The symmetry in the model of two coupled Kerr oscillators leads to simultaneous multi-photon transitions

TL;DR

This paper investigates a model of two coupled Kerr oscillators, revealing that symmetry causes simultaneous multi-photon transitions independent of coupling strength, with analysis spanning quantum and classical regimes.

Contribution

It demonstrates that symmetry in the coupled Kerr oscillator model leads to simultaneous multi-photon transitions and shows this phenomenon's independence from coupling strength.

Findings

Multi-photon transitions occur simultaneously between many pairs of states.

Resonance positions are unaffected by the coupling strength.

Symmetry of the perturbation series explains the observed phenomena.

Abstract

We consider the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. We demonstrate that for a certain set of parameters of the model, the multi-photon transitions occur between many pairs of the oscillator states simultaneously. Also, the position of the multi-photon resonances does not depend on the coupling strength between two oscillators. We prove rigorously that this is a consequence of a certain symmetry of the perturbation theory series for the model. In addition, we analyse the model in the quasi-classical limit by considering the dynamics of the pseudo-angular momentum. We identify the multi-photon transitions with the tunnelling transitions between the degenerate classical trajectories on the Bloch sphere.