New Normally Ordered Four-Mode Squeezing Operator for Standard Squeezing of Four-Mode Quadratures

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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[ir(Q1P2 + Q2P3 + Q3P4 + Q4P1)]. 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.
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