Abstract
Analytically exact solutions of a driven two-level system are extremely important in many areas of physics [E. Barnes and S. Das Sarma, Phys. Rev. Lett. 109, 060401 (2012)]. Here we present a simple method of synchronous and asynchronous combined modulations to generate such exact solutions, and apply several of the simplest solutions to perform the coherent control of quantum states. The interesting physical phenomena, such as the arbitrary population transfers between the different and/or asymptotic stationary states and the controlled coherent population oscillation, are achieved analytically and numerically. Simplification of the exact solutions and the modulated fields renders the control strategies more transparent and the qubit manipulation more convenient in experiments.
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