Pairing Superfluid–Insulator Transition Induced by Atom–Molecule Conversion in Bosonic Mixtures in Optical Lattice

Motivated by the recent experiment on bosonic mixtures of atoms and molecules, we investigate pairing superfluid–insulator (SI) transition for bosonic mixtures of atoms and molecules in a one-dimensional optical lattice, which is described by an extended Bose–Hubbard model with atom–molecule conservation (AMC). It is found that AMC can induce an extra pair–superfluid phase though the system does not demonstrate pair-hopping. In particular, the system may undergo several pairing SI or insulator–superfluid transitions as the detuning from the Feshbach resonance is varied from negative to positive, and the larger positive detuning can bifurcate the pair–superfluid phases into mixed superfluid phases consisting of single-atomic and pair-atomic superfluid. The calculation of the second-order Rényi entropy reveals that the discontinuity in its first-order derivative corresponds to the phase boundary of the pairing SI transition. This means that the residual entanglement in our mean-field treatment can be used to efficiently capture the signature of the pairing SI transition induced by AMC.