Photon statistics of the micromaser with a Kerr medium

We have established the master equation for the micromaser with a Kerr medium. We have studied the photon statistics of the micromaser with a Kerr medium field and analysed the influence of the Kerr effect on the photon statistics. The influence of the Kerr effect on the photon statistics is different in two regimes. In the thermal-atom regime, the Kerr effect produces quantum noise, and decreases the mean photon number. In the ultracold-atom regime, with the increase of the nonlinear parameter of the Kerr medium, the stability of the mean photon number and the normalized variance enhances the mean photon number, and the normalized variance exhibits collapse-revival phenomena periodically, their resonance peaks become lower, and the photon statistics of more and more regions are sub-Poissonian.