Manipulating many-body quantum states via single-photon resonance

For an atomic Bose-Hubbard dimer quantum control via multiphoton processes have been investigated widely. We here explore how to manipulate the many-body quantum states via single-photon resonance by treating the periodic driving as a weak perturbation. The transition probabilities up to second-order approximation are given as functions of the driving parameters, which are considerable only for the single-photon resonance case. Due to some transition matrix elements vanishing, the first-order quantum transition obeys a selection rule. The non-forbidden transitions involve states of different entanglement entropies and all (part) of the forbidden transitions relate to the entropy balances between two states for odd (even) number of particles. The results provide a new route for manipulating many-body quantum states and entanglement entropies, and controlling the atomic tunnelings of the Bose-Hubbard dimer.