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Atomic magnetometry is one of the most sensitive ways to measure magneticfields. We present a method for converting a naturally scalar atomicmagnetometer into a vector magnetometer by exploiting the polarizationdependence of hyperfine transitions in rubidium atoms. First, we fullydetermine the polarization ellipse of an applied microwave field using aself-calibrating method, i.e. a method in which the light-atom interactionprovides everything required to know the field in an orthogonal laboratoryframe. We then measure the direction of an applied static field using thepolarization ellipse as a three-dimensional reference defined by Maxwell'sequations. Although demonstrated with trapped atoms, this technique could beapplied to atomic vapors, or a variety of atom-like systems.

Self-calibrating vector atomic magnetometry through microwave polarization reconstruction