  By periodical two-step modulation, we demonstrate that the dynamics of
multilevel system can still evolve even in multiple large detunings regime, and
provide the effective Hamiltonian (of interest) for this system. We then
illustrate this periodical modulation in quantum state engineering, including
achieving direct transition from the ground state to the Rydberg state or the
desired superposition of two Rydberg states without satisfying two-photon
resonance condition, switching between Rydberg blockade regime and Rydberg
antiblockade regime, stimulating distinct atomic transitions by the same laser
field, and implementing selective transitions in the same multilevel system.
Particularly, it is robust against perturbation of control parameters. Another
advantage is that the waveform of laser field has simple square-wave form which
is readily implemented in experiments. Thus, it offers us a novel method of
quantum state engineering in quantum information processing.
