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Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice

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Abstract

We study the exact Bloch states of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) held in an optical lattice. Under a natural condition of the symmetry between the two species, we obtain two different forms of exact solutions corresponding to different existing conditions. Then, we analytically demonstrate that (a) the average atomic number per well can enlarge the region area (consisting of instability and stability parameter regions) existing exact solutions; (b) the sizes of the instability and stability parameter regions exhibit opposite variation trend with the increase in Rabi coupling strength, and the results of different solutions are just opposite. Besides, we find that spin-orbit coupling (SOC) results in the generation of spin-motion entanglement for the Bloch states, the SOC strength and lattice depth can influence the population transfer between two BEC components, and varying the SOC strength and lattice depth can also reveal the dynamical superfluid-insulator transition from the superfluid state to the critical insulating state. These results present a feasible scheme to manipulate the stable superfluid currents, which will be useful to control quantum transport of BEC.

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Acknowledgements

This work was supported by the Project of Hunan Provincial Education Office under Grant No. 20C1711,17B244, 19A459, the National Natural Science Foundation of China under Grant No. 11705155, Chenzhou science and technology project jsyf2017005, zdyf2020159, Science Research Project of Xiangnan University under Grant No.2016XJ32, Innovation and Entrepreneurship Training Program for College Students in Hunan Province([2020]191), and Research project of teaching reform in universities of Hunan province([2018]436). Chao Kong feels deeply indebted to Ling Liu for her support and encouragement during the completion of this work.

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  1. College of Electronic Information and Electrical Engineering, Xiangnan University, Chenzhou, 423000, China

    Chao Kong, ZhengHua Tang, Ning Lu, YaQi Chen, Gui Jin, DaJun Lei, ChunZhi Jiang, Min Yao & HaiMing Deng

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  1. Chao Kong
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  2. ZhengHua Tang
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Kong, C., Tang, Z., Lu, N. et al. Exact Bloch States of a Spin-orbit Coupled Bose-Einstein Condensate in an Optical Lattice. Int J Theor Phys 60, 3161–3176 (2021). https://doi.org/10.1007/s10773-021-04863-4

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