Communications in Theoretical Physics

Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

Gang Ren, Song Tong-Qiang

Published Dec 1, 2007• 0 citations

Abstract

We introduce the coordinate-dependent one- and two-mode squeezing transformations and discuss the properties of the corresponding one-and two-mode squeezed states. We show that the coordinate-dependent one-and two-mode squeezing transformations can be constructed by the combination of two transformations, a coordinate-dependent displacement followed by the standard squeezed transformation. Such a decomposition turns a nonlinear problem into a linear one because all the calculations involving the nonlinear one- and two-mode squeezed transformation have been shown to be able to reduce to those only concerning the standard one- and two-mode squeezed states.

DOI: 10.1088/0253-6102/48/6/027

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Communications in Theoretical Physics

Coordinate-Dependent One- and Two-Mode Squeezing Transformation and the Corresponding Squeezed States

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Published Dec 1, 2007• 0 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/48/6/027

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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.