一维准周期晶格的性质及应用
|
摘要
准周期晶格在冷原子领域被广泛研究,它使得人们可以在一维或者二维系统里研究扩展到安德森局域的转变. 2008年, Inguscio研究组在冷原子系统里制备了一维准周期晶格,并观测到了安德森局域化现象,这极大地推动了准周期系统的理论和实验研究.后来, Bloch研究组在制备的一维和二维准周期晶格中都观测到了多体局域的现象.最近,他们还在准周期晶格中成功观测到迁移率边以及存在迁移率边的系统的多体局域现象.这些冷原子实验推动了多体局域以及迁移率边等方向的研究.准周期晶格已经成为一个平台,它对很多物理现象的影响正在被广泛研究,并可以尝试在冷原子实验中观测到这种影响.本文结合作者的一些相关工作,对一维准周期晶格一些近期的研究进行了简要综述,介绍了一些相关的重要的冷原子实验,讨论了准周期晶格的一些重要性质,以及它对一些物理现象(比如拓扑态)的影响.
Quasiperiodic lattices have been widely studied in cold atoms, which make one study extended-Anderson localization transition in one-dimensional(1 D) or two-dimensional(2 D) systems. In 2008, Inguscio's group prepared one-dimensional quasiperiodic lattice in cold atomic system and observed Anderson localization, which promoted the theoretical and experimental studies of quasiperiodic systems. Later, Bloch's group observed the many body localization in their prepared 1 D and 2 D quasiperiodic lattices. Recently, they also successfully observed the mobility edge and many body localization in a system with mobility edge in quasiperiodic lattices.These cold atom experiments have promoted the researches of many body localization and mobility edge.Quasiperiodic lattices have become a platform and its effects on many physical phenomena are being extensively studied, which can be expectantly observed in cold atomic experiments. This paper is based on the authors' some related work and briefly review some recent studies on the 1 D quasiperiodic lattices, including some important cold atom experiments, some important properties of the quasiperiodic lattices and their effects on some physical phenomena, such as topological states.
Quasiperiodic lattices have been widely studied in cold atoms, which make one study extended-Anderson localization transition in one-dimensional(1 D) or two-dimensional(2 D) systems. In 2008, Inguscio's group prepared one-dimensional quasiperiodic lattice in cold atomic system and observed Anderson localization, which promoted the theoretical and experimental studies of quasiperiodic systems. Later, Bloch's group observed the many body localization in their prepared 1 D and 2 D quasiperiodic lattices. Recently, they also successfully observed the mobility edge and many body localization in a system with mobility edge in quasiperiodic lattices.These cold atom experiments have promoted the researches of many body localization and mobility edge.Quasiperiodic lattices have become a platform and its effects on many physical phenomena are being extensively studied, which can be expectantly observed in cold atomic experiments. This paper is based on the authors' some related work and briefly review some recent studies on the 1 D quasiperiodic lattices, including some important cold atom experiments, some important properties of the quasiperiodic lattices and their effects on some physical phenomena, such as topological states.
