Rapid phase-diffusion between atomic and molecular Bose-Einstein condensates

We study the collisional loss of atom-molecule coherence after coherently dissociating a small fraction of a molecular Bose-Einstein condensate into atoms. The obtained $n$-atoms states are two-atom (SU(1,1)) coherent states with number variance $\Delta n\propto n$ compared to $\Delta n\propto \sqrt{n}$ for the spin (SU(2)) coherent states formed by coherent splitting of an atomic condensate. Consequently, the Lorentzian atom-molecule phase-diffusion is faster than the Gaussian phase-diffusion between separated atomic condensates, by a $\sqrt{n}$ factor.