  We employ a method involving coherent periodic modulation of Raman laser
intensity to induce resonance transitions between energy levels of a spin-orbit
coupled atom in a symmetric double-well trap. By integrating photon-assisted
tunneling (PAT) technique with spin-orbit coupling (SOC), we achieve resonance
transitions between the predefined energy levels of the atom, thereby enabling
further precise control of the atom's dynamics. We observe that such
photon-like resonance can induce a transition from a localized state to atomic
Rabi oscillation between two wells, or effectively reduce tunneling as
manifested by a quantum beating phenomenon. Moreover, such resonance
transitions have the potential to induce spin flipping in a spin-orbit coupled
atom. Additionally, the SOC-mediated transition from multiphoton resonance to
fundamental resonance and the SOC-induced resonance suppression are also
discovered. In these cases, the analytical results of the effective coupling
coefficients of the resonance transition derived from a four-level model can
account for the entire dynamics, demonstrating surprisingly good agreement with
the numerically exact results based on the realistic continuous model.
