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arXiv:2605.27558

Radiative Response of Atomic Systems Illuminated with Approximate Spherical Vector Waves

F. Camas-Aquino, R. Jáuregui

Published May 26, 2026• 0 citations
arXivHTMLPDF

Abstract

The natural electromagnetic modes spontaneously emitted by an atom in free space are spherical vector waves (SVWs). Each SVW mode is uniquely linked to a specific dynamical--spherical--multipole--moment of the atomic system. In this work, we introduce a general formalism for evaluating spherical multipole transition rates under different boundary conditions, considering the superposition between a given SVW and the modes resulting from the boundary conditions. This formalism is applied to study the radiative properties of an atomic system trapped near the focus of a 4$π$ optical array. By appropriately selecting the external light field, the juxtaposed lenses of the optical array allow the atom to be illuminated with approximate spherical vector waves. Explicit expressions for the resulting multipole transition rates are presented as a function of the numerical aperture of the lenses. The feasibility of enhancing and inhibiting electric dipole-forbidden transitions using such an array, under current experimental capabilities, is briefly discussed.

DOI
10.48550/arxiv.2605.27558

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The natural electromagnetic modes spontaneously emitted by an atom in free space are spherical vector waves (SVWs). Each SVW mode is uniquely linked to a specific dynamical--spherical--multipole--moment of the atomic system. In this work, we introduce a general formalism for evaluating spherical multipole transition rates under different boundary conditions, considering the superposition between a given SVW and the modes resulting from the boundary conditions. This formalism is applied to study the radiative properties of an atomic system trapped near the focus of a 4πππ optical array. By appropriately selecting the external light field, the juxtaposed lenses of the optical array allow the atom to be illuminated with approximate spherical vector waves. Explicit expressions for the resulting multipole transition rates are presented as a function of the numerical aperture of the lenses. The feasibility of enhancing and inhibiting electric dipole-forbidden transitions using such an array, under current experimental capabilities, is briefly discussed.
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.
Each natural mode of the electromagnetic field within a parabolic mirror exhibits spatial localization and polarization properties that can be exploited for the quantum control of its interaction with atomic systems. The region of localization is not restricted to the focus of the mirror leading to a selective response of atomic systems trapped on its vicinity. We report calculations of the spontaneous emission rates for an atom trapped inside the mirror accounting for all atomic polarizations and diverse trapping regions. It is shown that electric dipole transitions can be enhanced near the focus of a deep parabolic mirror with a clear identification of the few vectorial modes involved. Out of the focus the enhancement vanishes gradually, but the number of relevant modes remains small. Ultimately this represents a quantum electrodynamic system where internal and external degrees of freedom cooperate to maximize a selective exchange and detection of single excitations.
We suggest to excite dipole-forbidden transitions in quantum mechanical systems by using appropriately designed optical nanoantennas. The antennas are tailored such that their near field contains sufficiently strong contributions of higher-order multipole moments. The strengths of these moments exceed their free-space analogs by several orders of magnitude. The impact of such excitation enhancement is exemplarily investigated by studying the dynamics of a three-level system. It decays upon excitation by an electric quadrupole transition via two electric dipole transitions. Since one dipole transition is assumed to be radiative, the enhancement of this emission serves as a figure of merit. Such self-consistent treatment of excitation, emission, and internal dynamics as developed in this contribution is the key to predict any observable quantity. The suggested scheme may represent a blueprint for future experiments and will find many obvious spectroscopic and sensing applications.
Radiation by the atoms of a resonant medium is a cooperative process in which the medium participates as a whole. In two previous papers we treated this problem for the case of a medium having slab geometry, which, under plane-wave excitation, supports coherent waves that propagate in one dimension. We extend the treatment here to the three-dimensional problem, focusing principally on the case of spherical geometry. By regarding the radiation field as a superposition of electric and magnetic multipole fields of different orders, we express it in terms of suitably defined scalar fields. The latter fields possess a sequence of exponentially decaying eigenmodes corresponding to each multipole order. We consider several examples of spherically symmetric initial excitations of a sphere. Small uniformly excited spheres, we find, tend to radiate superradiantly, while the radiation from a large sphere with an initially excited inner core exhibits temporal oscillations that result from the participation of a large number of coherently excited amplitudes in different modes. The frequency spectrum of the emitted radiation possesses a rich structure, including a frequency gap for large spheres and sharply defined and closely spaced peaks caused by the small frequency shifts and even smaller decay rates characteristic of the majority of eigenmodes.
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.
Atomic gases tightly trapped near the focus of an electromagnetic wave interact with photons that exhibit a complex structure, displaying strong gradients of field amplitude and local polarization that can lead to topological phase singularities. We illustrate the consequences of this structure on a paradigmatic nonlinear optical process: three-wave mixing. The process begins by proper selection of the pump field, whose spatial structure is tailored to present huge gradients of the EM field that enhance atomic excitations through forbidden transitions. Atoms can then be depopulated via two electric dipole decays in a cascade configuration, thus providing the three necessary waves. The properties of the down-converted photons are conditioned to those of the pump field through phase matching conditions. It is emphasized that the expression of the photons must incorporate both the structure of the vectorial EM modes and the spatial configuration of the atomic trap. Due to the three-dimensional focusing, the slowly varying envelope approximation becomes inadequate when describing the scattered EM field. We discuss an alternative using a Green function formalism valid for any configuration of the field that also allows to identify the phase matching conditions. Spherical vectorial waves exemplify most concepts here discussed, including the possibility of observing nonlinear quantum phenomena at the single photon level.