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The experimental realization of Rydberg dressing and spin-orbit coupling greatly broadens the research field of ultracold atoms as a quantum simulation platform. Very recently, moiré lattices have attracted intensive study, ranging from condensed matter to ultracold physics. In this paper, the ground-state structure of Rydberg-dressed Bose gas with spin-orbit coupling and confined in moiré lattices is studied, and the effects of nonlocal Rydberg interaction and spin-orbit coupling on the ground state of the system are explored. Our results show that the system has no translational symmetry due to the presence of nonlocal Rydberg interaction, and more and more regular periodic structures present with the increases of the strength of nonlocal Rydberg interaction. In the presence of spin-orbit coupling, the Hamiltonian of the system has an imaginary part, and the phase of the system is not uniformly distributed. It is found that the ground state of the system with spin-orbit coupling present more abundant internal structure base on these periodic structures. The results pave the way for future study of moiré physics in ultracold atom system.
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Keywords:
- Bose gas /
- Rydberg dressing /
- moiré lattices
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图 1 相同子晶格振幅下不同旋转角所对应的莫尔外势(
$ p_1=p_2=1 $ ) (a)$ \tan \theta =5/12 $ ; (b)$ \tan \theta = 3^{-1/2} $ ; (c)$ \tan \theta =3/4 $ Figure 1. Moiré potential corresponding to different rotation angles at the same sublattice amplitude (
$ p_1=p_2=1 $ ): (a)$ \tan \theta =5/12 $ ; (b)$ \tan \theta = 3^{-1/2} $ ; (c)$ \tan \theta =3/4 $ .
图 2 周期莫尔晶格中里德伯缀饰玻色气体的基态密度和相位分布图 (a)
$ {g}=1000 $ ,$ C_{6}=\kappa=0 $ ; (b)$ {g}=8000 $ ,$ C_{6}=\kappa=0 $ Figure 2. Density and phase distributions of Rydberg-dressed Bose gas confined in periodic moiré lattices: (a)
${g}=1000$ ,$ C_{6}=\kappa=0 $ ; (b)${g}=8000$ ,$ C_{6}=\kappa=0 $ .
图 3 周期莫尔晶格中里德伯缀饰玻色气体的基态密度和相位分布图 (a)
$ C_{6}=1000 $ ,${g}=\kappa=0$ ; (b)$ C_{6}=20000 $ ,${g}= \kappa=0$ Figure 3. Density and phase distributions of Rydberg-Dressed Bose gas confined in periodic moiré lattices: (a)
$ C_{6}=1000 $ ,${g}=\kappa=0$ ; (b)$ C_{6}=20000 $ ,${g}=\kappa=0$ .
图 4 周期莫尔晶格中里德伯缀饰玻色气体的基态密度和相位分布图 (a)
$ \kappa=3 $ ,${g}=C_{6}=1000$ ; (b)$ \kappa=5 $ ,${g}=C_{6}=1000$ ; (c)$ \kappa=10 $ ,${g}=C_{6}=1000$ Figure 4. Density and phase distributions of Rydberg-dressed Bose gas confined in periodic moiré lattices: (a)
$ \kappa=3 $ ,$ \text{g}=C_{6}=1000 $ ; (b)$ \kappa=5 $ ,${g}=C_{6}=1000$ ; (c)$ \kappa=10 $ ,${g}=C_{6}=1000$ . -
[1] Lin Y J, Jiménez-García K, Spielman I B 2011 Nature 471 83
Google Scholar
[2] Cheuk L W, Sommer A T, Hadzibabic Z, Yefsah T, Bakr W S, Zwierlein M W 2012 Phys. Rev. Lett. 109 095302
Google Scholar
[3] Wang P J, Yu Z Q, Fu Z K, Miao J, Huang L H, Chai S J, Zhai H, Zhang J 2012 Phys. Rev. Lett. 109 095301
Google Scholar
[4] Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J, Pan J W 2016 Science 354 83
Google Scholar
[5] Huang L H, Meng Z M, Wang P J, Peng P, Zhang S L, Chen L C, Li D H, Zhou Q, Zhang J 2016 Nat. Phys. 12 540
Google Scholar
[6] Chen H R, Lin K Y, Chen P K, Chiu N C, Wang J B, Chen C A, Hunag P P, Yip S K, Kawaguchi Y, Lin Y J 2018 Phys. Rev. Lett. 121 113204
