Creating Steady Atom-Molecule Entanglement by Demkov-Kunike Type Non-adiabatic Transition

We, based on the photoassociation of fermion atoms into bosonic molecules, propose a scheme to create the steady entanglement between the atom state and the molecule state inside an optical lattice. The stability of entanglement state is guaranteed by sweeping the frequency of Ramman laser beam through resonance according to the second Demkov-Kunike (DK2) nonadiabatic transition model\cite{DK,models}. The probability amplitude of each components can be precisely controlled by adjusting the sweeping parameter.