Integrability and correspondence of classical and quantum non-linear three-mode system

TL;DR

This paper explores the connection between classical and quantum three-mode nonlinear systems, analyzing their integrability, constructing coherent states, and providing explicit formulas with applications in quantum optics.

Contribution

It introduces a method to relate classical and quantum three-mode systems, constructs reduced coherent states, and derives explicit formulas for their measures.

Findings

Demonstrated integrability of the systems using reduction procedures

Constructed explicit reduced coherent states and their measures

Applied results to problems in nonlinear quantum optics

Abstract

The relationship between classical and quantum three one-mode systems interacting in a non-linear way is described. We investigate the integrability of these systems by using the reduction procedure. The reduced coherent states for the quantum system are constructed. We find the explicit formulas for the reproducing measure for these states. Examples of some applications of the obtained results in non-linear quantum optics are presented.