Higher-order properties and Bell-inequality violation for the three-mode enhanced squeezed state

TL;DR

This paper introduces a new three-mode squeezed coherent state using an extended squeezing operator, explores its higher-order quantum properties, and demonstrates its potential for Bell-inequality violation, indicating nonlocal quantum correlations.

Contribution

The paper develops a three-mode squeezing operator and state, analyzing higher-order squeezing, photon statistics, and Bell-inequality violation, which are novel extensions beyond traditional two-mode states.

Findings

State exhibits squeezing to all even orders

Enhanced squeezing compared to two-mode cases

Violates Bell-inequality indicating nonlocality

Abstract

By extending the usual two-mode squeezing operator $S_{2}=\exp [ i\lambda (Q_{1}P_{2}+Q_{2}P_{1}) ] $ to the three-mode squeezing operator $S_{3}=\exp {i\lambda [ Q_{1}(P_{2}+P_{3}) +Q_{2}(P_{1}+P_{3}) +Q_{3}(P_{1}+P_{2}) ]} $, we obtain the corresponding three-mode squeezed coherent state. The state's higher-order properties, such as higher-order squeezing and higher-order sub-Possonian photon statistics, are investigated. It is found that the new squeezed state not only can be squeezed to all even orders but also exhibits squeezing enhancement comparing with the usual cases. In addition, we examine the violation of Bell-inequality for the three-mode squeezed states by using the formalism of Wigner representation.