引文
[1]Wang Y Q 2007 Atomic Laser Cooling And Trapping(Beijing:Peking University Press)(in Chinese)[王义遒2007原子的激光冷却与陷俘(北京:北京大学出版社)]
[2]Stwalley W C 1976 Phys.Rev.Lett.37 1628
[3]Bloch I,Dalibard J,Zwerger W 2008 Rev.Mod.Phys.80885
[4]Lin Y J,Jimenez-Garcia K,Spielman I B 2011 Nature 47183
[5]Wu Z,Zhang L,Sun W,Xu X T,Wang B Z,Ji S C,Deng Y J,Chen S,Liu X J,Pan J W 2016 Science 354 83
[6]Zhang L,Liu X J 2018 ar Xiv:1806.05628
[7]Cooper N R,Dalibard J,Spielman I B 2018ar Xiv:1803.00249
[8]Jian C M,Zhai H 2011 Phys.Rev.B 84 060508
[9]Hu J,Feng L,Zhang Z,Chin C,2018 ar Xiv:1807.07504
[10]Aubry S,AndréG 1980 Ann.Israel Phys.Soc 3 18
[11]Das Sarma S,He S,Xie X C 1988 Phys.Rev.Lett.61 2144
[12]Das Sarma S,He S,Xie X C 1990 Phys.Rev.B 41 5544
[13]Biddle J,Das Sarma S 2010 Phys.Rev.Lett.104 070601
[14]Biddle J,Priour Jr D J,Wang B,Das Sarma S 2011 Phys.Rev.B 83 075105
[15]Roati G,D’Errico C,Fallani L,Fattori M,Fort C,Zaccanti M,Modugno G,Modugno M,Inguscio M 2008 Nature 453895
[16]Cai X,Lang L J,Chen S,Wang Y 2013 Phys.Rev.Lett.110 176403
[17]De Gottardi W,Sen D,Vishveshwara S 2013 Phys.Rev.Lett.110 146404
[18]Wang J,Liu X J,Gao X,Hu H 2016 Phys.Rev.B 93104504
[19]Wang Y,Wang Y,Chen S 2016 Eur.Phys.J.B 89 254
[20]Iyer S,Oganesyan V,Refael G,Huse D A 2013 Phys.Rev.B 87 134202
[21]Wang Y,Hu H,Chen S 2016 Eur.Phys.J.B 89 77
[22]Setiawan F,Deng D L,Pixley J H 2017 Phys.Rev.B 96104205
[23]Schreiber M,Hodgman S S,Bordia P,Lüschen H P,Fischer M H,Vosk R,Altman E,Schneider U,Bloch I 2015 Science349 842
[24]Anderson P W 1958 Phys.Rev.109 1492
[25]Thouless D J 1974 Phys.Rep.13 93
[26]Schreiber M 1985 J.Phys.C 18 2493
[27]Hashimoto Y,Niizeki K,Okabe Y 1992 J.Phys.A 25 5211
[28]Modugno M 2009 New J.Phys.11 033023
[29]Lang L J 2014 Ph.D.Dissertation(Beijing:University of Chinese Academy of Sciences)(in Chinese)[郎利君2014博士学位论文(北京:中国科学院大学)]
[30]Li X,Li X,Das Sarma S 2017 Phys.Rev.B 96 085119
[31]Lüschen H P,Scherg S,Kohlert T,Schreiber M,Bordia P,Li X,Das Sarma S,Bloch I 2018 Phys.Rev.Lett.120160404
[32]Basko D,Aleiner I,Altshuler B 2006 Ann.Phys.321 1126
[33]Nandkishore R,Huse D A 2015 Annu.Rev.Condens.Matter Phys.6 15
[34]Pal A,Huse D A 2010 Phys.Rev.B 82 174411
[35]Vosk R,Huse D A,Altman E 2015 Phys.Rev.X 5 031032
[36]Agarwal K,Gopalakrishnan S,Knap M,Müller,Demler E2015 Phys.Rev.Lett.114 160401
[37]Fan R,Zhang P,Shen H,Zhai H 2017 Sci.Bull.62 707
[38]Else D V,Bauer B,Nayak C 2016 Phys.Rev.Lett.117090402
[39]Oganesyan V,Huse D A 2007 Phys.Rev.B 75 155111
[40]Vosk R,Altman E 2013 Phys.Rev.Lett.110 067204
[41]Bauer B,Nayak C 2013 J.Stat.Mech.2013 P09005
