用光晶格模拟狄拉克、外尔和麦克斯韦方程
|
摘要
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.
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.
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.
引文
[1] Chu S 1998 Rev. Mod. Phys. 70 685
[2] Cohen-Tannoudji C N 1998 Rev. Mod. Phys. 70 707
[3] Phillips W D 1998 Rev. Mod. Phys. 70 721
[4]Anderson M H, Ensher J R, Matthews M R, Wieman C E,Cornell E A 1995 Science 269 198
[5]DavisKB,MewesMO,AndrewsMR,vanDrutenNJ,Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 753969
[6]Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod.Phys. 82 1225
[7] Jessen P, Deutsch I 1996 Adv. At. Mol. Opt. Phys. 37 95
[8]DalibardJ,GerbierF,JuzeliūnasG,?hbergP2011Rev.Mod. Phys. 83 1523
[9]GoldmanN,JuzeliūnasG,?hbergP,SpielmanIB2014Rep. Prog. Phys. 77 126401
[10] Zhai H 2015 Rep. Prog. Phys. 78 026001
[11]ZhangDW,ZhuYQ,ZhaoYX,HuiY,ZhuSL2018ar Xiv:1810.09228
[12]Zhu S L, Zhang D W, Wang Z D 2009 Phys. Rev. Lett. 102210403
[13]Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A,Sen U 2007 Adv. Phys. 56 243
[14] Jaksch D, Zoller P 2003 New J. Phys. 5 56
[15] Gerbier F, Dalibard J 2010 New J. Phys. 12 033007
[16]Struck J, Olschlager C, Weinberg M, et al. 2012 Phys. Rev.Lett. 108 225304
[17]Grimm R, Weidemüller M 2000 Adv. At. Mol. Opt. Phys. 4295
[18]ZhuSL,WangB,DuanLM2007Phys. Rev. Lett.98260402
[19]Zhang D W, Shan C J, Mei F, Yang M, Wang R Q, Zhu S L2014 Phys. Rev. A 89 015601
[20]MandelO,GreinerM,WideraA,RomT,HanschTW,Bloch I 2003 Phys. Rev. Lett. 91 010407
[21]Lee P J, Anderlini M, Brown B L, Sebby-Strabley J, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 99 020402
[22]MazzaL,BermudezA,GoldmanN,RizziM,MartinDelgado M A, Lewenstein M 2012 New J. Phys. 14 015007
[23] Aidelsburger M, Atala M, Nascimbène M, Trotzky S, Chen Y A, Bloch I 2011 Phys. Rev. Lett. 107 255301
[24]Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B,Bloch I 2013 Phys. Rev. Lett. 111 185301
[25]MiyakeH,SiviloglouGA,KennedyCJ,BurtonWC,Ketterle W 2013 Phys. Rev. Lett. 111 185302
[26]Tarruell L, Greif D, Uehlinger T, Jotzu G, Esslinger T 2012Nature 483 302
[27]Lim L K, Fuchs J N, Montambaux G 2012 Phys. Rev. Lett.108 175303
[28]UehlingerT,GreifD,JotzuG,TarruellL,EsslingerT,WangL,Troyer M2013Eur. Phys. J. Special Topics217121
[29]DucaL,LiT,ReitterM,BlochI,Schleier-SmithM,Schneider U 2015 Science 347 288
[30]ArmitageNP,MeleEJ,VishwanathA2018Rev. Mod.Phys. 90 015001
[31]Bermudez A, Mazza L, Rizzi M, Goldman N, Lewenstein M,Martin-Delgado M A 2010 Phys. Rev. Lett. 105 190404
[32]MazzaL,BermudezA,GoldmanN,RizziM,MartinDelgado M A, Lewenstein M 2012 New J. Phys. 14 015007
[33] Yang M, Zhu S L 2010 Phys. Rev. A 82 064102
[34]Lepori L, Mussardo G, Trombettoni A 2010 Europhys. Lett.92 50003
[35]Wilson K, New Phenomena in Subnuclear Physics, Plenum,New York, 1977.
