10. Electric Arcs

Unitary operator coherent states, as defined by Klauder (1963), Perelomov (1972) and Gilmore (1974), are considered for the harmonic series irreducible representations of U(p,q). Various properties of these states are reviewed, including their reproducing kernel and measure explicit forms, as well as the representation they lead to for the U(p,q) generators. Starting from a contraction of the su(p,q) Lie algebra, both Dyson and Holstein-Primakoff boson realisations of u(p,q) are obtained in terms of pq pairs of boson creation, annihilation operators and of the generators of a U(p)*U(q) intrinsic group. Such boson realisations are applied to determine the matrix elements of the U(p,q) generators between discrete bases classified according to the chain U(p,q) contains/implies U(p)*U(q). Finally, the isomorphism between so(4,2) and su(2,2) is employed to derive the corresponding properties of the SO(4,2) unitary operator coherent states for application in atomic physics.

A compact extended cavity laser using a micromachined silicon flexure for atomic spectroscopy

We overview the second solution of the Dirac equation for hydrogen atoms that became legitimate with the allowance for the actual charge density distribution inside the protons. It led to the possible existence of hydrogen atoms having only the S-states and therefore not interacting with the electromagnetic radiation – remaining dark . The actual existence of such Second Flavor of Hydrogen Atoms (SFHA) is evidenced by three different types of atomic experiments. In addition to their application for explaining the atomic experiments, they were the basis for resolving the long-standing puzzle of the neutron lifetime. Also, the SFHA was the basis for explaining the baffling astrophysical observation of the anomalous absorption in the 21 cm line from the early Universe, what made the SFHA the leading candidate for baryonic dark matter. Further, by comparing astrophysical observations with atomic experiments, it was demonstrated that the SFHA constitutes the majority of baryonic dark matter. Lastly, it was shown that neutron stars slowly but continuously generate new baryonic dark matter in the form of the SFHA and that there is astrophysical evidence of this process.

Considering Stark-effect applications in atomic physics and especially in plasma spectroscopy, we established several formulas for spectral line intensity, energy level, and ionization rate. In particular, by means of the systematic numerical check on an intermediate formula [Eq. (36d) in the text], we show that the ionization rate may be expressed completely in terms of the energy level according to $\ensuremath{\Gamma}({n}_{1},{n}_{2},m,\ensuremath{\lambda})=\frac{1}{2\ensuremath{\pi}}\frac{\ensuremath{\partial}E({n}_{1},{n}_{2},m,\ensuremath{\lambda})}{\ensuremath{\partial}{n}_{2}}\mathrm{exp}[\ensuremath{-}K({n}_{1},{n}_{2},m,\ensuremath{\lambda})],$ where $\ensuremath{\lambda}={({n}_{1}+{n}_{2}+m+1)}^{3}\frac{F}{4{Z}^{3}}$, and $K({n}_{1},{n}_{2},m,\ensuremath{\lambda})=\frac{1}{6\ensuremath{\lambda}}+\mathrm{ln}\frac{{\ensuremath{\lambda}}^{2{n}_{2}+m+1}{n}_{2}!({n}_{2}+m)!}{2\ensuremath{\pi}}+3({n}_{2}\ensuremath{-}{n}_{1})\ensuremath{-}\frac{1}{6}\ensuremath{\int}{0}^{\ensuremath{\lambda}}\left[{n}^{3}\frac{\ensuremath{\partial}E({n}_{1},{n}_{2},m,{\ensuremath{\lambda}}^{\ensuremath{'}})}{\ensuremath{\partial}{n}_{2}}\ensuremath{-}1+6(2{n}_{2}+m+1){\ensuremath{\lambda}}^{\ensuremath{'}}\right]\frac{d{\ensuremath{\lambda}}^{\ensuremath{'}}}{{\ensuremath{\lambda}}^{\ensuremath{'}2}}.$ The two factors on the right-hand side of (i) are interpreted, respectively, as the atomic-electron-collision frequency and transmission coefficient through the potential barrier created by the electric field $F$. By using the ninth-order perturbation series for resonance energy $E({n}_{1},{n}_{2},m,\ensuremath{\lambda})$ it is found that (i) is in fairly good agreement with the most recent numerical solutions of the Schr\"odinger equation. A discussion follows in connection with other analytical and empirical formulas.

