Abstract

We have studied the photon statistics of the non-degenerate two-photon laser composed of many noninteracting atoms with Kerr nonlinearity. Nonlinearity of the gain is accounted for by the Lamb–Scully approach. Under certain conditions, we obtain an approximate photon distribution function. In the region above lasing threshold, the first few moments of the photon numbers are calculated analytically, and the threshold condition for stable lasing that depends on the Kerr parameter and detuning are obtained. We analyze the properties of the cavity field through the Mandel $Q$ parameter, second-order correlation functions, Cauchy–Schwarz inequality for a range of Kerr parameters, atomic injection rate, and cavity detuning. Nonclassicality of the field is found through sub-Poissonian statistics, particularly at a low injection rate and high Kerr coupling with negative detuning. These nonclassicality conditions correspond to low photon numbers and depend on the sign of the detuning. The violation of the Cauchy–Schwarz inequality also occurs at low photon numbers but over a wide range of parameters, especially at short transient times. Our results show that the two-photon laser with Kerr nonlinearity is a promising quantum nonlinear optical system for developing controllable nonclassical light sources.

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