Quantum versus classical effects in the chirped-drive discrete nonlinear Schrödinger equation

A chirped parametrically driven discrete nonlinear Schrödinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous classical-like nonlinear phase locking (autoresonance). Two-level arguments are used to study the ladder-climbing process, and semiclassical theory describes the autoresonance effect. The regimes of efficient excitation in the problem are identified and characterized in terms of three dimensionless parameters describing the driving strength, the dispersion nonlinearity, and the Kerr-type nonlinearity, respectively. The nonlinearity alters the borderlines between the regimes and their characteristics.