Discrete-Time Quantum Walks of the One-Dimensional Dirac Oscillator

Recent experimental studies have demonstrated the simulation of Dirac equation using the discrete-time quantum walks. In this work, we add the oscillator potential and consider the simulation of a one-dimensional Dirac oscillator. Based on the coin operator, we run the quantum walk simulation and co...

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Bibliographic Details
Published in:Journal of low temperature physics 2022-10, Vol.209 (1-2), p.44-53
Main Authors: Jia, Siyong, Jia, Delong, Song, Ziteng, Xu, Junjun
Format: Article
Language:English
Subjects:
Characterization and Evaluation of Materials
Condensed Matter Physics
Dirac equation
Low temperature physics
Magnetic Materials
Magnetism
Oscillators
Physics
Physics and Astronomy
Simulation
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Summary:Recent experimental studies have demonstrated the simulation of Dirac equation using the discrete-time quantum walks. In this work, we add the oscillator potential and consider the simulation of a one-dimensional Dirac oscillator. Based on the coin operator, we run the quantum walk simulation and consider the effects of oscillator parameters, initial phase shifts, and masses. Compared to the Dirac equation, the probability distribution of a Dirac oscillator becomes more classical. Additionally, we find the probability distribution jumps between two spin states by changing the initial phase shift, and attribute this to the coherent nature of the two spin states. These results are hopefully to be realized in trapped-ion experiments.
ISSN:0022-2291
1573-7357
DOI:10.1007/s10909-022-02804-x