Selective excitations of a Kerr-nonlinear resonator: exactly solvable approach

TL;DR

This paper presents an exact quantum approach to Kerr nonlinear resonators, enabling non-perturbative analysis of selective resonant excitations and multi-photon processes in various quantum regimes.

Contribution

It introduces a non-perturbative, exact quantum theory of Kerr resonators using the Fokker-Planck equation, avoiding state truncation and perturbation methods.

Findings

Identifies conditions for selective resonant excitations.

Analyzes multi-photon non-resonant and resonant processes.

Provides detailed photon distribution and correlation insights.

Abstract

We study Kerr nonlinear resonators (KNR) driven by a continuous wave field in quantum regimes where strong Kerr interactions give rise to selective resonant excitations of oscillatory modes. We use an exact quantum theory of KNR in the framework of the Fokker-Planck equation without any quantum state truncation or perturbation procedure. This approach allows non-perturbative consideration of KNR for various quantum operational regimes including cascaded processes between oscillatory states. We focus on understanding of multi-photon non-resonant and selective resonant excitations of introcavity mode depending on the detuning, the amplitude of the driving field and the strength of nonlinearity. The analysis is provided on the base of photon number distributions, the photon-number correlation function and the Wigner function.