Unveiling the Quantum Toroidal Dipole

• URL: http://arxiv.org/abs/2401.15128v2
• Date: Sat, 01 Nov 2025 12:57:26 GMT
• Title: Unveiling the Quantum Toroidal Dipole
• Authors: Alexandru-Lucian Nastasia, Mircea Dolineanu, Dragos-Victor Anghel,
• Abstract summary: We present a complete quantum-mechanical formalism for the TD in a nanostructure.<n>We propose the first spectroscopic method for its direct measurement.<n>This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment.
• Score: 41.99844472131922
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The electromagnetic response of matter is governed by three fundamental multipole families: electric, magnetic, and toroidal. While the electric and magnetic are cornerstones of physics, the toroidal dipole (TD) has eluded direct, quantitative measurement for over 60 years. Its far-field signature is masked by the electric dipole, and its behavior in the quantum regime remains largely unexplored. We address this long-standing problem by presenting a complete quantum-mechanical formalism for the TD in a nanostructure and proposing the first spectroscopic method for its direct measurement. We analyze a particle confined to a toroidal manifold subjected to an external current. We demonstrate that the resulting Aharonov-Bohm-like energy shifts in the system's spectrum are directly proportional to the expectation value of the TD operator. The transition energies exhibit a linear dependence on this current, with a quantized slope that directly reveals the change in the TD quantum number between eigenstates. This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment and its quantum nature, opening new avenues in quantum metamaterials, nanoscience, and the study of fundamental symmetries.

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