  We investigate the many-body Landau-Zener (LZ) process in a two-site
Bose-Hubbard model driven by a time-periodic field. We find that the driving
field may induce sideband transitions in addition to the main LZ transitions.
These photon-induced sideband transitions are a signature of the
photon-assisted tunneling in our many-body LZ process. In the strong
interaction regime, we develop an analytical theory for understanding the
sideband transitions, which is confirmed by our numerical simulation.
Furthermore, we discuss the quantization of the driving field. In the effective
model of the quantized driving field, the sideband transitions can be
understood as the LZ transitions between states of different "photon" numbers.
