  Applying a magnetic field as a method for tuning the frequency of
Autler-Townes splitting for Rydberg electrometry has recently been
demonstrated. In this paper we provide a theoretical understanding of EIT
signals in the presence of a large magnetic field, as well as demonstrate some
advantages of this technique over traditional Autler-Townes based electrometry.
We show that a strong magnetic field provides a well-defined quantization axis
regardless of the optical field polarizations, we demonstrate that by
separating the $m_J$ levels of the Rydberg state we can perform an
Autler-Townes splitting with a single participating dipole moment, and we
demonstrate recovery of signal strength by populating a single $m_J$ level
using circularly polarized light.
