With this pilot study, we are hoping to test the feasibility of a larger study in the future and to learn whether positive airway pressure therapy reduces the recurrence risk of atrial fibrillation after successful catheter ablation procedure among patients with atrial fibrillation and obstructive sleep apnea. The results from this study will help us refine the design for a future larger study, and will ultimately improve care of patients with obstructive sleep apnea and atrial fibrillation.