Tunable molecular interactions near a bosonic atomic Feshbach resonance: stability and collapse of molecular condensates

Systematically understanding and gaining control over Feshbach molecules in the quantum degenerate regime has been a central goal in cold atom research. Here we address the challenge of identifying the microscopic origin of extensive instability regions which are known to be present experimentally; these inhibit the formation of Feshbach-molecular condensates comprised of bosonic atoms. In this paper, based on a calculation of the compressibility, we present ground-state stability phase diagrams for these condensates. With this analysis we are able to extract concrete results for an effective inter-molecular scattering length which assumes negative values in the unstable regions, likely reflecting condensate collapse. Our expressions for this scattering length, both in the many body and two body contexts, should, with future experiments, enable a full characterization of bosonic-Feshbach molecules and condensates and their associated many-body physics.