New application of Dirac's representation: N-mode squeezing enhanced operator and squeezed state

TL;DR

This paper introduces a novel n-mode squeezing operator based on Dirac's representation, demonstrating its ability to enhance standard squeezing and deriving associated squeezed states with their Wigner functions.

Contribution

It presents a new n-mode squeezing operator using Dirac's coordinate representation and derives the corresponding squeezed states and their Wigner functions.

Findings

The n-mode squeezing operator enhances standard squeezing.

Derived normally ordered expansion of the n-mode squeezing operator.

Calculated the Wigner function of the new squeezed states.

Abstract

It is known that exp[i\lamda(Q_1P_1-i/2)] is a unitary single-mode squeezing operator, where Q_1,P_1 are the coordinate and momentum operators, respectively. In this paper we employ Dirac's coordinate representation to prove that the exponential operator S_{n}=Exp[i\lamda sum_{i=1}^{n}](Q_{i}P_{i+1}+Q_{i+1}P_{i}))], (Q_{n+1}=Q_1P_{n+1}=P_1), is a n-mode squeezing operator which enhances the standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive S_{n}'s normally ordered expansion and obtain new n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.