Even if well controlled, atrial fibrillation is not something I would be comfortable knowing my pilot had.
The issue is not the heart rhythm itself, but what happens to blood as a result of the fibrillation. Atrial fibrillation causes the atria (the top part of the heart) to quiver instead of purposefully beating in sequence with the ventricles (bottom part of the heart). The quivering disrupts the smooth flow of blood, and this causes clots to form. These clots could kill someone in an instant, if they traveled to the brain (stroke), heart (myocardial infarct) or lung (pulmonary embolism).
I do not know the specifics of licensing, but would imagine it would involve several sequential EKGs showing the fibrillation is gone before license is granted.