Tunable Molecular Interactions Near an Atomic Feshbach Resonance: Stability and Collapse of a Molecular Bose-Einstein Condensate

Understanding and controlling interactions of ultracold molecules is a cornerstone of quantum chemistry. While the laboratory creation of degenerate molecular gases comprised of bosonic atoms has unlocked powerful new platforms for quantum simulation, progress is limited by the absence of a robust theoretical framework for characterizing inter-molecular interactions. This is in stark contrast to the situation for Fermi gases. In this Letter, we present such a framework providing universal expressions for these molecular scattering lengths as functions of experimentally measurable quantities. Our discoveries are crucial for understanding molecular condensate formation. Calculations of the compressibility reveal that a sign change in such molecular scattering lengths is directly correlated with the instability of these condensates. These results offer fresh insight with broad applications for atomic, molecular, and condensed matter physics, as well as quantum chemistry.