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Optical Bloch oscillation and Zener tunneling in the fractional Schrödinger equation
Yiqi Zhang1,2, Rong Wang3, Hua Zhong3
1Key Laboratory for Physical Electronics and Devices of the Ministry of Education & Shaanxi Key Lab of Information Photonic Technique, Xi'an Jiaotong University, Xi'an, 710049, China. zhangyiqi@mail.xjtu.edu.cn.
Abstract:
We demonstrate optical Bloch oscillation (OBO) and optical Zener tunneling (OZT) in the fractional Schrödinger equation (FSE) with periodic and linear potentials, numerically and theoretically. We investigate in parallel the regular Schrödinger equation and the FSE, by adjusting the Lévy index, and expound the differences between the two. We find that the spreading of the OBO decreases in the fractional case, due to the diminishing band width. Increasing the transverse force, due to the linear potential, leads to the appearance of OZT, but this process is suppressed in the FSE. Our results indicate that the adjustment of the Lévy index can effectively control the emergence of OBO and OZT, which can inspire new ideas in the design of optical switches and interconnects.
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