Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

New approach for calculating the normally ordered form of squeeze operators

Fan Hong‐Yi, Haider R. Zaidi, John R. Klauder

Published Mar 15, 1987• 369 citations

Abstract

A new method for directly obtaining the normally ordered form of single- and two-mode squeeze operators is presented. This method is based on the technique of ``integration within an ordered product.'' The operator expressions are derived using the coherent-state representation as well as the coordinate and the momentum representations. The method is very simple, and the approach has an intuitive basis that makes the squeezing property manifest at the outset.

DOI: 10.1103/physrevd.35.1831

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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

New approach for calculating the normally ordered form of squeeze operators

Fan Hong‐Yi, Haider R. Zaidi, John R. Klauder

Published Mar 15, 1987• 369 citations

Publisher

Abstract

DOI: 10.1103/physrevd.35.1831

Related papers

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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.