Inter-transition interference in spectrum of Kerr parametric oscillators

TL;DR

This paper develops a theoretical framework to analyze how interference effects between inter-level transitions in Kerr parametric oscillators influence their reflection and transmission spectra, revealing conditions where these effects are significant.

Contribution

It extends previous models by including off-diagonal density matrix elements and inter-level transition interactions, providing a more comprehensive understanding of spectral modifications in KPOs.

Findings

Interference significantly alters the spectrum of KPOs.

Conditions for the prominence of interference effects are identified.

The theory applies broadly beyond Kerr parametric oscillators.

Abstract

We theoretically investigate reflection and transmission measurements of two-photon and four-photon Kerr parametric oscillators (KPOs), introducing interference effects between inter-level transitions. Due to the level degeneracy of a KPO, a probe field can be resonant with multiple inter-level transitions. We extend the previous theory of reflection measurements by incorporating the interaction between inter-level transitions and off-diagonal elements of the density matrix which had previously been neglected. We demonstrate that interference among these transitions substantially modifies the spectrum. We identify the conditions for the interference, as well as those under which the off-diagonal elements of the density matrix affect the spectrum. The theory is also generalized to transmission measurements, and is applicable to a broad class of systems beyond KPOs.