New n-mode squeezing operator and squeezed states with standard squeezing

TL;DR

This paper introduces a new n-mode squeezing operator that produces standard squeezing, derives its normally ordered form, and characterizes the resulting n-mode squeezed vacuum states including their Wigner functions.

Contribution

The paper proposes a novel n-mode squeezing operator and provides explicit formulas for its normally ordered form and the associated squeezed vacuum states.

Findings

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

Obtained the Wigner function of the n-mode squeezed vacuum states

Established the operator's capability to generate standard squeezing in multiple modes

Abstract

We find that the exponential operator V=exp[ilamda (Q_1P_2+Q_2P_3+...+Q_{n-1}P_{n}+Q_{n}P_1)], Q_{i}, P_{i} are respectively the coordinate and momentum operators, is an n-mode squeezing operator which engenders standard squeezing. By virtue of the technique of integration within an ordered product of operators we derive V's normally ordered expansion and obtain the n-mode squeezed vacuum states, its Wigner function is calculated by using the Weyl ordering invariance under similar transformations.