[36]ZhangDW,MeiF,XueZY,ZhuSL,WangZD2015Phys. Rev. A 92 013612
[37] Ganeshan S, Sarma S D 2015 Phys. Rev. B 91 125438
[38] Jiang J H 2012 Phys. Rev. A 85 033640
[39] He W Y, Zhang S, Law K T 2016 Phys. Rev. A 94 013606
[40] Hou J M, Chen W 2016 Sci. Rep. 6 33512
[41]Dub?ekT,KennedyCJ,LuL,KetterleW,Solja?i?M,Buljan H 2015 Phys. Rev. Lett. 114 225301
[42] Xu Y, Duan L M 2016 Phys. Rev. A 94 053619
[43] Shastri K, Yang Z, Zhang B 2017 Phys. Rev. B 95 014306
[44] Kong X, He J, Liang Y, Kou S 2017 Phys. Rev. A 95 33629
[45]ZhuYQ,ZhangDW,YanH,XingDY,ZhuSL2017Phys. Rev. A 96 033634
[46] Tan X, Zhang D W, Liu Q, Xue G, Yu H F, Zhu Y Q, YanH, Zhu S L, Yu Y 2018 Phys. Rev. Lett. 120 130503
[47] Liang L, Yu Y 2016 Phys. Rev. B 93 045113
[48]LanZ,GoldmanN,BermudezA,LuW,?hbergP2011Phys. Rev. B 84 165115
[49] Kitaev A, Laumann C 2009 ar Xiv:0904.2771
[50]Trebst S, Troyer M, Wang Z, Ludwig A W W 2008 Prog.Theor. Phys. Supp. 176 384
[51]NayakC,SimonSH,SternA,FreedmanM,SarmaSD2008 Rev. Mod. Phys. 80 1083
[52] Read N, Rezayi E 1999 Phys. Rev. B 59 8084
[53]Liu S, Shan C J, Zhang Z M, Xue Z Y 2014 Quantum Inf.Process. 13 1813
[54] Vaishnav J Y, Clark C W 2008 Phys. Rev. Lett. 100 153002
[55]ZhangDW,XueZY,YanH,WangZD,ZhuSL2012Phys. Rev. A 85 013628
[56]LiZ,WangHQ,ZhangDW,ZhuSL,XingDY2016Phys. Rev. A 94 043617
[57] Xu Y, Duan L M 2017 Phys. Rev. B 96 155301
[58] Shen X, Zhu Y Q, Li Z(In preparation)
[59] Bliokh K Y, Smirnova D, Nori F 2015 Science 348 1448
[60]Qiu Y, He J, Wang Y H, Wang J, Zhang T C, Wang J M2008 Acta Phys. Sin. 57 6227(in Chinese)[邱英,何军,王彦华,王婧,张天才,王军民2008物理学报57 6227]
[61]Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E, Bloch I 2013 Nat. Phys. 9 795
[62]Fisher M P A, Weichwan P B, Grinstein G, Fisher D S 1989Phys. Rev. B 40 546
[63]JakschD,BruderC,CiracJI,ZollerP1998Phys. Rev.Lett. 81 3108
[64]Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T,Greif D, Esslinger T 2014 Nature 515 237
[65]Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T,NascimbèneS,CooperNR,BlochI,GoldmanN2015Nat. Phys. 11 162
[66]Yang Y, Chen S, Li X B 2018 Acta Phys. Sin. 67 237101(in Chinese)[杨圆,陈帅,李小兵2018物理学报67 237101]
[67] Fan H 2018 Acta Phys. Sin. 67 120301(in Chinese)[范桁2018物理学报67 120301]
[2] Cohen-Tannoudji C N 1998 Rev. Mod. Phys. 70 707
[3] Phillips W D 1998 Rev. Mod. Phys. 70 721
[4]Anderson M H, Ensher J R, Matthews M R, Wieman C E,Cornell E A 1995 Science 269 198
