Communications in Theoretical Physics

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

Fan Hong-Yi, Cao He-Lin

Published Jan 1, 2007• 1 citation

Abstract

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.

DOI: 10.1088/0253-6102/47/1/026

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Communications in Theoretical Physics

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

Fan Hong-Yi, Cao He-Lin

Published Jan 1, 2007• 1 citation

Publisher

Abstract

DOI: 10.1088/0253-6102/47/1/026

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We find that the exponential operators U=exp[-i(${\ensuremath{\lambda}}_{1}$

{\mathit{Q}}_{1}

{\mathit{P}}_{2}

+${\ensuremath{\lambda}}^{2}$

{\mathit{Q}}_{2}

{\mathit{P}}_{1}

] and W=exp[-i(${\ensuremath{\lambda}}_{1}$

{\mathit{Q}}_{1}

{\mathit{Q}}_{2}

-${\ensuremath{\lambda}}_{2}$p

{\mathrm{P}}_{1}

{\mathit{P}}_{2}

)] (where ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ are real;

{P}_{i}

and

{Q}_{i}

are coordinate and momentum operators, respectively; and i=1,2) are two types of generalized squeezing operators responsible for generating two types of one- and two-mode combination squeezed states, respectively. The coordinate and/or momentum representations of U and W are presented, and their normal product forms are first derived in terms of the newly developed technique of integration within an ordered product, which provides us with a direct approach to constructing these new squeezed states. The fluctuations in quadrature phases for these states are analyzed.