In the present work we review the twisted field construction of quantum field\ntheory on noncommutative spacetimes based on twisted Poincar\\'e invariance. We\npresent the latest development in the field, in particular the notion of\nequivalence of such quantum field theories on a noncommutative spacetime, in\nthis regard we work out explicitly the inequivalence between twisted quantum\nfield theories on Moyal and Wick-Voros planes; the duality between deformations\nof the multiplication map on the algebra of functions on spacetime\n$\\mathscr{F}(\\mathbb{R}^4)$ and coproduct deformations of the Poincar\\'e-Hopf\nalgebra $H\\mathscr{P}$ acting on~$\\mathscr{F}(\\mathbb{R}^4)$; the appearance of\na nonassociative product on $\\mathscr{F}(\\mathbb{R}^4)$ when gauge fields are\nalso included in the picture. The last part of the manuscript is dedicated to\nthe phenomenology of noncommutative quantum field theories in the particular\napproach adopted in this review. CPT violating processes, modification of\ntwo-point temperature correlation function in CMB spectrum analysis and\nPauli-forbidden transition in ${\\rm Be}^4$ are all effects which show up in\nsuch a noncommutative setting. We review how they appear and in particular the\nconstraint we can infer from comparison between theoretical computations and\nexperimental bounds on such effects. The best bound we can get, coming from\nBorexino experiment, is $\\gtrsim 10^{24}$ TeV for the energy scale of\nnoncommutativity, which corresponds to a length scale $\\lesssim 10^{-43}$ m.\nThis bound comes from a different model of spacetime deformation more adapted\nto applications in atomic physics. It is thus model dependent even though\nsimilar bounds are expected for the Moyal spacetime as well as argued\nelsewhere.\n

Vibration modes in spherical geometry can be classified based on the number and position of nodal planes. However, the geometry of these planes is non-trivial and cannot be easily displayed in two dimensions. We present 3D-printed models of those vibration modes, enabling a haptic approach for understanding essential features of bound states in quantum physics and beyond. In particular, when applied to atomic physics, atomic orbitals are obtained in a natural manner. Applied to nuclear physics, the same patterns of vibration modes emerge as cornerstone for the nuclear shell model. These applications of the very same model in a range of more than 5 orders of magnitude in length scales leads to a general discussion of the applicability and limits of validity of physical models in general.

This review presents a comprehensive overview of field‐programmable gate array (FPGA)‐based laser frequency stabilization systems employing modulation‐based spectroscopy techniques. The transition from traditional analog servo controllers to digital and hybrid FPGA‐based architectures is discussed, highlighting the advantages of FPGAs in terms of low latency, high bandwidth, flexibility, and long‐term stability. Particular emphasis is placed on modulation transfer spectroscopy, which has emerged as one of the most widely used and robust approaches for high‐precision laser frequency locking due to its background‐free error signals and reduced sensitivity to residual amplitude modulation. Representative system architectures, control strategies, and performance metrics reported in the literature are critically compared, with applications in atomic physics, quantum technologies, and high‐resolution spectroscopy. Finally, emerging directions such as adaptive digital control and machine‐learning‐assisted optimization are discussed as future perspectives for FPGA‐based laser stabilization systems.

This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.

This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.

This concise and accessible book provides a detailed introduction to the fundamental principles of atomic physics at an undergraduate level. Concepts are explained in an intuitive way and the book assumes only a basic knowledge of quantum mechanics and electromagnetism. With a compact format specifically designed for students, the first part of the book covers the key principles of the subject, including the quantum theory of the hydrogen atom, radiative transitions, the shell model of multi-electron atoms, spin-orbit coupling, and the effects of external fields. The second part provides an introduction to the four key applications of atomic physics: lasers, cold atoms, solid-state spectroscopy and astrophysics. This highly pedagogical text includes worked examples and end of chapter problems to allow students to test their knowledge, as well as numerous diagrams of key concepts, making it perfect for undergraduate students looking for a succinct primer on the concepts and applications of atomic physics.

The whole theoretical framework of physics rests only on a few but profound principles. Wigner enlightened us by elucidating that “It is now natural for us to try to derive the laws of nature and to test their validity by means of the laws of invariance, rather than to derive the laws of invariance from what we believe to be the laws of nature.” Issues pertaining to symmetry, invariance principles and fundamental laws challenge the most gifted minds today. These topics require a deep and extensive understanding of both ‘quantum mechanics’ and the ‘theory of relativity’. We attempt in this pedagogical article to present a heuristic understanding of these fascinating relationships based only on rather elementary considerations in classical and quantum mechanics. An introduction to some fundamental considerations regarding continuous symmetries, dynamical symmetries (Part 1), and discrete symmetries (Part 2) (parity, charge conjugation and time-reversal), and their applications in atomic, nuclear and particle physics, will be presented.

