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This paper presents a novel mathematical framework for calculating Rabi frequencies in atomic and nuclear systems by utilizing vector spherical harmonics to analyze the geometric interaction between laser fields and multipole moments. By connecting these calculations directly to far-field spontaneous-emission patterns, it offers researchers new tools for visualizing complex beam effects beyond standard perturbative corrections. The work advances fundamental quantum physics methods with potential implications for precision spectroscopy and quantum control protocols.
Angular Geometry of Atomic Multipole Transitions
arXiv:2510.07451v4 Announce Type: replace Abstract: A simple way to calculate Rabi frequencies is outlined for interactions of atomic or nuclear multipole moments with laser fields that focuses on their relative geometry. The resulting expression takes the form of a dot product between the laser polarization and a vector spherical harmonic, thereby naturally connecting to the multipole's far-field spontaneous-emission pattern and providing a way to visualize the interaction. Since the vector spherical harmonics are not yet a standard tool in quantum science, their relevant properties are reviewed. This approach is illustrated in the calculation of a variety of beam effects, yielding both perturbative corrections and some nontrivial cases with non-vanishing coupling.
Abstract:A simple way to calculate Rabi frequencies is outlined for interactions of atomic or nuclear multipole moments with laser fields that focuses on their relative geometry. The resulting expression takes the form of a dot product between the laser polarization and a vector spherical harmonic, thereby naturally connecting to the multipole's far-field spontaneous-emission pattern and providing a way to visualize the interaction. Since the vector spherical harmonics are not yet a standard tool in quantum science, their relevant properties are reviewed. This approach is illustrated in the calculation of a variety of beam effects, yielding both perturbative corrections and some nontrivial cases with non-vanishing coupling.
Quantum Physics (quant-ph); Nuclear Experiment (nucl-ex); Atomic Physics (physics.atom-ph)
arXiv:2510.07451 [quant-ph]
(or arXiv:2510.07451v4 [quant-ph] for this version)
Full text under the publisher's open licence · 122 words
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