“…The semiclassical periodically driven two-level model is an important prototype in diverse phenomena in nearly every sub-fields of optics, physics, and chemistry, [1−9] such as nuclear magnetic resonance technique related applications, [9,10] acoustically induced transparency, [11] Josephson junction devices, [12] lasernucleus interaction, [13] various effects of few-cycle ultrashort pulses, [7,14] and high harmonic generation. [15−17] However, solving analytically this important model even approximately remains to be a great challenge although intensive studies with some progress have been pursued for more than sixty years.…”