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Chinese Physics Letters

Squeezing for n -Mode Quadratures Studied by Integration Within an Ordered Product Technique

Hong-Yi Fan, Nai-Le Liu

Published Jul 1, 1999• 16 citations
Publisher

Abstract

The squeezing operator S (n) and the corresponding squeezed state |0⟩ s for n -mode quadrature operators are founded. The normally ordered form of S (n) is derived by means of the technique of integration within an ordered product of operators. Moreover, the existence of higher-order squeezing for n-mode quadratures in the state |0⟩ s is demonstrated.

DOI
10.1088/0256-307x/16/7/002

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The squeezing operator S (n) and the corresponding squeezed state |0⟩ s for n -mode quadrature operators are founded. The normally ordered form of S (n) is derived by means of the technique of integration within an ordered product of operators. Moreover, the existence of higher-order squeezing for n-mode quadratures in the state |0⟩ s is demonstrated.
By virtue of the technique of integration within an ordered product of operators a new four-mode squeezing operator that squeezes the four-mode quadrature operators of light field in the standard way is found. This operator differs from the direct product of two two-mode squeezing operators. It is the exponential operator V ≡exp [ i r ( Q 1 P 2 + Q 2 P 3 + Q 3 P 4 + Q 4 P 1 )]. The Wigner function of the new four-mode squeezed state is calculated, which quite differs from that of the direct-product state of two usual two-mode squeezed states.