Trapped atoms in spatially-structured vector light fields

TL;DR

This paper develops a comprehensive framework to analyze how complex, structured light fields influence atomic electronic and motional states, enabling tailored quantum interactions for advanced quantum technologies.

Contribution

It introduces a general spherical tensor decomposition method to compute atomic transition matrix elements for arbitrary structured light fields, including their spatial and polarization effects.

Findings

Spatially-structured beams exhibit longitudinal fields affecting selection rules.

The framework applies to various beam types like Hermite-Gaussian and Laguerre-Gaussian.

It aids in designing quantum protocols with trapped atoms in complex light fields.

Abstract

Spatially-structured laser beams, eventually carrying orbital angular momentum, affect electronic transitions of atoms and their motional states in a complex way. We present a general framework, based on the spherical tensor decomposition of the interaction Hamiltonian, for computing atomic transition matrix elements for light fields of arbitrary spatial mode and polarization structures. We study both the bare electronic matrix elements, corresponding to transitions with no coupling to the atomic center-of-mass motion, as well as the matrix elements describing the coupling to the quantized atomic motion in the resolved side-band regime. We calculate the spatial dependence of electronic and motional matrix elements for tightly focused Hermite-Gaussian, Laguerre-Gaussian and for radially and azimuthally polarized beams. We show that near the diffraction limit, all these beams exhibit longitudinal fields and field gradients, which strongly affect the selection rules and could be used to tailor the light-matter interaction. The presented framework is useful for describing trapped atoms or ions in spatially-structured light fields and therefore for designing new protocols and setups in quantum optics, -sensing and -information processing.