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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Center of mass transitions in the quadrupole interaction of atomic systems with Laguerre-Gaussian beams

Adrian Alexandrescu, Enzo Mario Di Fabrizio, Dan Cojoc

Published Aug 15, 2005• 0 citations
Publisher

Abstract

In the frame of paraxial approximation, we consider the case of free atoms interacting with an Lagtierre-Gaussian beam. Using Power-Zienaii-Wooley scheme, we calculate the interaction Hamiltonian in the quadrupole approximation and including center of mass motion of the atomic system. The expression of the center of mass transition probability is derived in analytic form. The influence of the beam and atomic system parameters on the center of mass transition probability are discussed.

DOI
10.1117/12.639778

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In the frame of paraxial approximation, we consider the case of free atoms interacting with an Lagtierre-Gaussian beam. Using Power-Zienaii-Wooley scheme, we calculate the interaction Hamiltonian in the quadrupole approximation and including center of mass motion of the atomic system. The expression of the center of mass transition probability is derived in analytic form. The influence of the beam and atomic system parameters on the center of mass transition probability are discussed.
We derive the interaction Hamiltonian of a Laguerre–Gaussian beam with a simple atomic system, under the assumption of a small spread of the centre of mass wavefunction in comparison with the waist of the Laguerre–Gaussian beam and taking into account the centre of mass motion of the atomic system. Using the properties of regular spherical harmonics the internal and centre of mass dynamical variables are separated without making any multipolar expansion. The features of angular momentum exchange process assisted by Laguerre–Gaussian beams and the influence of their winding number on the selection rules and transition probability of internal and centre of mass motion are discussed.
We derive the interaction Hamiltonian between a diatomic molecule and a Laguerre-Gaussian beam under the assumption of a small spread of the center of mass wave function of the molecule in comparison with the beam waist. Considering the dynamical variables of the center of mass, vibrational, rotational, and electronic motion, we show that, within the electronic dipole approximation, the orbital angular momentum of the field couples with the rotational and electronic motion. The changes in the transition probabilities and selection rules induced by the field orbital angular momentum and the applicability of the derived interaction mechanisms for polyatomic molecules are discussed.
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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.
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.