双光子激光器的量子理论

QUANTUM THEORY OF TWO-PHOTON LASER

从双光子激光器三能级模型的微观哈密顿量出发,应用慢变幅度近似和双光子旋波近似,在双光子过程压倒其它辐射过程的情形下,导出二能级双光子模型的等效哈密顿量,从而建立三能级模型与二能级双光子模型的正确关系。得到的等效哈密顿量包含通常讨论中所忽略的光学斯塔克效应项,其系数在一般情形下可与等效互作用常数具有相间的数量级。根据这等效哈密顿量,应用Haken激光理论的标准方法研究定态的阈值,平均光子数,自生频移,光子统计和涨落,并与以前未计及光学斯塔克效应的结果作比较。

Starting from the microscopic Hamiltonian of the three-level model and making use of the slowly varying amplitude approximation and the two-photon rotating wave approximation, we derive an effective Hamiltonian for the two-level two photon model under conditions where the two-photon process dominates the other radiartive processes, so that an exact relation between the three-level model and the two-level two-photon model is established. The effective Hamiltonian includes a term come from the optical Stark effect which was neglected in the conventional treatment. The coefficient of this term may have the same order of magnitude as the effective coupling constant. Based on this effective Hamiltonian, the standard method of Haken's laser theory is applied to study the threshold, the mean photon number, the self-induced frequency shift, the photon statistics and the fluctuation in steady states. Results are compared with previous ones which neglect the Strk effect.