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相对论性量子力学波动方程, 如狄拉克、外尔和麦克斯韦方程, 是描述微观粒子运动的基石. 最近的实验和理论研究表明, 冷原子系统中几乎所有参数都可精确调控, 因此冷原子系统被认为是实现量子模拟的理想平台, 可以用来研究高能和凝聚态物理中的一些基本问题. 本文介绍了设计原子光晶格哈密顿量的思路和方法, 主要涉及激光辅助跳跃的理论. 基于这些方法, 物理学界提出了利用光晶格体系模拟相对论性量子力学波动方程, 包括狄拉克、外尔和麦克斯韦方程等, 并且预言了一些在基本粒子物理中很难观察到, 但在冷原子体系可能观察到的物理现象. 本文综述了国际上此领域的研究进展.
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关键词:
- 量子模拟 /
- 光晶格 /
- 激光辅助跳跃 /
- 相对论性量子力学方程
Relativistic wave equations, such as Dirac, Weyl or Maxwell equations, are fundamental equations which we use to describe the dynamics of the microscopic particles. On the other hand, recent experimental and theoretical studies have shown that almost all parameters in cold atomic systems are precisely tunable, so the cold atom systems are considered as an ideal platform to perform quantum simulations. It can be used to study some topics in high energy and condensed matter physics. In this article, we will first introduce the ideas and methods for engineering the Hamiltonian of atoms, mainly related to the theories of laser-assisted tunneling. Based on these methods, one can simulate the equations of motion of relativistic particles and observe some interesting behaviors which are hard to be observed in other systems. The article reviews these recent advances.-
Keywords:
- quantum simulations /
- optical lattices /
- laser-assisted tunneling /
- relativistic wave equations
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Google Scholar
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图 1 基于激光辅助跳跃实现人工磁场, 黑(灰)色圆分别表示内态为
$ |g\rangle $ $ (|e\rangle) $ 的Yb原子 (a)内态被标记为$ |g\rangle $ 和$ |e\rangle $ 的原子被囚禁在自旋依赖的光晶格势$ V_g $ 和$ V_e $ 中, 其中$ V_g=-V_e $ ; (b)$ x $ 方向上的激光辅助跃迁; (c)自旋依赖光晶格示意图.$ y $ 方向存在自然跳跃,$ x $ 方向由一束拉曼光$ \varOmega_{\rm R} $ 诱导跳跃Fig. 1. Realization of artificial magnetic field based on laser-assisted tunneling. Gray and black dots represent the Yb atoms correspond to internal states
$|g\rangle$ and$|e\rangle$ , respectively: (a) The atoms$|g\rangle$ and$|e\rangle$ are trapped in the state-dependent optical lattice potentials$V_g$ and$V_e$ , where$V_g=-V_e$ ; (b) laser-assisted tunneling along$x$ direction; (c) sketch of state-dependent optical lattice. Nature tunneling occurs along the$y$ direction, and the tunneling along$x$ direction is induced by a Raman beam$\varOmega_{\rm R}$ .图 3 实现外尔半金属的三维立方晶格示意图. 合理设计
$x$ 和$z$ 方向跳跃, 在动量空间会出现外尔点. 虚线和实线分别表示获得相位${\text{π}}$ 和0[41]Fig. 3. Schematic diagram of a three-dimensional cubic lattice of a Weyl semimetal. The Weyl points will be created in the momentum space if the tunneling along
$x$ and$z$ directions are well-designed . The dashed and solid lines indicate the phase${\text{π}}$ and 0, respectively. -
[1] Chu S 1998 Rev. Mod. Phys. 70 685
Google Scholar
[2] Cohen-Tannoudji C N 1998 Rev. Mod. Phys. 70 707
Google Scholar
[3] Phillips W D 1998 Rev. Mod. Phys. 70 721
Google Scholar
[4] Anderson M H, Ensher J R, Matthews M R, Wieman C E, Cornell E A 1995 Science 269 198
Google Scholar
[5] Davis K B, Mewes M O, Andrews M R, van Druten N J, Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 75 3969
Google Scholar
[6] Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod. Phys. 82 1225
Google Scholar
[7] Jessen P, Deutsch I 1996 Adv. At. Mol. Opt. Phys. 37 95
Google Scholar
[8] Dalibard J, Gerbier F, Juzeliūnas G, Öhberg P 2011 Rev. Mod. Phys. 83 1523
