Quantum Stochastic Dynamics in Multi-Photon Optics

TL;DR

This paper develops a rigorous quantum stochastic model for multi-photon optical systems with multiple pump and subharmonic fields, demonstrating the existence of dynamics and measurement schemes using quantum stochastic differential equations.

Contribution

It introduces a comprehensive quantum stochastic differential equation framework for multi-photon optics with multiple fields, extending measurement theory in open quantum systems.

Findings

Proves the existence of the quantum dynamics for multi-photon systems.

Provides a continuous measurement scheme for such systems.

Models multi-photon interactions with unbounded coefficients in stochastic equations.

Abstract

In this work a generic model of \emph{multi-photon optics} is studied. It is considered $m$ pump and $n$ subharmonic fields. It shows how the multi-photon system, with direct and homodyne detection, can be obtained rigorously in the context of \emph{Measurement theory in Open Quantum System} (see \cite{Bar-OQS}, \cite{Bar-1990-QO} and \cite{RCS-LAP}). This is done trough the \emph{Quantum Stochastic Differential Equations} with unbounded coefficients (see \cite{Fagnola-Wills}, and \cite{RCS-LAP}). In particular the existence of the dynamics is proved, and a continuous measurements scheme is provided.