic time scale is too short for conventional recording and measurement techniques. The advent of free electron lasers allow laser pulses of high intensity and small temporal duration such that ultra-fast dynamics in matter systems and resulting non-linear effects can be resolved experimentally. This thesis discusses some theories to mathematically model such light-matter interactions and presents results based both on analytical expressions—where such expressions are available— from the Schrödinger and the Dirac equations as well as numerical calculations. Some models presented are a semi-classical model where light is treated classically and the atomic system quantum-mechanically and a statistical model which describes the light as quantized to feature effects like spontaneous emission and thermal excitation. The main theme of the thesis is relativistic effects and scalings of interaction effects with nuclear charge Z. The results discussed in the work shows that the equivalent characteristics of the dynamics of highly ionized hydrogen-like atoms predicted by the Schrödinger equation fail when relativistic effects are taken into account. This is shown to be a result of the quantities such as energy and mean radial distance from the nucleus not being exactly proportional to powers of Z in Dirac’s description of quantum mechanics. Further, deviations occur due to the necessary detuning of the driving laser field when spin-orbit interactions (a relativistic effect) split states of non-zero orbital momentum. Also, it is shown that as the characteristic time scales of interactions and inherent effects such as spontaneous emission scale differently with Z, the characteristic dynamics are not invariant to atomic number and it is not possible to rescale quantities to make them so. This work provides a guide for future Free-electron laser experiments on highly charged ions at X-ray wave- lengths.
In this thesis we investigate strong-field relativistic processes in highly charged ions. In the first part,we study resonance fluorescence of laser-driven highly charged ions in the relativistic regime by solving the time-dependent master equation in a multi-level model. Our ab initio approach based on the Dirac equation allows for investigating highly relativistic ions, and, consequently, provides a sensitive means to test correlated relativistic dynamics, bound-state quantum electrodynamic phenomena and nuclear effects by applying coherent light with x-ray frequencies. Atomic dipole or multipole moments may be determined to unprecedented accuracy by measuring the interference-narrowed fluorescence spectrum. Furthermore, we investigate the level structure of heavy hydrogenlike ions in laser beams. Interaction with the light field leads to dynamic shifts of the electronic energy levels, which is relevant for spectroscopic experiments. We apply a fully relativistic description of the electronic states by means of the Dirac equation. Our formalism goes beyond the dipole approximation and takes into account non-dipole effects of retardation and interaction with the magnetic field components of the laser beam. We predicted cross sections for the inter-shell trielectronic recombination (TR) and quadruelectronic recombination processes which have been experimentally confirmed in electron beam ion trap measurements, mainly for C-like ions, of Ar, Fe and Kr. For Kr30+, inter-shell TR contributions of nearly 6% to the total resonant photorecombination rate were found.
Hyperfine splittings play an important role in quantum information and spintronics applications. They allow for the readout of the spin qubits, while at the same time providing the dominant mechanism for the detrimental spin decoherence. Their exact knowledge is thus of prior relevance. In this work, we analytically investigate the relativistic effects on the hyperfine splittings of hydrogen-like atoms, including finite-size effects of the nucleis’ structure. We start from exact solutions of Dirac’s equation using different nuclear models, where the nucleus is approximated by (i) a point charge (Coulomb potential), (ii) a homogeneously charged full sphere, and (iii) a homogeneously charged spherical shell. Equivalent modelling has been done for the distribution of the nuclear magnetic moment. For the 1s ground state and 2s excited state of the one-electron systems H1, H2, H3, and He+3, the calculated finite-size related hyperfine shifts are quite similar for the different structure models and in excellent agreement with those estimated by comparing QED and experiment. This holds also in a simplified approach where relativistic wave functions from a Coulomb potential combined with spherical-shell distributed nuclear magnetic moments promises an improved treatment without the need for an explicit solution of Dirac’s equation within the nuclear core. Larger differences between different nuclear structure models are found in the case of the anisotropic 2p3/2 orbitals of hydrogen, rendering these excited states as promising reference systems for exploring the proton structure.
In this thesis we discuss a theoretical description of ultrafast and non-linear spectroscopy. Due to the high intensities and ultrashort pulse durations involved in such experiments, it is necessary to use an explicitly time-dependent formalism. In addition, many of the systems we have considered exhibit strong interactions between the constituent particles, such as electron-electron, electron-nuclear and electron-photon interactions. To properly account for such interactions we have made extensive use of effective models, designed to capture the qualitative aspects of the systems.The thesis is based on six papers, that can be broadly categorized as follows: In Papers III and VI we study the non-linear interaction of light and matter. In Paper III we look at the multi-photon photo-emission from InAs nanowires, and in particular at the polarization dependence of the photo-emission signal on the crystal structure. In Paper VI we discuss second harmonic generation in a two-level system, and compare the fluorescence spectra from a quantum and semi-classical treatment of radiation.The remaining four papers are concerned with ultrafast dynamical processes: In Papers I and II we study atomic desorption from a surface, resulting from strong electron-nuclear interactions. To account for these interactions we consider a finite system that can be solved using exact diagonalization. We show that the desorption yield can be controlled by using a protocol with two ultrashort pulses and varying their delay. To assess finite size effects we compare the exact solution of the finite system to an approximate solution of a semi-infinite system based on non-equilibrium Green's functions and Ehrenfest dynamics. In Paper V we study Auger decay in a real-time description, and propose a protocol to induce the quantum Zeno effect by driving the system during decay. The Zeno effect leads to an increase in the Auger lifetime, that is experimentally measurable and can be controlled by varying the intensity of the driving field. In Paper IV we discuss the role of electron-electron interactions for charge-separation in donor-acceptor systems. We identify a regime where the charge-separation is driven solely by electronic correlations, that are captured by treating interactions to first order beyond a mean-field description.
