One active topic in Atomic Physics is the study of highly charged ions (HCI). These physical systems have a strong Coulomb field that provides a unique opportunity to investigate and validate relativistic, Quantum ElectroDynamics (QED), and many-body e ects. Moreover, fundamental test on symmetries and parity violation gives clues to the physics beyond the Standard Model. Thus, nowadays, a primary goal of Atomic Physics is the existence of precise experimental data and accurate theoretical calculations for these systems. In this thesis I focus on the investigation of forbidden radiative transitions in HCI. The main emphasis of this work is on atomic transitions, in which the selection rules forbids the emission of electric dipole photons. In this special type of radiative transition, the electron decays mainly through the emission of a single magnetic dipole photon, or two electric dipole photons. Both types of decay are investigated either experimentally or theoretically. The two-photon decay is only theoretically investigated, using a full relativistic formalism,in HCI with one or two electrons. Several physical e ects in the two photon decay, such as resonances, the Dirac’s negative continuum or angular correlations are considered. Related with the decay, two-photon excitation is also investigated. According to these evaluations, I stress the importance of relativistic and nondipolar e ects. Moreover, a new approach based on the B-polynomials basis set is employed on two-photon transitions. The second part of the work is devoted to the precise measurement of transitions in highly charged Ar with two to four electrons. For that matter, I describe the technical features of a double crystal spectrometer used to perform those measurements in HCI for the first time. This kind of spectrometer is able to perform absolute and precise measurements with an accuracy never achieved in these systems, which enables a comparison with recent QED calculations. I describe a Monte-Carlo code developed with the purpose of studying several systematic errors, as well as testing the various methods of retrieving physical quantities from raw data. Finally, I present the first absolute 2 ppm measurements on HCI with this spectrometer, paying special attention on the forbidden magnetic dipole transition in He-like Ar.
One active topic in Atomic Physics is the study of highly charged ions (HCI). These physical systems have a strong Coulomb field that provides a unique opportunity to investigate and validate relativistic, Quantum ElectroDynamics (QED), and many-body e ects. Moreover, fundamental test on symmetries and parity violation gives clues to the physics beyond the Standard Model. Thus, nowadays, a primary goal of Atomic Physics is the existence of precise experimental data and accurate theoretical calculations for these systems. In this thesis I focus on the investigation of forbidden radiative transitions in HCI. The main emphasis of this work is on atomic transitions, in which the selection rules forbids the emission of electric dipole photons. In this special type of radiative transition, the electron decays mainly through the emission of a single magnetic dipole photon, or two electric dipole photons. Both types of decay are investigated either experimentally or theoretically. The two-photon decay is only theoretically investigated, using a full relativistic formalism,in HCI with one or two electrons. Several physical e ects in the two photon decay, such as resonances, the Dirac’s negative continuum or angular correlations are considered. Related with the decay, two-photon excitation is also investigated. According to these evaluations, I stress the importance of relativistic and nondipolar e ects. Moreover, a new approach based on the B-polynomials basis set is employed on two-photon transitions. The second part of the work is devoted to the precise measurement of transitions in highly charged Ar with two to four electrons. For that matter, I describe the technical features of a double crystal spectrometer used to perform those measurements in HCI for the first time. This kind of spectrometer is able to perform absolute and precise measurements with an accuracy never achieved in these systems, which enables a comparison with recent QED calculations. I describe a Monte-Carlo code developed with the purpose of studying several systematic errors, as well as testing the various methods of retrieving physical quantities from raw data. Finally, I present the first absolute 2 ppm measurements on HCI with this spectrometer, paying special attention on the forbidden magnetic dipole transition in He-like Ar.
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.
