We study time evolution of the interacting system consisting of quantized photon field and electron field in semiconductor superlattices analytically/numerically. In the single-subband condition, the electron dynamics is able to generate several nonclassical photon states depending on the external dc bias. Effects of the intersubband transition for the quantized photon states is investigated in the multi-subband condition. Competition of two-kinds of intersubband electron dynamics, Rabi oscillation and Zener tunneling, is discussed.