Polarization-Sensitive Imaging in Magnetic Environments

TL;DR

This paper models and demonstrates how magnetic field-induced birefringence causes polarization-dependent aberrations in ultracold atomic gas imaging, and proposes a correction method using holography and phase masks.

Contribution

It introduces a coupled model of atomic polarizability and spin orientation to predict aberrations and develops a holographic correction technique for magnetic field effects.

Findings

Model accurately predicts image distortions across temperatures.

Holographic correction removes magnetically induced aberrations.

Residual optical asymmetries cause minor offsets.

Abstract

Nondestructive spin-resolved imaging of ultracold atomic gases requires calculating the differences of the refractive indices seen by two circular probe polarizations. Perfect overlap of the two images, corresponding to two different polarizations, is required well below the feature size of interest. In this paper, we demonstrate that the birefringence of atoms in magnetic field gradients results in polarization-dependent aberrations in the image, which deteriorates the overlap. To that end, we develop a model that couples atomic tensor polarizability with position-dependent spin orientation and yields aberration predictions for accumulated phase shifts in arbitrary field geometries. Applied to data from an ultra-cold atomic cloud trapped in a Ioffe-Pritchard trap, the model quantitatively reproduces the observed distortion across a range of temperatures. A residual offset of $\sim1\;\mu\mathrm{m}$ remains even under uniform field conditions, likely due to optical asymmetries. For images obtained through off-axis holography, the full complex field of the probe enables post-processing removal of all magnetically induced aberrations through a single numerically calculated Fourier-space phase mask.