Communications in Theoretical Physics

New Representation for Squeezing-Rotating Entangled Unitary Transformation

Fan Hong-Yi, Fan Yue

Published Jun 15, 2000• 14 citations

Abstract

We introduce a new unitary operator which can engender a squeezing and rotating entangled transformation. The operator has a concise expression in a new representation in two-mode Fock space. The normally ordered form of can be derived by using the technique of integration within an ordered product of operators. The fluctuation in quadrature phases for these squeezing-rotating entangled states are analyzed.

DOI: 10.1088/0253-6102/33/4/701

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Communications in Theoretical Physics

New Representation for Squeezing-Rotating Entangled Unitary Transformation

Fan Hong-Yi, Fan Yue

Published Jun 15, 2000• 14 citations

Publisher

Abstract

DOI: 10.1088/0253-6102/33/4/701

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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.