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We study the quantum dynamics of superfluids of bosons hybridized with Cooperpairs near Feshbach resonances and the influence of fermion-boson conversion onMott states. We derive a set of equations of motion which describe novel lowenergy dynamics in superfluids and obtain a new distinct branch of {\em gapped}collective modes in superfluids which involve anti-symmetric phase oscillationsin fermionic and bosonic channels. We also find that Mott states in general areunstable with respect to fermion-boson conversion; particles become delocalizedand the off-diagonal long-range order of superfluids can be developed when afinite conversion is present. We further point out a possible hidden order inMott states. It is shown that the quantum dynamics of Fermi-Bose states can becharacterized by either an effective coupled $U(1)\otimes U(1)$ quantum rotorHamiltonian in a large-N limit or a coupled XXZ $\otimes$ XXZ spin Hamiltonianin a single-orbit limit.Comment: 15 pages, 4 figure

Quantum dynamics, particle delocalization and instability of Mott states: the effect of fermion–boson conversion on Mott states