In this thesis, I describe the development of a novel approach to atomic vector magnetometry
that utilizes the directional information contained in microwave-driven Rabi oscillations between
the hyperfine manifolds of 87Rb. These measurements take place in a heated microfabricated vapor
cell embedded within a microwave cavity with a single optical axis. By utilizing a complete model
for the atom-microwave coupling and collisional decoherence, I show how nontrivial spin dynamics
during Rabi oscillations from spin-exchange collisions in the strong-driving limit characterizes basic
properties of the atomic vapor. Additionally, I illustrate how this theoretical framework enables the
in-situ correction of heading errors in free induction decay (FID) signals, operating under realistic
conditions of imperfect pumping and high buffer gas pressures that often hinder other methods
of heading error-free measurements. Finally, I demonstrate vector magnetometry by referencing
Rabi measurements from multiple hyperfine transitions against calibrated microwave polarization
ellipses (MPEs). I further show how to accurately reference an intrinsic magnetometer frame to
the attitude of a probe beam from the magnetic field orientation where the Rabi oscillation signal
zeroes. This Rabi Amplitude Nulling to determine Beam Attitude (RANBA) technique could be
applied to calibrate a vector gradiometer and to monitor overall drifts in the intrinsic magnetometer
frame. While state-of-the-art vector magnetometers calibrate systematic errors arising from drifts
through sensor or bias field rotations, this research lays the groundwork towards achieving practical
vector calibration by only leveraging electromagnetic field manipulations; thereby circumventing
the need for intricate mechanical rotations or the application of large bias fields.
