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From fractional Fourier transformation to quantum mechanical fractional squeezing transformation 被引量:1

From fractional Fourier transformation to quantum mechanical fractional squeezing transformation
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摘要 By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation(FrST) which satisfies additivity.By virtue of the integration technique within the ordered product of operators(IWOP) we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa+a/2 and exp[iα/2(a^2 +a^+2).The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches. By converting the triangular functions in the integration kernel of the fractional Fourier transformation to the hyperbolic function,i.e.,tan α → tanh α,sin α →〉 sinh α,we find the quantum mechanical fractional squeezing transformation(FrST) which satisfies additivity.By virtue of the integration technique within the ordered product of operators(IWOP) we derive the unitary operator responsible for the FrST,which is composite and is made of e^iπa+a/2 and exp[iα/2(a^2 +a^+2).The FrST may be implemented in combinations of quadratic nonlinear crystals with different phase mismatches.
出处 《Chinese Physics B》 SCIE EI CAS CSCD 2015年第2期35-38,共4页 中国物理B(英文版)
基金 supported by the National Natural Science Foundation of China(Grant No.11304126) the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20130532) the Natural Science Fund for Colleges and Universities in Jiangsu Province,China(Grant No.13KJB140003) the Postdoctoral Science Foundation of China(Grant No.2013M541608) the Postdoctoral Science Foundation of Jiangsu Province,China(Grant No.1202012B)
关键词 fractional Fourier transformation fractional squeezing transformation unitary operator the IWOPtechnique fractional Fourier transformation, fractional squeezing transformation, unitary operator, the IWOPtechnique
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