In 1928, the brilliance of Paul Dirac granted him the insight to develop a particle equation that was fully consistent with both the principles of quantum mechanics and the theory of special relativity. In this bachelor thesis we have studied the fundamentals of relativistic quantum mechanics including the derivation of the Dirac equation in a similar fashion to the way originally done by Paul Dirac. Additionally we have studied the analytical solution for hydrogen-like atoms. Furthermore we have numerically analysed the energy spectrum, radial characteristics and correctional terms using programs written in Python and MATLAB. Finally we have investigated the implications and applications ofthe Dirac Hamiltonian and its use to effectively describe the attributes of gold atoms.We find that relativistic contribution scales approximately by Z2 for large Z. In addition, we conclude that the Dirac Hamiltonian is of vital importance for an accurate description of chemical and physical properties of large atoms. Furthermore, we have completed calculations of the radial solution for the Coulomb potential and also for a free particle.
This dissertation demonstrates the usefulness of exactly solvable quantum models in the investigation of light-matter interaction phenomena associated with the propagation of ultrashort laser pulses through gaseous media. This work fits into the larger research effort towards remedying the weaker portions of the standard set of medium modeling equations commonly used in simulations. The ultimate goal is to provide a self-consistent quantum mechanical description that can integrate Maxwell and Schrödinger systems and provide a means to realistically simulate nonlinear optical experiments on relevant scales. The study of exactly solvable models begins with one of the simplest quantum systems available, one with a 1D Dirac-delta function potential plus interaction with the light field. This model contains, in the simplest form, the most important "ingredients" that control optical filamentation, i.e. discrete and continuum electronic states. The importance of both states is emphasized in the optical intensity regime in which filaments form, where both kinds of electronic states simultaneously play a role and may not even be distinguishable. For this model atom, an analytical solution for the time-dependent light-induced atomic response from an arbitrary excitation waveform is obtained. Although this system is well-known and has been studied for decades, this result is probably the most practically useful and general one obtained thus far. Numerical implementation details of the result are also given as the task is far from trivial. Given an efficient implementation, the model is used in light-matter interaction simulations and from these it is apparent that even this toy model can qualitatively reproduce many of the nonlinear phenomena seen in experiments. Not only does this model capture the basic physics of optical filamentation, but it is also well-suited for high harmonic generation simulations. Next, a theoretical framework for using Stark resonant states (or metastable states) to represent the medium's polarization response is presented. Researchers have recognized long ago the utility of Gamow resonant states as a description of various decay processes. Even though a bound electron experiences a similar decay-like process as it transitions into the continuum upon ionization, it was unclear whether field-induced Stark resonant states carry physically relevant information. It is found that they do, and in particular it is possible to use them to capture a medium's polarization response. To this end, two quantum systems with potentials represented by a 1D Dirac-delta function and a 1D square well are solved, and all the necessary quantities for their use as medium models are presented. From these results it is possible to conjecture some general properties that hold for all resonance systems, including systems that reside in higher than one dimensional space. Finally, as a practical application of this theory, the Metastable Electronic State Approach (MESA) is presented as a quantum-based replacement for the standard medium modeling equations.
Niels Bohr’s model of the hydrogen and hydrogen-like atoms, in which the electron is allowed to revolve in certain circular orbits around the nucleus, was extended by Arnold Sommerfeld to allow for the possibility of elliptical orbits. Each elliptical orbit was constrained by two quantization conditions specified by a positive integer nφ and a non-negative integer nr. If, in the presence of the attractive Coulomb force between the electron and the nucleus, the dynamics of the atom were taken to be governed by the Newtonian laws of motion, the energy Ɛ of the two-particle system was found to be a function of the positive integer n = nr + nφ. The atomic energy levels thus exhibited an n-fold degeneracy, which would be lifted in the presence of external electric or magnetic fields, thus accounting for the fine-structure of the spectral lines emitted by the atom—phenomena observed, respectively, in the Stark effect and the Zeeman effect. Sommerfeld also examined the behavior of his elliptical orbits by allowing the revolving electron to obey Einstein’s relativistic dynamics. In this case, the energy-level degeneracies were lifted (even in the absence of external perturbations), and the elliptical orbits were found to precess around the nucleus—similarly to the precession of, say, the orbit of the planet Mercury around the Sun. What is astonishing about Sommerfeld’s relativistic expression of the energy Ɛ as a function of nφ and nr is that it is precisely the same expression as obtained for hydrogen and hydrogen-like atoms from Dirac’s equation, which came more than a decade later. Recall that the spin of the electron was not yet discovered when Sommerfeld developed his model, and that in Dirac’s fully-relativistic quantum mechanics, the spectral fine-structure arises from the coupling of the electron’s spin to its orbital motion. The present paper provides a streamlined yet detailed account of Sommerfeld’s elliptical orbits in hopes of bringing about a deeper appreciation for the miraculous coincidence of Sommerfeld’s result with that derived from Dirac’s equation.