Rogue decoherence in the formation of a macroscopic atom-molecule superposition

We theoretically examine two-color photoassociation of a Bose-Einstein condensate, focusing on the role of rogue decoherence in the formation of macroscopic atom-molecule superpositions. Rogue dissociation occurs when two zero-momentum condensate atoms are photoassociated into a molecule, which then dissociates into a pair of atoms of equal-and-opposite momentum, instead of dissociating back to the zero-momentum condensate. As a source of decoherence that may damp quantum correlations in the condensates, rogue dissociation is an obstacle to the formation of a macroscopic atom-molecule superposition. We study rogue decoherence in a setup which, without decoherence, would yield a macroscopic atom-molecule superposition, and find that the most favorable conditions for said superpositions are a density $\rho\sim10^{12}\,{\rm cm}^{-3}$ and temperature $T\sim0.1$~nK.