New 3-mode squeezing operator and squeezed vacuum state in 3-wave mixing

TL;DR

This paper introduces a new 3-mode squeezing operator in 3-wave mixing, deriving the associated squeezed vacuum state, its uncertainty relations, and Wigner function, revealing enhanced squeezing effects in nonlinear optical media.

Contribution

The paper presents a novel 3-mode squeezing operator and explicitly derives the corresponding squeezed vacuum state and its properties, advancing quantum optics in nonlinear media.

Findings

Derived the new 3-mode squeezed vacuum state.

Demonstrated enhanced squeezing effects.

Calculated the Wigner function of the state.

Abstract

In a 3-wave mixing process occurring in some nonlinear optical medium when }$a_{1}^{\dagger}${\small mode interacts with both }$a_{2}^{\dagger}% ${\small mode and }$a_{3}^{\dagger}${\small mode, we theoretically study the squeezing effect generated by the operator }$S_{3}\equiv \exp[\mu(a_{1}% a_{2}-a_{1}^{\dagger}a_{2}^{\dagger})+\nu(a_{1}a_{3}-a_{1}^{\dagger}% a_{3}^{\dagger})]${\small . The new 3-mode squeezed vacuum state in Fock space is derived, and the uncertainty relation for it is demonstrated, It turns out that }$S_{3}${\small may exhibit enhanced squeezing. By virtue of the technique of integration within an ordered product (IWOP) of operators, we also derive }$S_{3}${\small 's normally ordered expansion. The Wigner function of new 3-mode squeezed vacuum state is calculated by using the Weyl ordering invariance under similar transformations.