Quantum theory of multiphoton lasers. II. Systems without detailed balance

A quantum-mechanical model for a multiphoton laser is proposed by an obvious generalization of the usual one-photon laser model. The authors consider a class of lasers which preserve detailed balance. This condition is ensured by assuming a multiphoton loss mechanism for the laser light of the same order as the multiphoton gain from the stimulated emission process. Solutions for the stationary density operator of the light field are obtained by a straightforward generalization of the techniques of Scully and Lamb. The multiphoton laser around threshold exhibits behaviour analogous to a second-order phase transition. A non-thermal distribution of multiphoton laser light is achieved above threshold.