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Cambridge University Press eBooks

“Forbidden” transitions

P. van der Straten, Harold J. Metcalf

Published Dec 31, 2015• 0 citations
Publisher

Abstract

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.

DOI
10.1017/cbo9781316106242.005

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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.
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].
Introduction Series of atomic spectral lines had been studied by emission from excited vapors even before Balmer described the regularity of the visible lines of hydrogen in 1884. However, direct excitation had been restricted to the few lowest-lying levels, particularly those accessible by electric dipole transitions from the ground state using classical light sources. The advent of tunable lasers in the 1970s changed such spectroscopic limitations enormonsly, allowing excitation to a very much larger number of states. Atoms in highly excited states, typically with principal quantum numbers n ≥ 10, are called Rydberg atoms. They are oversize, fragile states of significant intrinsic interest. They are very rare in nature because of their size and fragility, but they are found in interstellar space (H I regions). One of the best sources for comprehensive descriptions of Rydberg atoms and references to the literature describing their exploration is Ref. [120]. It describes their characteristic properties and behavior both classically and quantum mechanically, and especially their strongly enhanced interactions with external fields. The first thing to note is that Rydberg atoms are usually characterized by a single, highly excited electron while all the other electrons remain in their original states. Thus their properties are very nearly classical, and the atoms are much closer to the ideal hydrogen-like model of Chap. 7, along with appropriate quantum defects (see Chap. 10). The spectroscopy of such states is especially interesting because the active electron is much less perturbed by the other electrons in the atom than when it is in lower states. Moreover, there are some special circumstances in which the energy of a Rydberg state is degenerate with an atomic state having two electrons excited to lower levels, and such configurations yield further new information. Second, Rydberg atoms do not usually decay back to the ground state by emission of characteristic radiation, so their study is mediated by other techniques that reveal new and interesting properties. Such properties arise because Rydberg atoms have a huge dipole moment and very low binding energy resulting from the large average distance between the excited electron and the nucleus-plus-core of the rest of the atom with net charge e . Third, transitions between Rydberg states are quite different from those connecting to the ground state for at least three reasons.
Almost everything we know about atomic energy levels comes from the spectra resulting from radiative transitions between these levels. It is possible that the electric dipole moment of a charge distribution may vanish, in which case the radiation depends on the higher moments. The source of magnetic dipole radiation is a circulating current that reverses direction harmonically, as in a loop antenna. Since a steady-current loop can be regarded as equivalent to a static magnetic dipole, the oscillating current is equivalent to an oscillating dipole. If the electric dipole radiation is impossible, but magnetic dipole radiation can occur, the radiative process would be classed as "forbidden" because of its low intrinsic intensity. An oscillating linear dipole emits no radiation along the direction of its axis of vibration. Although the physical origin of magnetic moments is circulating currents, the effect of an oscillating circular current can be calculated by considering an equivalent linear magnetic dipole.
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 addition to electric and magnetic multipoles, the expansion of current density also yields toroidal terms, a lesser-known family of multipoles. A recent proposal, I. Kuprov et al.\textit{et al.}et al., Science Adv. 8 abq6751 (2022), explores the possibility of a direct observation of optical toroidal transitions in hydrogen and alkali atoms in the presence of a large magnetic field that decouples the spin and the angular momentum of the electron. However, the difficulty of observing these transitions against the nearby electric dipole (E1) transitions were underestimated because of extra admixture coming from diamagnetic coupling. Here, we revisit the toroidal coupling in atoms, taking diamagnetic contribution into account, and discuss the technical challenges of observing toroidal coupling in atomic physics. We show that toroidal transition should be searched in transitions with low principal quantum numbers. The remaining strong electric-dipole contribution could be removed using an appropriate differential measurement.