# A path integral description of quantum nonlinear optics in arbitrary media

## TL;DR

This paper introduces a path integral approach to model quantum nonlinear optics in any medium, providing a unified framework for understanding second-order nonlinear processes and their dependence on medium properties.

## Contribution

It develops a general path integral method for quantum nonlinear optics applicable to arbitrary media and nonlinear orders, with specific focus on second-order processes under the undepleted pump approximation.

## Key findings

- Second-order nonlinear processes can be modeled as an effective free field in a medium-dressed vacuum.
- The probability of nonlinear processes is linked to the biphoton propagator, revealing medium and pump structure.
- The method applies to arbitrary media and nonlinear orders, unifying various quantum nonlinear optical phenomena.

## Abstract

We present a method, based on Feynman path integrals, to describe the propagation and properties of the quantised electromagnetic field in an arbitrary, nonlinear medium. We provide a general theory, valid for any order of optical nonlinearity, and we then specialise the the case of second order nonlinear processes. In particular, we show, that second-order nonlinear processes in arbitrary media, under the undepleted pump approximation, can be described by an effective free electromagnetic field, propagating in a vacuum, dressed by the medium itself. Moreover, we show,that the probability of such processes to occur is related to the biphoton propagator, which contains informations about the structure of the medium, its nonlinear properties, and the structure of the pump beam.

---
Source: https://tomesphere.com/paper/1904.02548