Measuring non-linear Faraday rotation in cold atoms in presence of persistent transverse fields using tunable differential imaging.

Non-linear Faraday rotation in cold atoms promises precision magnetometry due to narrower magnetic resonance linewidth compared to the linear Faraday effect. Imaging techniques based on linear Faraday effect have emerged as a tool to characterize the dynamics of ultracold atomic clouds. Using a camera instead of balanced detectors, we can obtain the spatial distribution of polarization rotation in a uniformly intense optical beam. However, the finite dynamic range of the imaging device limits the sensitivity to measure non-linear Faraday rotation at a given incident power. Here, we experimentally demonstrate a differential imaging technique in which we can tune parameters to improve contrast and the sensitivity to the non-linear Faraday rotation signal by a factor of ≈7 over existing imaging methods. The atomic cloud experiences a uniform optical field even when shifted by persistent magnetic fields making the method robust. This allows us to study the effect of transverse fields on non-linear Faraday rotation in ultra-cold atoms, paving the way toward spatially resolved vector magnetometry.