摘要
进一步研究了我们在前一篇论文中采用Lewis-Riesenfeld不变量理论和采用纠缠态表象所求得的非简并光学参量下转换系统薛定谔方程两个解间的关系.发现我们所求得的在k2>1,k2=1,k2<1和k=0时的解析表达式,分别对应于非简并参量下转换系统在域值以上、域值、域值以下以及参量共振情形的解;当k=-1时,此解与范等的结果完全一致,而范氏解实际上相应于频率简并但偏振非简并的失谐参量下转换系统的域值解;还对在特殊情况下如何从此解析解过渡到范氏解进行了详细的推导.
The relation between the solutions of the Schrcdinger equation for a non-degenerate parametric down-conversion system is investigated, one was obtained by the Lewis-Riesenfeld invariant theory, and another one by the entangled state representation in Fan et al. It is found that the analytical expressions for k^2 〉 1, k^2 = 1, k^2 〈 1, and k = 0, correspond to the ones for the cases of the above-threshold, threshold, below-threshold and parametric resonance. In the case of k = -1 ,our solution returns to the Fan＇s solution which corresponds to the threshold solution for the parametric down-conversion operated in a frequency-degenerate but polarization-nondegenerate mode. In particular,we present an analysis of the basic features in a detailed derivation of transformation from our analytical solution into Fan＇s one in the special condition.
出处
《湖南师范大学自然科学学报》
CAS
北大核心
2007年第4期40-45,共6页
Journal of Natural Science of Hunan Normal University
基金
湖南省自然科学基金资助项目(07JJ3123)
湖南省教育厅科学与技术研究资助项目(O6C163)