Fundamental interactions and symmetries define the structure and properties of all matter, in particular of its small and diverse visible constituents—the atoms. The study of their distinctive spectra through precision spectroscopy is therefore a vital tool to advance our understanding of nature. Highly charged ions (HCIs) constitute the largest fraction of all atoms since every atom has as many charge states as electrons it can bind. Although most of the matter on Earth is neutral, HCIs are ubiquitous in the universe and their systematic study is essential not only for atomic physics but eminently for astrophysics, nuclear physics, and fusion research, among others. Recently, HCIs have been identified as ideal candidates for sensitive tests of physics beyond the Standard Model of particle physics and for use in future high-accuracy optical atomic clocks. However, the realization of such proposals has been hindered by the hitherto constrained laboratory control and limited spectroscopic accuracy of about parts-per-million fractional uncertainty levels. This thesis reports the first coherent laser spectroscopy of HCIs, boosting the achievable spectroscopic precision by eight orders of magnitude compared to traditional spectroscopy methods. The 2P1/2–2P3/2 fine-structure ground-state transition in highly charged 40Ar13+ at an optical wavelength of 441 nm was chosen as a proof-of-principle case. A single ion of this species was isolated from a megakelvin-hot plasma cloud and co-trapped together with a laser-cooled singly charged 9Be+ ion in a two-ion crystal, confined in the harmonic potential of a cryogenic linear Paul trap. This coupled quantum-mechanical system was then cooled to its ground state of axial motion, corresponding to the lowest temperature of a HCI ever achieved. The spectroscopy was realized by implementing quantum logic techniques which allow preparation of the quantum state of the HCI and to map its electronic state after spectroscopy onto the 9Be+ logic ion in order to detect it there with high efficiency through electron shelving. In addition to the increase of spectroscopic precision, the excited-state lifetime and g-factor were measured—the latter one to unprecedented accuracy, resolving effects from special relativity, interelectronic interactions, and quantum electrodynamics. Moreover, it settled a discrepancy between theoretical predictions. The demonstrated techniques are not limited to the specific 40Ar13+ species but universally applicable to other HCIs. Thereby, this work unlocks the potential of HCIs for unrivaled tests of fundamental physics, the search for new physics—such as a 5th force, variations of fundamental constants and dark matter candidates—as well as the use of HCIs in novel optical atomic clocks.
Summary form only given. Although it is often assumed that all light-matter interactions at optical frequencies are mediated by electric dipole transitions, strong optical-frequency magnetic dipoles do exist. In fact, we see magnetic dipole emission every day from the many lanthanide ions (such as erbium, europium, and terbium) that help to illuminate everything from fluorescent lighting to telecom fiber amplifiers. Higher-order processes such as magnetic dipole and electric quadrupole transitions also play an important part in the light emission from transition metal ions and semiconductor quantum dots. Nevertheless, most applications have overlooked the device implications of these electric-dipole-forbidden transitions throughout the visible and near-infrared regime, and their contributions to many important emitters have not been fully characterized.In this presentation, we will experimentally characterize the "forbidden" transitions in a range of solid-state emitters and investigate their applications and implications for nanophotonics. We will examine the electric dipole approximation commonly used to describe light-matter interactions and discuss naturally occurring systems that exhibit higher-order magnetic dipole and electric quadrupole emission. We will illustrate how these nanoscale quantum transitions can provide both a new way to probe magnetic light-matter interactions and a new degree of design freedom for active electronic and photonic devices. Specifically, we will demonstrate how the different symmetries of multipolar transitions can be exploited to identify, quantify, and control light emission, even at sub-lifetime scales. Despite similar radiation patterns, magnetic and electric dipole emitters have different symmetries with respect to polarization and phase. Thus, in an inhomogeneous environment, we can tailor interference effects and the local density of optical states to selectively enhance either electric or magnetic dipole emission [1,2]. To examine the scope of such higher-order transitions, we will present quantum mechanical calculations that identify all the magnetic dipole and electric quadrupole emission lines in the trivalent lanthanide series in the visible to near-infrared spectrum [3]. Then, we will present an energyand momentum-resolved spectroscopy technique to directly quantify the electric and magnetic dipole contributions from any mixed transition. [4] Using energy-momentum spectroscopy, we will experimentally examine the higher order transitions in lanthanide ions [4,5], transition metal ions [6], and epitaxial quantum dots [7]. If time permits, we will then show how the symmetry differences between magnetic and electric dipoles can be used to address specific electronic states [6] and to dynamically tune emission spectra at sub-lifetime-scales [8].