[5]DavisKB,MewesMO,AndrewsMR,vanDrutenNJ,Durfee D S, Kurn D M, Ketterle W 1995 Phys. Rev. Lett. 753969
[6]Chin C, Grimm R, Julienne P, Tiesinga E 2010 Rev. Mod.Phys. 82 1225
[7] Jessen P, Deutsch I 1996 Adv. At. Mol. Opt. Phys. 37 95
[8]DalibardJ,GerbierF,JuzeliūnasG,?hbergP2011Rev.Mod. Phys. 83 1523
[9]GoldmanN,JuzeliūnasG,?hbergP,SpielmanIB2014Rep. Prog. Phys. 77 126401
[10] Zhai H 2015 Rep. Prog. Phys. 78 026001
[11]ZhangDW,ZhuYQ,ZhaoYX,HuiY,ZhuSL2018ar Xiv:1810.09228
[12]Zhu S L, Zhang D W, Wang Z D 2009 Phys. Rev. Lett. 102210403
[13]Lewenstein M, Sanpera A, Ahufinger V, Damski B, Sen A,Sen U 2007 Adv. Phys. 56 243
[14] Jaksch D, Zoller P 2003 New J. Phys. 5 56
[15] Gerbier F, Dalibard J 2010 New J. Phys. 12 033007
[16]Struck J, Olschlager C, Weinberg M, et al. 2012 Phys. Rev.Lett. 108 225304
[17]Grimm R, Weidemüller M 2000 Adv. At. Mol. Opt. Phys. 4295
[18]ZhuSL,WangB,DuanLM2007Phys. Rev. Lett.98260402
[19]Zhang D W, Shan C J, Mei F, Yang M, Wang R Q, Zhu S L2014 Phys. Rev. A 89 015601
[20]MandelO,GreinerM,WideraA,RomT,HanschTW,Bloch I 2003 Phys. Rev. Lett. 91 010407
[21]Lee P J, Anderlini M, Brown B L, Sebby-Strabley J, Phillips W D, Porto J V 2007 Phys. Rev. Lett. 99 020402
[22]MazzaL,BermudezA,GoldmanN,RizziM,MartinDelgado M A, Lewenstein M 2012 New J. Phys. 14 015007
[23] Aidelsburger M, Atala M, Nascimbène M, Trotzky S, Chen Y A, Bloch I 2011 Phys. Rev. Lett. 107 255301
[24]Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B,Bloch I 2013 Phys. Rev. Lett. 111 185301
[25]MiyakeH,SiviloglouGA,KennedyCJ,BurtonWC,Ketterle W 2013 Phys. Rev. Lett. 111 185302
[26]Tarruell L, Greif D, Uehlinger T, Jotzu G, Esslinger T 2012Nature 483 302
[27]Lim L K, Fuchs J N, Montambaux G 2012 Phys. Rev. Lett.108 175303
[28]UehlingerT,GreifD,JotzuG,TarruellL,EsslingerT,WangL,Troyer M2013Eur. Phys. J. Special Topics217121
[29]DucaL,LiT,ReitterM,BlochI,Schleier-SmithM,Schneider U 2015 Science 347 288
[30]ArmitageNP,MeleEJ,VishwanathA2018Rev. Mod.Phys. 90 015001
[31]Bermudez A, Mazza L, Rizzi M, Goldman N, Lewenstein M,Martin-Delgado M A 2010 Phys. Rev. Lett. 105 190404
[32]MazzaL,BermudezA,GoldmanN,RizziM,MartinDelgado M A, Lewenstein M 2012 New J. Phys. 14 015007
[33] Yang M, Zhu S L 2010 Phys. Rev. A 82 064102
[34]Lepori L, Mussardo G, Trombettoni A 2010 Europhys. Lett.92 50003
[35]Wilson K, New Phenomena in Subnuclear Physics, Plenum,New York, 1977.
