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Journal of the Optical Society of America B

Quadrupole interaction of Tricomi–Gaussian beams with atoms

Shuaishuai Ren, Mengyuan Han, Xinyi Cao, Lanbo Liu, Zhiwei Cui

Published Nov 25, 2024• 4 citations
Publisher

Abstract

The interaction of light beams with atoms is one of the most important fields in physics, and the quadrupole transitions play an important role in such an interaction. In this work, we focus on the quadrupole interaction of Tricomi–Gaussian beams with atoms. The analytical expression of the paraxial Tricomi–Gaussian beams is derived using the angular spectrum representation. The formulas for describing the quadrupole interaction of Tricomi–Gaussian beams with two-level atoms are presented. The Cs atom is taken as an example, and the spatial distributions of the quadrupole Rabi frequency for such a two-level atom in Tricomi–Gaussian beams with different parameters are simulated and analyzed. It is revealed that the Rabi frequency of an atom in Tricomi–Gaussian beams can be flexibly controlled by choosing the asymmetric constants and order of the beams, which provides a pathway for tuning the repulsive potential and trapping potential acting on the atoms. This study is expected to provide useful insights into the interactions of Tricomi–Gaussian beams with atoms and their further applications.

DOI
10.1364/josab.533781

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The interaction of light beams with atoms is one of the most important fields in physics, and the quadrupole transitions play an important role in such an interaction. In this work, we focus on the quadrupole interaction of Tricomi–Gaussian beams with atoms. The analytical expression of the paraxial Tricomi–Gaussian beams is derived using the angular spectrum representation. The formulas for describing the quadrupole interaction of Tricomi–Gaussian beams with two-level atoms are presented. The Cs atom is taken as an example, and the spatial distributions of the quadrupole Rabi frequency for such a two-level atom in Tricomi–Gaussian beams with different parameters are simulated and analyzed. It is revealed that the Rabi frequency of an atom in Tricomi–Gaussian beams can be flexibly controlled by choosing the asymmetric constants and order of the beams, which provides a pathway for tuning the repulsive potential and trapping potential acting on the atoms. This study is expected to provide useful insights into the interactions of Tricomi–Gaussian beams with atoms and their further applications.
We examine the applicability and limitations of several established measures of paraxiality in the context of electric quadrupole interactions between light and trapped atoms. Focusing on Laguerre–Gaussian beams, we compare analytical predictions—particularly transition amplitudes and selection rules—derived under the paraxial assumption with full numerical solutions obtained via diffraction integrals that account for the complete vectorial field structure. This comparison allows us to assess the validity and relevance of these measures across a range of beam parameters. We also investigate the role of the power-series expansion in the paraxial parameter in bridging paraxial and nonparaxial regimes.
Recently it has been shown that the quadrupole interactions can be improved significantly as the atom interacts at near resonance with the Laguerre-Gaussian (LG) mode. In this paper, we illustrate that other kinds of optical vortex can be also led to a considerable enhancement of quadrupole interaction when the atom interacts with optical modes at near resonance. The calculations are performed on an interesting situation with Cs atom, where the process is concerned with dipole-forbidden and quadrupole-allowed transitions with a convenable choice of atomic and optical mode parameters. In this direction, we show that the quadrupole transitions can be significantly enhanced and therefore they can play an interesting role and lead to new features of atom-light interaction, which can have some constructive implications in experiments.
This article investigates the quadrupole excitation of a trapped atom exposed to the tightly focused Laguerre-Gaussian (LG) beams with parallel and antiparallel spin angular momentum (SAM) and orbital angular momentum (OAM) under nonparaxial conditions. The Rabi frequency profile of allowed quadrupole transition channels, modified by SAM and OAM interaction, in the focal plane is provided. In the case of antiparallel SAM and OAM, the excitation probability undergoes substantial modification due to the considerable contribution of longitudinal intensity variations in tightly focused condition. The findings offer insights into controlling localized atom transition, including OAM transfer, with potential applications in qudit-based technologies.
Recent studies have confirmed the coupling of optical vortices, such as Laguerre-Gaussian and Bessel-Gaussian modes, to quadrupole-active atomic transitions. This interaction has been shown to be enhanced considerably in the case of Laguerre-Gaussian beams due to the gradient coupling, particularly, in the case of a relatively large winding number. Here, we consider the trapping and the dynamics of atoms in the optical quadrupole potential generated by two coaxial counterpropagating optical vortex beams. We focus on the atomic transition $6{\phantom{\rule{0.16em}{0ex}}}^{2}{S}_{1/2}\ensuremath{\rightarrow}5{\phantom{\rule{0.16em}{0ex}}}^{2}{D}_{5/2}$ in Cs which is a dipole-forbidden but a quadrupole-allowed transition. We show how this atomic transition engages with the optical vortex fields at near resonance, leading to atom trapping in the optical quadrupole potential well accompanied by translational motion. We show how the optical forces generate the motion of the atoms trapped within the quadrupole potential, illustrating the results using typical experimentally accessible parameters.
ENGLISH ABSTRACT : Structured light has seen many applications in the fields of telecommunications, optical microscopy, and quantum information processing, however, few works exist that explore the interactions of structured light with atoms. In this thesis, we seek to explore these interactions further, both theoretically and experimentally. Of particular interest is the interaction between an atom and a Laguerre-Gauss beam of topological charge l = 1. Such a beam is easily constructed in a lab setting, and also carries an additional unit of orbital angular momentum that has been shown to couple with atomic transitions. Theoretically, we derive a framework upon which to describe atomic transitions due structured light. We find that tailoring light’s structure will have a direct influence on the strength of quadrupole transitions in atoms. A theoretical analysis of the effects of an atom situated in a magnetic field interacting with a Laguerre-Gauss beam of topological charge l = 1 was conducted. It was found that atoms placed in a region of zero intensity, such as the beam centre, can undergo quadrupole transitions – in contrast to dipole transitions that rely on the field intensity. We go on to show the differences between this beam and a gaussian beam, and find that the former can cause transitions between magnetic sub-levels that are typically considered forbidden in quadrupole spectroscopy under certain conditions. We explain this through the principle of conservation of angular momentum. Experimentally, we chose to use a potassium vapour cell as our medium, as the linewidth of its quadrupole transition was relatively large, and could be simply modelled as a three-level system to easily understand its dynamics. We performed an experiment where we indirectly measured a 4 2S1/2 → 3 2Dj quadrupole transition for j = 3/2, 5/2, induced by a custom-built external cavity diode laser operating at ∼ 464.3 nm. The 4 2S1/2 → 3 2Dj transition was measured by monitoring the fluorescence due to a dipole decay 4 2Pj 0 → 4 2S1/2 during the decay cascade from 3 2Dj → 4 2Pj 0 → 4 2S1/2 , where j 0 = 1/2, 3/2. We then used our theoretical framework to fit the sum of two gaussian peaks to our measured fluorescence spectrum, and find an excellent agreement with our data.