Quantum interference and sub-Poissonian statistics for time-modulated driven dissipative 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 in 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.