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Measurement and Analysis of Atomic Hydrogen and Diatomic Molecular AlO, C2, CN, and TiO Spectra Following Laser-induced Optical Breakdown

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Toroidal optical transitions in hydrogen-like atoms.

Ilya Kuprov¹, David Wilkowski^2,3,4, Nikolay Zheludev^2,5,6

¹School of Chemistry, University of Southampton, Southampton, UK.

Science Advances

|November 9, 2022

Summary

This study reveals that toroidal dipole spectroscopy, previously overlooked, is feasible by including relativistic quantum mechanics. This opens new avenues for distinguishing toroidal dipole transitions from electric and magnetic ones.

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Area of Science:

Quantum Optics
Atomic and Molecular Physics
Condensed Matter Physics

Background:

Electromagnetic spectra traditionally rely on electric and magnetic multipoles.
Toroidal multipoles, particularly toroidal absorption lines in metamaterials, are a recent discovery.
The toroidal dipolar interaction has been largely neglected in spectroscopy.

Purpose of the Study:

To demonstrate the feasibility of a new type of spectroscopy focusing on toroidal dipolar interactions.
To incorporate the spin-dependent term (r x σ) into toroidal dipole calculations.
To differentiate toroidal dipole transitions from electric and magnetic multipole transitions.

Main Methods:

Inclusion of the classical r × r × p toroidal dipole density term.
Incorporation of the spin-dependent r × σ term from relativistic quantum mechanics.
Analysis of parity and time-reversal symmetries of toroidal dipole operators.

Main Results:

A novel spectroscopic method for toroidal dipolar interactions is proposed.
The spin-dependent term is shown to be crucial for toroidal transitions.
Toroidal dipole transitions exhibit unique symmetry properties (odd under parity and time-reversal).

Conclusions:

Toroidal dipole spectroscopy offers a new tool for understanding light-matter interactions.
Relativistic quantum mechanics is essential for a complete description of toroidal phenomena.
The distinct symmetry properties of toroidal dipoles allow for their clear identification.