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

We study the quantum dynamics of superfluids of bosons hybridized with Cooper pairs near Feshbach resonances and the influence of fermion-boson conversion on Mott states. We derive a set of equations of motion which describe novel low energy dynamics in superfluids and obtain a new distinct branch of {\em gapped} collective modes in superfluids which involve anti-symmetric phase oscillations in fermionic and bosonic channels. We also find that Mott states in general are unstable with respect to fermion-boson conversion; particles become delocalized and the off-diagonal long-range order of superfluids can be developed when a finite conversion is present. We further point out a possible hidden order in Mott states. It is shown that the quantum dynamics of Fermi-Bose states can be characterized by either an effective coupled $U(1)\otimes U(1)$ quantum rotor Hamiltonian in a large-N limit or a coupled XXZ $\otimes$ XXZ spin Hamiltonian in a single-orbit limit.