Quantum dynamics of the dissociation of a molecular BEC into fermionic atoms

We numerically simulate the exact quantum many-body dynamics of bosonic dimers dissociating into fermionic atoms by applying a Gaussian phase-space representation. The accuracy for higher-order correlations is demonstrated by comparison with a standard matrix representation for small systems of $10$ molecules and $10$ atomic modes. We then give results for systems of $10^{2}-10^{4}$ molecules and $10^{3}$ atomic modes, illustrating the potential capability of the phase-space representation for first-principles quantum dynamical simulations for fermionic systems of realistic sizes in current experiments. Molecule-atom correlations and the decoherence of the initially condensed molecules are studied as time evolves, with clear deviations from the approximate pairing mean-field theory.