Chinese Physics B

Wave functions of a new kind of nonlinear single-mode squeezed state

Hong-Yi Fan, Cheng Da, Junhua Chen

Published Nov 28, 2014• 2 citations

Abstract

We explore the theoretical possibility of extending the usual squeezed state to those produced by nonlinear single-mode squeezing operators. We derive the wave functions of exp[−(i g /2)( P + P )|0⟩ in the coordinate representation. A new operator's disentangling formula is derived as a by-product.

DOI: 10.1088/1674-1056/23/12/120302

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Chinese Physics B

Wave functions of a new kind of nonlinear single-mode squeezed state

Hong-Yi Fan, Cheng Da, Junhua Chen

Published Nov 28, 2014• 2 citations

Publisher

Abstract

DOI: 10.1088/1674-1056/23/12/120302

Related papers

Squeezed states: Operators for two types of one- and two-mode squeezing transformations

Fan Hong-Yi

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.

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范洪义, 笪诚, 陈俊华

中国物理B：英文版Jan 1, 20140 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.

{\mathit{a}}^{2}

)exp(\ensuremath{\alpha}${\mathit{a}}^{\mathrm{^}}$-${\mathrm{\ensuremath{\alpha}}}^{\mathrm{*}}$a)\ensuremath{\Vert}0〉. The wave function is a displaced Gaussian with center and width depending upon the parameters \ensuremath{\alpha} and \ensuremath{\zeta}.