Existence and stability of coupled atomic-molecular Bose-Einstein condensates

Recent progress in the study of Bose-Einstein condensation ~BEC! is associated with the possibility of creating multicomponent condensates of different, coherently coupled, atomic species. Furthermore, the possibility of creating a hybrid condensate of atomic and molecular fractions has been suggested @1#, and has recently received some experimental support @2#. In such an atomic-molecular BEC ~AMBEC!, atoms would bind into molecules coherently, through a ~possibly reversible! photoassociation-induced stimulated recombination in two-body collisions. The problem of generation of coupled atomic and molecular condensates is fascinating from different viewpoints ~see, e.g., Refs. @2–5#!. Apart from the prospect of observing the first molecular condensate, this problem offers a unique atom-optics analog to the process of second-harmonic generation in nonlinear optics. The nonlinearity produced by coherent atomic-molecular coupling is expected to be responsible for a number of dynamical effects, including interspecies Josephson-like population oscillations @3,6,7#, ‘‘clumping’’ of the condensate due to the atom-optical analog of modulational instability @4,5#, etc. In a yet to be realized AMBEC, the atom-molecular parametric coupling would compete with other collisional interactions, which corresponds to the competing quadratic and cubic effects in nonlinear optics @8#, and suggests the existence of liquidlike droplets of the atomic-molecular condensates @6#. In this paper, we present a comprehensive analysis of the mean-field model for an AMBEC created via a coherent stimulated Raman photoassociation process. Using the recently reported data for the intraspecies and interspecies scattering lengths @2#, we analyze the spatial structure of the AMBEC with and without a trap. We show that even when the condensate is unstable in a confining trap, self-confined, stable AMBEC droplets can be created, after the condensate is released from the trap. Untrapped droplets of the coherent matter waves resemble self-trapped spatial optical solitons supported by parametric interaction @8#.