# Measuring the polarization of electromagnetic fields using Rabi-rate measurements with spatial resolution: experiment and theory

## TL;DR

This paper introduces a method to measure and characterize the polarization of electromagnetic fields with spatial resolution using Rabi-rate measurements on atoms, combining experiment and theory for applications in field sensing.

## Contribution

It develops a comprehensive framework linking Rabi rates to polarization parameters, enabling full polarization characterization with minimal measurements.

## Key findings

- Successfully measured 2D RF electric field distribution at 25.6 GHz.
- Derived equations relating Rabi rates to polarization parameters.
- Demonstrated potential for field sensing and characterization in various applications.

## Abstract

When internal states of atoms are manipulated using coherent optical or radio-frequency (RF) radiation, it is essential to know the polarization of the radiation with respect to the quantization axis of the atom. We first present a measurement of the two-dimensional spatial distribution of the electric-field amplitude of a linearly-polarized pulsed RF electric field at $\sim 25.6\,$GHz and its angle with respect to a static electric field. The measurements exploit coherent population transfer between the $35$s and $35$p Rydberg states of helium atoms in a pulsed supersonic beam. Based on this experimental result, we develop a general framework in the form of a set of equations relating the five independent polarization parameters of a coherently oscillating field in a fixed laboratory frame to Rabi rates of transitions between a ground and three excited states of an atom with arbitrary quantization axis. We then explain how these equations can be used to fully characterize the polarization in a minimum of five Rabi rate measurements by rotation of an external bias-field, or, knowing the polarization of the driving field, to determine the orientation of the static field using two measurements. The presented technique is not limited to Rydberg atoms and RF fields but can also be applied to characterize optical fields. The technique has potential for sensing the spatiotemporal properties of electromagnetic fields, e.g., in metrology devices or in hybrid experiments involving atoms close to surfaces.