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Coherent control via interplay between driving field and two-body interaction in a double well

We investigate interplay between external field and interatomic interaction and its applications to coherent control of quantum tunneling for two repulsive bosons confined in a high-frequency driven double well. A full solution of the system is generated analytically as a coherent non-Floquet state by using the Floquet states as a set of complete bases. It is demonstrated that the photon resonance of interaction leads to translation of the Floquet level-crossing points, and the non-resonant interaction causes avoided crossing of partial levels. In the non-Floquet states, the bosons beyond the crossing points slowly vary their populations, and the resonant (non-resonant) interactions enhance (decrease) the tunneling rate of the paired particles. Three different kinds of the coherent destructions of tunneling (CDT) at the crossing, avoided-crossing and uncrossing points, and the corresponding stationary-like states, are illustrated. The analytical results are numerically confirmed and perfect agreements are found. Based on the results, an useful scheme of quantum tunneling switch between stationary-like states is presented.