Phase Doubling and Entanglement in Coherent Many-Body Chemical Reactions

In the quantum degenerate regime, atoms and molecules can occupy a single quantum state, forming coherent matter waves. Here reactions are described by nonlinear mixing of the matter waves, giving rise to quantum many-body chemistry, where spatial coherence is preserved between the reactants and products. While the phase matching of matter waves during the reaction process has been theoretically predicted, experimental confirmation has remained elusive. Here we report on the observation of matter wave phase doubling when bosonic atoms pair into molecules. Using matter wave diffraction, we verify spatial phase coherence and observe a two-fold increase of phase in the molecular wavefunction, confirming the matter-wave version of phase doubling. The diffraction patterns also reveal non-classical correlations indicative of entangled atom pairs formed during the reaction. Our results establish molecular matter-wave diffraction as a powerful tool to probe quantum coherence and entanglement generation in chemically reactive quantum gases.