[36]ZhangDW,MeiF,XueZY,ZhuSL,WangZD2015Phys. Rev. A 92 013612
[37] Ganeshan S, Sarma S D 2015 Phys. Rev. B 91 125438
[38] Jiang J H 2012 Phys. Rev. A 85 033640
[39] He W Y, Zhang S, Law K T 2016 Phys. Rev. A 94 013606
[40] Hou J M, Chen W 2016 Sci. Rep. 6 33512
[41]Dub?ekT,KennedyCJ,LuL,KetterleW,Solja?i?M,Buljan H 2015 Phys. Rev. Lett. 114 225301
[42] Xu Y, Duan L M 2016 Phys. Rev. A 94 053619
[43] Shastri K, Yang Z, Zhang B 2017 Phys. Rev. B 95 014306
[44] Kong X, He J, Liang Y, Kou S 2017 Phys. Rev. A 95 33629
[45]ZhuYQ,ZhangDW,YanH,XingDY,ZhuSL2017Phys. Rev. A 96 033634
[46] Tan X, Zhang D W, Liu Q, Xue G, Yu H F, Zhu Y Q, YanH, Zhu S L, Yu Y 2018 Phys. Rev. Lett. 120 130503
[47] Liang L, Yu Y 2016 Phys. Rev. B 93 045113
[48]LanZ,GoldmanN,BermudezA,LuW,?hbergP2011Phys. Rev. B 84 165115
[49] Kitaev A, Laumann C 2009 ar Xiv:0904.2771
[50]Trebst S, Troyer M, Wang Z, Ludwig A W W 2008 Prog.Theor. Phys. Supp. 176 384
[51]NayakC,SimonSH,SternA,FreedmanM,SarmaSD2008 Rev. Mod. Phys. 80 1083
[52] Read N, Rezayi E 1999 Phys. Rev. B 59 8084
[53]Liu S, Shan C J, Zhang Z M, Xue Z Y 2014 Quantum Inf.Process. 13 1813
[54] Vaishnav J Y, Clark C W 2008 Phys. Rev. Lett. 100 153002
[55]ZhangDW,XueZY,YanH,WangZD,ZhuSL2012Phys. Rev. A 85 013628
[56]LiZ,WangHQ,ZhangDW,ZhuSL,XingDY2016Phys. Rev. A 94 043617
[57] Xu Y, Duan L M 2017 Phys. Rev. B 96 155301
[58] Shen X, Zhu Y Q, Li Z(In preparation)
[59] Bliokh K Y, Smirnova D, Nori F 2015 Science 348 1448
[60]Qiu Y, He J, Wang Y H, Wang J, Zhang T C, Wang J M2008 Acta Phys. Sin. 57 6227(in Chinese)[邱英,何军,王彦华,王婧,张天才,王军民2008物理学报57 6227]
[61]Atala M, Aidelsburger M, Barreiro J T, Abanin D, Kitagawa T, Demler E, Bloch I 2013 Nat. Phys. 9 795
[62]Fisher M P A, Weichwan P B, Grinstein G, Fisher D S 1989Phys. Rev. B 40 546
[63]JakschD,BruderC,CiracJI,ZollerP1998Phys. Rev.Lett. 81 3108
[64]Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T,Greif D, Esslinger T 2014 Nature 515 237
[65]Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T,NascimbèneS,CooperNR,BlochI,GoldmanN2015Nat. Phys. 11 162
[66]Yang Y, Chen S, Li X B 2018 Acta Phys. Sin. 67 237101(in Chinese)[杨圆,陈帅,李小兵2018物理学报67 237101]
[67] Fan H 2018 Acta Phys. Sin. 67 120301(in Chinese)[范桁2018物理学报67 120301]