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Journal of Changzhou Institute of Technology

An Approach for Deriving the Explicit Form of Squeezed State by Virtue of the Weyl-Wigner Correspondence Scheme

Lei Chen

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Squeezed state is theoretically obtained by performing the squeezing operator on an initial state.Due to non-commutable operators each other,it is not easy to directly obtain the explicit expression of squeezed state.Here,a general approach is provided for deriving the squeezed state′s explicit form,namely,by virtue of the Weyl-Wigner correspondence scheme the explicit forms of single-mode and two-mode squeezed state is obtained,respectively.Without disentangling the squeezing operator,this adopted method is applicable to explicitly solve the general multimode case.

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Squeezed state is theoretically obtained by performing the squeezing operator on an initial state.Due to non-commutable operators each other,it is not easy to directly obtain the explicit expression of squeezed state.Here,a general approach is provided for deriving the squeezed state′s explicit form,namely,by virtue of the Weyl-Wigner correspondence scheme the explicit forms of single-mode and two-mode squeezed state is obtained,respectively.Without disentangling the squeezing operator,this adopted method is applicable to explicitly solve the general multimode case.
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We find that the exponential operator V ≡exp[ i λ( Q 1 P 2 + Q 2 P 3 +⋅⋅⋅+ Q n −1 P n + Q n P 1 )], Q i , P i are, respectively, the coordinate and momentum operators, is an n -mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V 's normally ordered expansion and obtain the n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.
It is known that exp [iλ ( Q 1 P 1 – i/2)] is a unitary single-mode squeezing operator, where Q 1 , P 1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator , is an n -mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S n 's normally ordered expansion and obtain new n -mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.