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arXiv · 2011.12473

Two-level systems with periodic $N$-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
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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.

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Zhi-Cheng Shi, Ye-Hong Chen, Wei Qin, Yan Xia, X. X. Yi, Shi-Biao Zheng, Franco Nori. 2020-11-25. Two-level systems with periodic $N$-step driving fields: Exact dynamics and quantum state manipulations. https://doi.org/10.1103/physreva.104.053101

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