Selective multi-photon excitations in the Kerr nonlinear resonator

We study the Kerr nonlinear resonator (KNR) driven by a continuous wave field in quantum regimes where the strong Kerr interactions give rise to selective resonant excitations of oscillatory mode. We use an exact quantum theory of the KNR without any limitation on quantum noise and without any quantum state truncation procedure. We focus on understanding of various regimes of selective multi-photon resonant excitations of mode depending on the detuning, amplitude of the driving field and the strength of nonlinearity. The analysis is provided on the basis of the photon number distributions and photon-number correlation function.