Google Scholar
[7] Zhang D F, Gao T Y, Zou P, Kong L R, Li R Z, Shen X, Chen X L, Peng S G, Zhan M S, Pu H, Jiang K J 2019 Phys. Rev. Lett. 122 110402
Google Scholar
[8] Li D H, Huang L H, Peng P, Bian G Q, Wang P J, Meng Z M, Chen L C, Zhang J 2020 Phys. Rev. A 102 013309
Google Scholar
[9] Wang Z Y, Cheng X C, Wang B Z, Zhang J Y, Lu Y H, Yi C R, Niu S, Deng Y, Liu X J, Chen S, Pan J W 2021 Science 372 271
Google Scholar
[10] Wang C J, Gao C, Jian C M, Zhai H 2010 Phys. Rev. Lett. 105 160403
Google Scholar
[11] Ho T L, Zhang S 2011 Phys. Rev. Lett. 107 150403
Google Scholar
[12] Qu C L, Zheng Z, Gong M, Xu Y, Mao L, Zou X B, Guo G C, Zhang C W 2013 Nat. Commun. 4 2710
Google Scholar
[13] Li J R, Lee J, Huang W, Burchesky S, Shteynas B, Top F C, Jamison A O, Ketterle W 2017 Nature 543 91
Google Scholar
[14] Cabrera C R, Tanzi L, Sanz J, Naylor B, Thomas P, Cheiney P, Tarruell L 2018 Science 359 301
Google Scholar
[15] Heidemann R, Raitzsch U, Bendkowsky V, Butscher B, Low R, Pfau T 2008 Phys. Rev. Lett. 100 033601
Google Scholar
[16] Henkel N, Nath R, Pohl T 2010 Phys. Rev. Lett. 104 195302
Google Scholar
[17] Hsueh C H, Tsai Y C, Wu K S, Chang M S, Wu W C 2013 Phys. Rev. A 88 043646
Google Scholar
[18] Zhou Y J, Li Y Q, Nath R, Li W B 2020 Phys. Rev. A 101 013427
Google Scholar
[19] Han W, Zhang X F, Wang D S, Jiang H F, Zhang W, Zhang S G 2018 Phys. Rev. Lett. 121 030404
Google Scholar
[20] Zhang X F, Wen L, Wang L X, Chen G P, Tan R B, Saito H 2022 Phys. Rev. A 105 033306
Google Scholar
[21] Cinti F, Jain P, Boninsegni M, Micheli A, Zoller P, Pupillo G 2010 Phys. Rev. Lett. 105 135301
Google Scholar
[22] Henkel N, Cinti F, Jain P, Pupillo G, Pohl T 2012 Phys. Rev. Lett. 108 265301
Google Scholar
[23] McCormack G, Nath R, Li W B 2020 Phys. Rev. A 102 023319
Google Scholar
[24] Hsueh C, Wang C W, Wu W C 2020 Phys. Rev. A 102 063307
Google Scholar
[25] 王鹏, 傅其栋, 李雨芮, 叶芳伟 2021 中国光学 14 986
Google Scholar
Wang P, Fu Q D, Li Y R, Ye F W 2021 Chinese Optics 14 986
Google Scholar
[26] Wang P, Zheng Y L, Chen X F, Huang C M, Kartashov Y V, Torner L, Konotop V V, Ye F W 2020 Nature 577 42
Google Scholar
[27] López M R, Peñaranda F, Christensen J, San-Jose P 2020 Phys. Rev. Lett. 125 214301
Google Scholar
[28] O'Riordan L J, White A C, Busch Th 2016 Phys. Rev. A 93 023609
Google Scholar
[29] González-Tudela A, Cirac J I 2019 Phys. Rev. A 100 053604
Google Scholar
[30] Liu Y, Holder T, Yan B 2021 Innovation 2 100085
[31] Meng Z M, Wang L W, Han W, Liu F D, Wen K, Gao C, Wang P J, Chin C, Zhang J 2021 arXiv: 2110.00149 v2 [cond-mat.quant-gas]
[32] Eddy T, Paolo T, Mahir H, Arthur K 1999 Phys. Rep. 315 199
Google Scholar
[33] 张晓斐, 张培, 陈光平, 董彪, 谭仁兵, 张首刚 2015 物理学报 64 060302
Google Scholar
Zhang X F, Zhang P, Chen G P, Dong B, Tan R B, Zhang S G 2015 Acta Phys. Sin. 64 060302
Google Scholar
[34] Boninsegni M, Prokof’ev N V 2012 Rev. Mod. Phys. 84 759
Google Scholar
[35] 施婷婷, 汪六九, 王璟琨, 张威 2020 物理学报 69 016701
Google Scholar
Shi T T, Wang L J, Wang J K, Zhang W 2020 Acta Phys. Sin. 69 016701
Google Scholar
[36] White A C, Zhang Y, Busch T 2017 Phys. Rev. A 95 041604
Google Scholar
[37] Han W, Zhang X F, Song S W, Saito H, Zhang W, Liu W M, Zhang S G 2016 Phys. Rev. A 94 033629
Google Scholar
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