Generation of Fock states and qubits in periodically pulsed nonlinear oscillator

We demonstrate a quantum regime of dissipative nonlinear oscillator where creation of Fock states as well as superpositions of Fock states are realized for time-intervals exceeding the characteristic decoherence time. Preparation of quantum states is conditioned by strong Kerr nonlinearity as well as by excitation of resolved lower oscillatory energy levels with specific train of Gaussian pulses. This provides practical signatures to look for in experiments with cooled nonlinear oscillators.