中国物理B ›› 2007, Vol. 16 ›› Issue (3): 644-649.doi: 10.1088/1009-1963/16/3/015

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The solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification and its application to the optimum realization of EPR paradox

谭维翰1, 赵超樱2   

  1. (1)Department of Physics, Shanghai University，Shanghai 200444，China; (2)Institute of Materials Physics, Hangzhou Dianzi University, Zhejiang 310018, China
  • 收稿日期:2005-11-14 修回日期:2006-09-08 出版日期:2007-03-20 发布日期:2007-03-20
  • 基金资助:
    Project supported by the National Key Laboratory of Plasma Physics Foundation of China (Grant No 51480040203QT0601).

The solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification and its application to the optimum realization of EPR paradox

Zhao Chao-Ying(赵超樱)a)† and Tan Wei-Han(谭维翰)b)   

  1. a Institute of Materials Physics, Hangzhou Dianzi University, Zhejiang 310018, China; b Department of Physics, Shanghai University，Shanghai 200444, China
  • Received:2005-11-14 Revised:2006-09-08 Online:2007-03-20 Published:2007-03-20
  • Supported by:
    Project supported by the National Key Laboratory of Plasma Physics Foundation of China (Grant No 51480040203QT0601).

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摘要： In this paper, the solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein--Podolsky--Rosen (EPR) paradox. The analytics and numerical calculation show the influence of pump depletion on the error in the measurement of continuous variables. The optimum realization of EPR paradox can be achieved by adjusting the parameter of squeezing. This result is of practical importance when the realistic experimental conditions are taken into consideration.

关键词: the non-degenerate optical parametric amplification (NOPA), the time-dependent Fokker--Planck equation, EPR paradox

Abstract: In this paper, the solution of the time-dependent Fokker--Planck equation of non-degenerate optical parametric amplification is used to deduce the condition demonstrating the Einstein--Podolsky--Rosen (EPR) paradox. The analytics and numerical calculation show the influence of pump depletion on the error in the measurement of continuous variables. The optimum realization of EPR paradox can be achieved by adjusting the parameter of squeezing. This result is of practical importance when the realistic experimental conditions are taken into consideration.

Key words: the non-degenerate optical parametric amplification (NOPA), the time-dependent Fokker--Planck equation, EPR paradox

中图分类号:  (Stochastic analysis methods)

  • 05.10.Gg
03.65.Ud (Entanglement and quantum nonlocality) 42.50.Dv (Quantum state engineering and measurements) 42.50.Lc (Quantum fluctuations, quantum noise, and quantum jumps)