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.
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.
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