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We study Kerr nonlinear resonators (KNR) driven by a continuous wave field inquantum regimes where strong Kerr interactions give rise to selective resonantexcitations of oscillatory modes. We use an exact quantum theory of KNR in theframework of the Fokker-Planck equation without any quantum state truncation orperturbation procedure. This approach allows non-perturbative consideration ofKNR for various quantum operational regimes including cascaded processesbetween oscillatory states. We focus on understanding of multi-photonnon-resonant and selective resonant excitations of introcavity mode dependingon the detuning, the amplitude of the driving field and the strength ofnonlinearity. The analysis is provided on the base of photon numberdistributions, the photon-number correlation function and the Wigner function.

the european physical journal. d, atomic, molecular and optical physics/the european physical journal. d, atomic, molecular, optical and plasma physics

Selective excitations of a Kerr-nonlinear resonator: exactly solvable approach