Time Evolution and Squeezing of Degenerate and Non-degenerate Coupled Parametric Down-Conversion with Driving Term

By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving te...

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Bibliographic Details
Published in:Communications in theoretical physics 2009-03, Vol.51 (3), p.514-518
Main Author: LI Jiang-Fan FANG Jia-Yuan XIAO Fu-Liang LIU Xin-Hai WANG Cheng-Zhi
Format: Article
Language:English
Subjects:
压缩简并
参量下转换
时间依赖性
时间演化
非退化
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Summary:By properly selecting the time-dependent unitary transformation for the linear combination of the number operators, we construct a time-dependent invariant and derive the corresponding auxiliary equations for the degenerate and non-degenerate coupled parametric down-conversion system with driving term. By means of this invariant and the Lewis-Riesenfeld quantum invariant theory, we obtain closed formulae of the quantum state and the evolution operator of the system. We show that the time evolution of the quantum system directly leads to production of various generalized one- and two-mode combination squeezed states, and the squeezed effect is independent of the driving term of the Hamiltonian. In some special cases, the current solution can reduce to the results of the previous works.
ISSN:0253-6102
DOI:10.1088/0253-6102/51/3/27