Quantum mechanical solutions of the laser masterequation
Quantum mechanical solutions of the laser masterequation
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激光主方程的量子力学解
DOI：
10.1007/bf01326496
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发表时间：
1967
期刊：
影响因子：
--
通讯作者：
W. Weidlich
中科院分区：
文献类型：
--
作者：
H. Haken;H. Risken;W. Weidlich
我们处理的激光器由一个模式描述的行波和一组原子的两个光学活性的水平，这是均匀加宽。我们从Weidlich和Haake的激光密度矩阵方程出发，定义了光场和原子变量的分布函数f，其中光场采用相干态表示，原子系统采用Schmid和Risken在前一篇论文中所用的分布函数的修正形式。我们导出了f的一个完全精确的偏微分方程，它是广义Fokker-Planck方程的类型，即它含有高阶导数。使用最近陈述的定理的哈肯和Weidlich，我们表明，这种分布函数允许计算单时间以及多时间量子力学相关函数。如果保留广义Fokker-Planck方程的首项，我们得到Risken，Schmid和Weidlich的半经典Fokker-Planck方程。我们的处理可以扩展到几个模式与驻波和多级原子。
We treat a laser consisting of one mode described by a running wave and a set of atoms with two optically active levels which are homogeneously broadened. We start from the laser density matrix equations ofWeidlich andHaake and define a distribution functionf for lightfield and atomic variables, where we use for the lightfield the coherent state representation and for the atomic system a modified version of the distribution function used bySchmid andRisken in a previous paper. We derive a partial differential equation forf which is completely exact and is of the type of a generalized Fokker-Planck equation, i.e. it contains higher derivatives. Using a recently stated theorem ofHaken andWeidlich we show that this distribution function allows to calculate single-time as well as multitime quantum mechanical correlation functions. If the leading terms of the generalized Fokker-Planck equation are retained we find the semiclassical Fokker-Planck equation ofRisken,Schmid andWeidlich. Our treatment can be extended to several modes connected with standing waves and multilevel atoms.