Tunneling and multiphoton transitions in a model of two coupled oscillators with Kerr nonlinearities

In the semiclassical limit, eigenstates of a system of two coupled oscillators with Kerr nonlinearities correspond to a discrete set of classical phase trajectories. When a certain resonant condition is met, tunneling between trajectories with close energies is possible. I will show that this resonant condition does not depend on the magnitude of the coupling constant. The absence of such a dependence is a consequence of the symmetry of perturbative corrections to the oscillator levels, observed in many orders. The symmetry of the corrections is derived from the exact symmetry of the generalized Hamiltonian extended to an abstract space of Fock states with arbitrary real occupation numbers.