First-Order Phase Transition in Atom-Molecule Quantum Degenerate Mixtures with Coherent Three-Body Recombination.

We map the phase diagram of a two-mode atom-molecule Bose-Einstein condensate with Fano-Feshbach and coherent three-body recombination (cTBR) terms. The standard second-order phase transition observed as the molecular energy is tuned through the Fano-Feshbach resonance is replaced by a first-order transition when cTBR becomes prominent, due to a double-well structure in the free energy landscape. This transition is associated with atom-molecule entanglement, bistability, and molecular metastability. Our results establish cTBR as a powerful knob for quantum state engineering and control of reaction dynamics in ultracold chemistry.