The technique of stimulated Raman adiabatic passage (STIRAP), which allows\nefficient and selective population transfer between quantum states without\nsuffering loss due to spontaneous emission, was introduced in 1990 (Gaubatz\n\\emph{et al.}, J. Chem. Phys. \\textbf{92}, 5363, 1990). Since then STIRAP has\nemerged as an enabling methodology with widespread successful applications in\nmany fields of physics, chemistry and beyond. This article reviews the many\napplications of STIRAP emphasizing the developments since 2000, the time when\nthe last major review on the topic was written (Vitanov \\emph{et al.}, Adv. At.\nMol. Opt. Phys. \\textbf{46}, 55, 2001). A brief introduction into the theory of\nSTIRAP and the early applications for population transfer within three-level\nsystems is followed by the discussion of several extensions to multi-level\nsystems, including multistate chains and tripod systems. The main emphasis is\non the wide range of applications in atomic and molecular physics (including\natom optics, cavity quantum electrodynamics, formation of ultracold molecules,\nprecision experiments, etc.), quantum information (including single- and\ntwo-qubit gates, entangled-state preparation, etc.), solid-state physics\n(including processes in doped crystals, nitrogen-vacancy centers,\nsuperconducting circuits, etc.), and even some applications in classical\nphysics (including waveguide optics, frequency conversion, polarization optics,\netc.). Promising new prospects for STIRAP are also presented (including\nprocesses in optomechanics, detection of parity violation in molecules,\nspectroscopy of core-nonpenetrating Rydberg states, and population transfer\nwith X-ray pulses).\n

The physics and chemistry of exotic atoms

The Hulthén potential is a short-range potential widely used in various fields of physics. In this paper, we investigate the distribution functions for the Hulthén potential by using statistical and superstatistical methods. We first review the ordinary statistics and superstatistics methods. We then consider distribution functions, such as uniform, 2-level, gamma, and log-normal and F distributions. Finally, we investigate the behavior of the Hulthén potential for statistical and superstatistical methods and compare the results with each other. We use the Tsallis statistics of the superstatistical system. We conclude that the Tsallis behavior of different distribution functions for the Hulthén potential exhibits better results than the statistical method. We examined the thermal properties of the Hulthén potential for five different distributions: Uniform, 2-level, Gamma, Log-normal, and F. We plotted the Helmholtz free energy and the entropy as functions of temperature for various values of q. It shows that the two uniform and 2-level distributions have the same results due to the universal relationship and that the F distribution does not become ordinary statistics at q = 1. It also reveals that the curves of the Helmholtz free energy and the entropy change their order and behavior as q increases and that some distributions disappear or coincide at certain values of q. One can discuss the physical implications of our results and their applications in nuclear and atomic physics in the future.

We review studies of two kinds of dips in spectral line profiles emitted by plasmas – the dips that have been predicted theoretically and observed experimentally: Langmuir-wave-caused dips (L-dips) and charge-exchange-caused dips (X-dips). There is a principal difference with respect to positions of L-dips and X-dips relative to the unperturbed wavelength of a spectral line: positions of L-dips scale with the electron density Ne roughly as Ne1/2, while positions of X-dips are almost independent of Ne (the dependence is much weaker than for L-dips). L-dips and X-dips phenomena are important both fundamentally and practically. The fundamental importance is due to a rich physics behind each of these phenomena. As for important practical applications, they are as follows. Observations of L-dips constitute a very accurate method to measure the electron density in plasmas – the method that does not require the knowledge of the electron temperature. L-dips also allow measuring the amplitude of the electric field of Langmuir waves – the only one spectroscopic method available for this purpose. Observations of X-dips provide an opportunity to determine rate coefficient of charge exchange between multi-charged ions. This is an important reference data virtually inaccessible by other experimental methods. The rate coefficients of charge exchange are important for magnetic fusion in Tokamaks, for population inversion in the soft x-ray and VUV ranges, for ion storage devices, as well as for astrophysics (e.g., for the solar plasma and for determining the physical state of planetary nebulae).