In this paper, we extend to three-photon radiative transitions in hydrogenic ions our fully relativistic multipole approach [Z. Bona et al., Phys. Rev. A 89, 022514 (2014)], which has proven so far to yield extremely accurate results for two-photon emission processes. Closed-form formulas of double and single differential frequency distributions as well as total emission probabilities are derived for arbitrary multipole channels by using the Dirac-Coulomb Sturmian functions of the first order. Two cases of atomic systems are considered in the study, namely, ions with a spinless nucleus and those with a nonzero nuclear spin to check the validity of the Bose-Einstein statistics for three-photon emission investigated by Zalialiutdinov et al. [J. Phys. B: At. Mol. Opt. Phys. 49, 055001 (2016)]. In an effort to assess relativistic effects and the influence of the negative spectrum of the set of Dirac-Coulomb Sturmians, we formulate two nonrelativistic schemes that involve Schr\"odinger-Coulomb Sturmians, a transition operator with retardation, on one hand, and a transition operator in the long wavelength approximation, on the other hand. An application of these theories is made for the relativistic and nonrelativistic atomic transitions $2{s}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}, 2{p}_{1/2}\ensuremath{\rightarrow}1{s}_{1/2}, 2{p}_{3/2}\ensuremath{\rightarrow}2{s}_{1/2}$ and $2s\ensuremath{\rightarrow}1s, 2p\ensuremath{\rightarrow}1s$, respectively, with nuclear charge ranging from 1 to 100. Some of our numerical values are compared with the scarce data available in the literature and they enable us to draw inferences as to the improvements obtained with our approach, while the others are additional results that we provide as a further step for more investigations of three-photon decays.
Introduction The selection rules discussed in Sec. 3.5 forbid many kinds of transitions that are frequently observed or exploited. It must be remembered that these “rules” are based on the approximations of Sec. 3.2, but of course, those can be extended. Such expansions to higher orders of approximation may seem to be little more than a tedious exercise, but this chapter will show that the results are extremely important, because they cause qualitatively different kinds of transitions. Since they involve both the electric and magnetic components of the light, their atomic dipole moments will be identified with the superscript E and B for the remainder of this chapter. The magnetic dipole transitions, called M1, discussed in Sec. 4.2.1 that arise from extension of the electric dipole approximation encompass all of magnetic resonance, including atomic clocks, forced evaporative cooling in Bose–Einstein Condensation (BEC), MRI, and astrophysical processes such as generation of the all-important 21 cm radio frequency line. The electric quadrupole transitions, called E2, discussed in Sec. 4.2.2 describe myriad stellar spectral features as well as the vast majority of nuclear γ-ray transitions. Even with these extensions there are many cases where the relaxation of the electric dipole (E1) selection rules to include M1 and E2 transitions as in Sec. 4.2 still do not account for observed processes. Thus other approximations have to be extended so that their limitations can be relaxed as well. Extension of the perturbation approximation (see Sec. 4.3.1) provides an analytical description of most of non-linear optics, including second harmonic generation, four wave mixing, Raman spectroscopy, and the fabled decay of the hydrogen 2S state. A semi-classical description of the interaction between radiation and atoms can begin with a multipole expansion of the Hamiltonian. The lowest-order term is just from the point charges α located at, and vanishes for neutral atoms. The next-order term is the electric dipole interaction that arises from the non-isotropic distribution of charges induced by the electric field of the light. This term produces the electric dipole transitions (E1) that have been described in some detail in Chap. 3.
The estimation of the adequacy of theoretical calculations on the atomic structure requires availability of the precise experimental data on radiative properties of the atoms. Such data is also required in astronomy and some important areas of technology. The lack of precision of traditional spectroscopic studies of atom presents a fundamental obstacle for progress in these areas. For example, in atomic rubidium, the best precision of the traditional spectroscopic results is on the order of about 1 - 5%, which does not allow for clear assessment of the latest sophisticated theoretical calculations on atomic rubidium structure, with emphasis on different, in nature, effects. This situation is typical for atomic physics in general. The purpose of present study is obtaining the experimental data on the radiative properties of atomic rubidium with precision considerably higher than that of the traditional spectroscopic methods. This is accomplished by means of the two-photon quantum interference polarization spectroscopy. A two-photon polarization spectrum of the rubidium atom is obtained in the range of detunings -417 cm-1 to +99 cm-1 from atomic 5s2S1/2-5p 2P3/2-*8s2S1/2resonance. From analysis of the spectra the relativistic and many body effects on the wavefiinctions are revealed in the form of a uniquely defined parameter q = 2 x 10-6 (5) cm and an exact relation between parameters R and p which quantitatively describes the process: R = 1.01756 (57) + 81.466 (15) p where R is dimensionless and p is in cm. The obtained results can be thought of as specific experimentally established two-photon sum rules and can be used for testing the accuracy of the theoretical wavefiinctions. The experimental technique has important advantages comparing to some traditional spectroscopic methods and is essentially free of systematic effects.