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Admixture of Dipole and Quadrupole Atomic Transitions in the Presence of External Magnetic Field

Yee Yee Oo, Win Moe Thant, K. N. Nagendra, G. Ramachandran

Published Jan 1, 2019• 0 citations
Publisher

Abstract

The admixture effect of dipole and quadrupole type atomic transitions on the Stokes parameters characterizing the emitted radiation in the presence of an external magnetic field is studied. The transition from an upper level with angular momentum Ju = 3/2 to a lower level with angular momentum Jl = 1/2 is considered to take account of the admixture effect. The analytical expressions showing the emitted Stokes parameters for the case of upper and lower levels having same parities are derived. It is shown that the radiative transition probabilities of magnetic dipole (M1) and electric quadrupole transition (E2) are more intense than those of electric dipole transition (E1) and magnetic quadrupole transition (M2). The polarization components that are not usually seen in the Stokes I; Q and V profiles appear due to the admixture effect. The interference of the polarization components with opposite signs is responsible for the smaller strength of Stokes I; Q; V in admixture transition compared to those observed in pure transition. In pure dipole transition case, U Stokes profile is always zero for all emitted radiation directions. However, the Stokes U profile arises only due to the admixture effect.

DOI
10.17617/2.3188298

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The admixture effect of dipole and quadrupole type atomic transitions on the Stokes parameters characterizing the emitted radiation in the presence of an external magnetic field is studied. The transition from an upper level with angular momentum Ju = 3/2 to a lower level with angular momentum Jl = 1/2 is considered to take account of the admixture effect. The analytical expressions showing the emitted Stokes parameters for the case of upper and lower levels having same parities are derived. It is shown that the radiative transition probabilities of magnetic dipole (M1) and electric quadrupole transition (E2) are more intense than those of electric dipole transition (E1) and magnetic quadrupole transition (M2). The polarization components that are not usually seen in the Stokes I; Q and V profiles appear due to the admixture effect. The interference of the polarization components with opposite signs is responsible for the smaller strength of Stokes I; Q; V in admixture transition compared to those observed in pure transition. In pure dipole transition case, U Stokes profile is always zero for all emitted radiation directions. However, the Stokes U profile arises only due to the admixture effect.
General expressions for the dependence of the polarization of the radiation emitted in an atomic electronic transition upon the angle of emission are derived on the basis of a vector-spherical-harmonic/Bessel-function description of the photon. The concept of a photon of a specific multipolarity, i.e. quadrupole, octupole, etc, and identifiable as such, is found to be unviable. The angular distribution and dependence upon distance from the source of the transverse and parallel components of the electric and magnetic fields arising from E1, E2, M1 and M2 atomic electronic emissions are elucidated.
An ion is located in a crystal at a site that is not a centre of inversion, with a Zeeman field directed at right angles to the crystal axis c. Periodic intensity variations in the optical spectrum that occur when the crystal is rotated about c are due to magnetic dipole transitions between levels of different type and to electric dipole transitions between levels having admixed opposite-parity parts of different type. Use of an antiunitary operator that commutes with the total Hamiltonian demonstrates that interference between electric and magnetic dipole radiation (or interference between any opposite-parity multipole radiation) does not occur for transitions appearing in the axial spectrum, but does occur for those appearing in the pi or sigma transverse spectrum. Depending on the site symmetry, two or four of the Zeeman components of a doublet-doublet transition have an additional periodicity as a result of this interference. Eigenstates are constructed that show the relationship between the M values of a Zeeman level, the crystal quantum number that labels it, and its type, and are used to calculate the angular dependence of certain doublet-doublet dipole transitions for ions at sites of point symmetries D 2d and C 3h . With explicit expressions for dipole matrix elements, it is discovered that two Zeeman components having the same angular dependence when interference is neglected exhibit dissimilar angular behaviour when the interference cross-term is included.
We report here the first observation and measurement of the transition magnetic moment for a strongly forbidden S-S transition of an alkali atom. By using single-photon excitation of the 6S1/2-7S1/2 caesium transition in a quasi-static electric field, we have detected an electronic polarization of the excited state, specific to an interference effect occurring in mixed electric magnetic dipole transitions. Our measurements, independent of the vapour density, indicate that the magnetic dipole amplitude M 1 has the same size as the electric dipole amplitude E1 , induced by an electric field, parallel to the light wave polarization, and equal to 2.62 ± 0.21 V/cm. We also obtain the relative sign of M 1 and E1. Using a theoretical value of E 1 and a well-defined phase convention, we deduce for the magnetic moment of the transition < 7S, 1/ 2 | μ z | 6S, 1/ 2 > = - (4.24 ± 0.34) 10-5 |μB|, in good agreement with a theoretical estimate. This result can also be expressed in terms of the oscillator strength in zero electric field f6S-7S = 4.05 × 10-15, or of the single-photon M1 decay rate Γ 7S-6S = 0.93 x 10-6 s-1.
Under the conditions of the total Paschen-Back effect the diamagnetic interaction determines the dependence of the intensity of the Zeeman components of atomic radiation lines on a magnetic field. The change in the matrix elements of the radiative transitions is due to the magnetically induced corrections to the wavefunctions of the initial and final states, whose contributions are of the same order of magnitude for the head lines of the optical series. For the high-frequency lines the positive corrections to the matrix element from the wavefunction of the upper level dominate. A magnetic field also induces dipole radiative transitions with selection rules for the orbital angular momentum | Δ l | ≥ 3. The matrix elements of such transitions increase rapidly with the energy of the upper level, making possible efficient single-photon population of the dipole-inaccessible Rydberg states in moderate magnetic fields.
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.
It is shown that the description of polarization based on quantization of classical Stokes parameters is incomplete in quantum domain. For example, the polarization of the electric dipole radiation of the atomic or molecular transitions is described by nine generators of the SU(3) subalgebra in the Weyl-Heisenberg algebra of photons, in other words, by nine independent Stokes operators instead of four dependent classical Stokes parameters. Although some of the Stokes operators have one and the same averages, they describe absolutely different physical quantities with strongly different quantum fluctuations. The quantum polarization properties of the electric dipole and quadrupole radiation are examined as a function of distance for the near, intermediate, and far zones. Application of results in the near-field optics and quantum entanglement research is discussed.