Journal of Modern Optics

Squeezed States Generated by Boson Creation Operator

Anil Roy, C. L. Mehta

Published Aug 1, 1992• 7 citations

Abstract

Using the normal ordering techniques of an operator, we show that a general squeezed state may be expressed in the form N exp [1/2 ξ â σ2 m nâ σ] S 0 ¢, where S 0 ¢ is the vacuum state. We obtain the normalization constant N and various other representations. We also discuss conditions for squeezing and photon antibunching.

DOI: 10.1080/713823596

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Journal of Modern Optics

Squeezed States Generated by Boson Creation Operator

Anil Roy, C. L. Mehta

Published Aug 1, 1992• 7 citations

Publisher

Abstract

DOI: 10.1080/713823596

Related papers

Squeezed State Caused by Inverse of Photon Creation Operator

Xuefen Xu

Communications in Theoretical PhysicsFeb 1, 20062 citations

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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.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.

Physical Review AFeb 1, 199088 citations

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.