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Tunnelling of a two-level atom is investigated in the two-photon mazer when the atom is initially prepared in a coherent superposition state and the cavity in various quantum states. For a strong coherent field, the tunnelling exhibits more regular oscillations but less remarkable switch effect than that in the one-photon mazer. It is discovered that in the presence of atomic coherence, the transmission probabilities in the ultracold regime are significantly different when the cavity field is initially in coherent, squeezed vacuum, even cat and odd cat states,respectively.