Physical Review A

Simple approach to the wave functions of one- and two-mode squeezed states

Fan Hong‐Yi, Jack Vanderlinde

Published Feb 1, 1989• 31 citations

Abstract

With use of the coordinate representation of the one-mode squeeze operator, the coordinate representation wave function of the one-mode squeezed state is simply rederived. A parallel treatment for the two-mode squeeze operator yields the two-mode squeezed state wave function.

DOI: 10.1103/physreva.39.1552

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Physical Review A

Simple approach to the wave functions of one- and two-mode squeezed states

Fan Hong‐Yi, Jack Vanderlinde

Published Feb 1, 1989• 31 citations

Publisher

Abstract

DOI: 10.1103/physreva.39.1552

Related papers

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{\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}.

{q}_{1}

{q}_{1}

)${\ensuremath{\Vert}}^{2}$. The center of the two-mode Gaussian is again predicted by the classical mapping.

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.