We investigate scattering phenomena in a one-dimensional attractive Bose-Hubbard model with a time-periodically-modulated impurity. We analyze both single-particle and pair (doublon) transmission, exploring a range of interaction strengths and drive amplitudes. Our exact numerical results reveal excellent quantitative agreement with analytical predictions in the high-frequency limit. At intermediate and weak attractive interactions, we observe significant pair dissociation and the emergence of dynamically localized single-particle modes. These features are reminiscent of Floquet bound states in the continuum. These findings provide avenues for engineering controllable quantum transport and localized states in ultracold-atom experiments.

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• Quantum transport
• Floquet systems
• Bose-Hubbard model