Spinor atom-molecule conversion via laser-induced three-body recombination

We study the theory of several aspects of the dynamics of coherent atom-molecule conversion in spin-one Bose-Einstein condensates. Specifically, we discuss how, for a suitable dark-state condition, the interplay of spin-exchange collisions and photo association leads to the stable creation of an atom-molecule pair from three initial spin-zero atoms. This process involves two two-body interactions and can be intuitively viewed as an effective three-body recombination. We investigate the relative roles of photo association and of the initial magnetization in the "resonant" case, where the dark-state condition is perfectly satisfied. We also consider the "nonresonant" case, where that condition is satisfied either only approximately-the so-called adiabatic case-or not at all. In the adiabatic case, we derive an effective nonrigid pendulum model that allows one to conveniently discuss the onset of an antiferromagnetic instability in an "atom-molecule pendulum," as well as large-amplitude pair oscillations and atom-molecule entanglement.