# Vector magnetometry using electromagnetically induced transparency with $lin\perp lin$ polarization

## TL;DR

This paper demonstrates a method for vector magnetometry using electromagnetically induced transparency with lin perpendicular lin polarization in rubidium atoms, enabling determination of magnetic field direction and strength through spectral analysis.

## Contribution

It introduces a novel EIT-based vector magnetometry technique utilizing polarization-dependent spectral features and provides both experimental and theoretical analysis.

## Key findings

- Magnetic field direction can be determined from the relative strengths of EIT peaks.
- Magnetic field strength can be calculated from the separation of EIT peaks.
- EIT peak amplitudes oscillate with polarization orientation, aiding in magnetic field analysis.

## Abstract

Vector magnetometry was studied using the electromagnetically induced transparency (EIT) with linear $\perp$ linear ($lin \perp lin$) polarization of the probe and the pump beams in $^{87}Rb$ - $D_2$ transition. The dependence of the EIT on the direction of the quantization axis and the relative orientation of the polarization of the applied electric fields was studied experimentally. We have shown that from the relative strengths of the $\sigma$ and $\pi$ EIT peaks, the direction of the magnetic field can be found. Moreover from the relative separation between the $\sigma$ and $\pi$ EIT peaks, the strengths of the magnetic field can be calculated. We have also demonstrated that the EIT peak amplitudes show oscillatory behaviour depending upon the orientation of the laser polarization relative to the magnetic field direction. Using the positions of the maxima and minima, the direction of the magnetic field can be calculated. To understand the experimental observation, a theoretical study has been done numerically considering all the thirteen Zeeman sub-levels. Apart from the numerical model, a toy model has also been considered to obtain an analytical response of the medium considering the velocity distribution. The dependencies of the magnetic field direction and the polarization direction of the electric fields have been explicitly derived in the analytical model. Further the direction of the magnetic field is calculated using the analytical solution. This study can be helpful in order to make an EIT based atomic vector magnetometer at room temperature.