Quantum properties of the three-mode squeezed operator: triply concurrent parametric amplifiers

TL;DR

This paper investigates the quantum properties of a three-mode squeezed operator generated by a three concurrent nonlinear optical process, revealing significant nonclassical effects and the potential to produce Schrödinger-cat states.

Contribution

It provides a comprehensive analysis of the quantum properties of the three-mode squeezed operator, including symmetric and asymmetric nonlinearities, and explores their nonclassical effects and state generation capabilities.

Findings

Asymmetric nonlinearities produce stronger nonclassical effects than symmetric ones.

The system can generate various types of Schrödinger-cat states.

Nonclassical effects are evident in squeezing, correlations, and quasiprobability functions.

Abstract

In this paper, we study the quantum properties of the three-mode squeezed operator. This operator is constructed from the optical parametric oscillator based on the three concurrent $\chi^{(2)}$ nonlinearities. We give a complete treatment for this operator including the symmetric and asymmetric nonlinearities cases. The action of the operator on the number and coherent states are studied in the framework of squeezing, second-order correlation function, Cauchy-Schwartz inequality and single-mode quasiprobability function. The nonclassical effects are remarkable in all these quantities. We show that the nonclassical effects generated by the asymmetric case--for certain values of the system parameters--are greater than those of the symmetric one. This reflects the important role for the asymmetry in the system. Moreover, the system can generate different types of the Schr\"odinger-cat states.