Two-level systems with periodic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>N</mml:mi></mml:math>-step driving fields: Exact dynamics and quantum state manipulations
Zhi‐Cheng Shi, Ye‐Hong Chen, Wei Qin, Yan Xia, X. X. Yi, Shi‐Biao Zheng, Franco Nori
Abstract
In this work, we derive exact solutions of a dynamical equation, which can represent all two-level Hermitian systems driven by periodic $N$-step driving fields. For different physical parameters, this dynamical equation displays various phenomena for periodic $N$-step driven systems. The time-dependent transition probability can be expressed by a general formula that consists of cosine functions with discrete frequencies, and, remarkably, this formula is suitable for arbitrary parameter regimes. Moreover, only a few cosine functions (i.e., one to three main frequencies) are sufficient to describe the actual dynamics of the periodic $N$-step driven system. Furthermore, we find that a beating in the transition probability emerges when two (or three) main frequencies are similar. Some applications are also demonstrated in quantum state manipulations by periodic $N$-step driving fields.