Solution of Cross-Kerr Interaction Combined with Parametric Amplification

TL;DR

This paper introduces an exact operator-based method to analyze the combined effects of cross-Kerr interaction and parametric amplification, simplifying an infinite-dimensional problem into a manageable six-dimensional form.

Contribution

The authors develop a full operator approach and an orthogonal transformation technique to exactly solve the combined cross-Kerr and parametric amplification problem.

Findings

Exact integration of the combined interaction using higher-order operators

Reduction of an infinite-dimensional basis to a six-dimensional basis

Facilitates more efficient analysis of complex quantum interactions

Abstract

We present a full operator approach to treatment of the cross-Kerr interaction combined with parametric amplification. It is shown that this problem can be exactly integrated using the method of higher-order operators. While the initial basis is infinite-dimensional, an orthogonal transformation can reduce the problem exactly into a six-dimensional basis which can be integrated conveniently.