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

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.

Automated summary

This paper studies the model of two coupled oscillators with Kerr nonlinearities in the rotating-wave approximation. It is demonstrated that multi-photon transitions occur simultaneously between many pairs of oscillator states when certain parameters are set in the model. Additionally, the position of multi-photon resonances is independent of the coupling strength between the oscillators. The authors rigorously prove that this is a result of a specific symmetry in the perturbation theory series of the model. Moreover, the model is analyzed in the quasi-classical limit by examining the dynamics of pseudo-angular momentum, and the multi-photon transitions are identified as tunneling transitions between degenerate classical trajectories on the Bloch sphere.