In this paper, we establish the general quantum theory of the micromazer wi
th Kerr medium. When a two-Level atom enters into the Kerr medium cavity fi
eld of a coherent state via z-motion, we analyze and calculate the atomic e
mission probability of different regimes ( thermal-atom and ultracold-atom
regimes) The influence of coupling constant chi, detuning Delta and the ato
mic injection rate r on the atomic emission probability is discussed emphat
ically.