Google Scholar
[9] Goldman N, Juzeliūnas G, Öhberg P, Spielman I B 2014 Rep. Prog. Phys. 77 126401
Google Scholar
[10] Zhai H 2015 Rep. Prog. Phys. 78 026001
Google Scholar
[11] Zhang D W, Zhu Y Q, Zhao Y X, Hui Y, Zhu S L 2018 arXiv: 1810.09228
[12] Zhu S L, Zhang D W, Wang Z D 2009 Phys. Rev. Lett. 102 210403
Google Scholar
[13] Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A, Sen U 2007 Adv. Phys. 56 243
Google Scholar
[14] Jaksch D, Zoller P 2003 New J. Phys. 5 56
Google Scholar
[15] Gerbier F, Dalibard J 2010 New J. Phys. 12 033007
Google Scholar
[16] Struck J, Olschlager C, Weinberg M, et al. 2012 Phys. Rev. Lett. 108 225304
Google Scholar
[17] Grimm R, Weidemüller M 2000 Adv. At. Mol. Opt. Phys. 42 95
Google Scholar
[18] Zhu S L, Wang B, Duan L M 2007 Phys. Rev. Lett. 98 260402
Google Scholar
[19] Zhang D W, Shan C J, Mei F, Yang M, Wang R Q, Zhu S L 2014 Phys. Rev. A 89 015601
Google Scholar
[20] Mandel O, Greiner M, Widera A, Rom T, Hansch T W, Bloch I 2003 Phys. Rev. Lett. 91 010407
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[21] Lee P J, Anderlini M, Brown B L, Sebby-Strabley J, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 99 020402
Google Scholar
[22] Mazza L, Bermudez A, Goldman N, Rizzi M, Martin-Delgado M A, Lewenstein M 2012 New J. Phys. 14 015007
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[27] Lim L K, Fuchs J N, Montambaux G 2012 Phys. Rev. Lett. 108 175303
Google Scholar
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Google Scholar
[29] Duca L, Li T, Reitter M, Bloch I, Schleier-Smith M, Schneider U 2015 Science 347 288
Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
[49] Kitaev A, Laumann C 2009 arXiv: 0904.2771
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Google Scholar
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Google Scholar
[52] Read N, Rezayi E 1999 Phys. Rev. B 59 8084
Google Scholar
[53] Liu S, Shan C J, Zhang Z M, Xue Z Y 2014 Quantum Inf. Process. 13 1813
Google Scholar
[54] Vaishnav J Y, Clark C W 2008 Phys. Rev. Lett. 100 153002
Google Scholar
[55] Zhang D W, Xue Z Y, Yan H, Wang Z D, Zhu S L 2012 Phys. Rev. A 85 013628
Google Scholar
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Google Scholar
[57] Xu Y, Duan L M 2017 Phys. Rev. B 96 155301
Google Scholar
[58] Shen X, Zhu Y Q, Li Z (In preparation)
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Google Scholar
[60] 邱英, 何军, 王彦华, 王婧, 张天才, 王军民 2008 57 6227
Google Scholar
Qiu Y, He J, Wang Y H, Wang J, Zhang T C, Wang J M 2008 Acta Phys. Sin. 57 6227
Google Scholar
[61] Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E, Bloch I 2013 Nat. Phys. 9 795
Google Scholar
[62] Fisher M P A, Weichwan P B, Grinstein G, Fisher D S 1989 Phys. Rev. B 40 546
Google Scholar
[63] Jaksch D, Bruder C, Cirac J I, Zoller P 1998 Phys. Rev. Lett. 81 3108
Google Scholar
[64] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, Esslinger T 2014 Nature 515 237
Google Scholar
[65] Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T, Nascimbène S, Cooper N R, Bloch I, Goldman N 2015 Nat. Phys. 11 162
Google Scholar
[66] 杨圆, 陈帅, 李小兵 2018 67 237101
Google Scholar
Yang Y, Chen S, Li X B 2018 Acta Phys. Sin. 67 237101
Google Scholar
[67] 范桁 2018 67 120301
Google Scholar
Fan H 2018 Acta Phys. Sin. 67 120301
Google Scholar
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