We demonstrate multiphoton blockades (PB) in the pulsed regime by using Kerr nonlinear dissipative resonator driven by a sequence of Gaussian pulses. It is shown that the results obtained for single-photon, two-photon and three-photon blockades in the pulsed excitation regime differ considerably from analogous results obtained for the case of continuous-wave (cw) driving. We strongly demonstrate that for the case of cw pumping of the Kerr-nonlinear resonator there are fundamental limits on populations of lower photonic number-states (with n = 0, 1, 2, 3). Thus, such detailed comparison demonstrates that PB due to excitation with a suitable photon pulses is realized beyond the fundamental limits established for cw excitations. We analyze photon-number effects and investigate phase-space properties of PB on the base of photon number populations, the second-order correlation functions and the Wigner functions in phase space. Generation of Fock states due to PB in the pulsed regime is analysed in details.

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

We show that quantum-interference phenomena can be realized for the dissipative nonlinear systems exhibiting hysteresis-cycle behavior and quantum chaos. Such results are obtained for a driven dissipative nonlinear oscillator with time-dependent parameters and take place for the regimes of long time intervals exceeding dissipation time and for macroscopic levels of oscillatory excitation numbers. Two schemas of time modulation: (i) periodic variation of the strength of the χ(3) nonlinearity; (ii) periodic modulation of the amplitude of the driving force, are considered. These effects are obtained within the framework of phase-space quantum distributions. It is demonstrated that the Wigner functions of oscillatory mode in both bistable and chaotic regimes acquire negative values and interference patterns in parts of phase-space due to appropriately time-modulation of the oscillatory nonlinear dynamics. It is also shown that the time-modulation of the oscillatory parameters essentially improves the degree of sub-Poissonian statistics of excitation numbers.

We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.