[42]Wang Y 2018 Ph.D.Dissertation(Beijing:University of Chinese Academy of Sciences)(in Chinese)[王玉成2018博士学位论文(北京:中国科学院大学)]
[43]Serbyn M,Papi?,Abanin D A 2013 Phys.Rev.Lett.111127201
[44]Bardarson J H,Pollmann F,Moore J E 2012 Phys.Rev.Lett.109 017202
[45]Serbyn M,Papi?Z,Abanin D A 2013 Phys.Rev.Lett.110260601
[46]Bordia P,Lüschen H P,Scherg S,Gopalakrishnan S,Knap M,Schneider U,Bloch I 2017 Phys.Rev.X 7 041047
[47]Kohlert T,Scherg S,Li X,Lüschen H P,Das Sarma S,Bloch I,Aidelsburger M 2018 ar Xiv:1809.04055
[48]Hiramoto H,Abe S 1988 J.Phys.Soc.Jpn.57 230
[49]Hiramoto H,Abe S 1988 J.Phys.Soc.Jpn.57 1365
[50]Metzler R,Klafter J 2000 Phys.Rep.339 1
[51]Battiato M,Carva K,Oppeneer P M 2012 Phys.Rev.B 86024404
[52]Foster S,Thesberg M,Neophytou N 2017 Phys.Rev.B 96195425
[53]Ketzmerick R,Petschel G,Geisel T 1992 Phys.Rev.Lett.69 695
[54]Ketzmerick R,Kruse K,Kraut S,Geisel T 1997 Phys.Rev.Lett.79 1959
[55]Qin P,Yin C,Chen S 2014 Phys.Rev.B 90 054303
[56]Floquet G 1883 Ann.ENS 12 47
[57]Grifoni M,H?nggi P 1998 Phys.Rep.304 229
[58]Blümel R,Smilansky U 1984 Phys.Rev.Lett.52 137
[59]Izrailev F M 1988 Phys.Lett.A 134 13
[60]Amico L,Fazio R,Osterloh A,Vedral V 2008 Rev.Mod.Phys.80 517
[61]Wilcox R M 1967 J.Math.Phys.8 962
[62]Heyl M,Polkovnikov A,Kehrein S 2013 Phys.Rev.Lett.110 135704
[63]Heyl M 2014 Phys.Rev.Lett.113 205701
[64]Heyl M 2015 Phys.Rev.Lett.115 140602
[65]Heyl M 2018 Rep.Prog.Phys.81 054001
[66]Yang C,Wang Y,Wang P,Gao X,Chen S 2017 Phys.Rev.B 95 184201
[67]Jalabert R A,Pastawski H M 2001 Phys.Rev.Lett.86 2490
[68]Cucchietti F M,Dalvit D A R,Paz J P,Zurek W H 2003Phys.Rev.Lett.91 210403
[69]Gorin T,Prosen T,Seligman T H,Znidaric M 2006 Phys.Rep.435 33
[70]Quan H T,Song Z,Liu X F,Zanardi P,Sun C P 2006Phys.Rev.Lett.96 140604
[71]Jafari R,Johannesson H 2017 Phys.Rev.Lett.118 015701
[72]Yang B J,Nagaosa N 2014 Nat.Commun.5 4898
[73]Hassan M Z,Kane C L 2010 Rev.Mod.Phys.82 3045
[74]Qi X L,Zhang S C 2011 Rev.Mod.Phys.83 1057
[75]Fang C,Weng H,Dai X,Fang Z 2016 Chin.Phys.B 25117106
[76]Su W P,Schrieffer J R,Heeger A J 1979 Phys.Rev.Lett.42 1698
[77]Guo H,Chen S 2015 Phys.Rev.B 91 041402
[78]Thouless D J 1983 Phys.Rev.B 27 6083
[79]Wang L,Troyer M,Dai X 2013 Phys.Rev.Lett.111 026802
[80]Nakajima S,Tomita T,Taie S,Ichinose T,Ozawa H,Wang L,Troyer M,Takahashi Y 2016 Nat.Phys.12 296
[81]Xu Z,Zhang Y,Chen S 2017 Phys.Rev.A 96 013606
[82]Kitaev A Y 2001 Phys.Usp.44 131
[83]Wan X,Turner A M,Vishwanath A,Savrasov S Y 2011Phys.Rev.B 83 205101
[84]Xu G,Weng H,Wang Z,Dai X,Fang Z 2011 Phys.Rev.Lett.107 186806
[85]Lv B Q,Xu N,Weng H M,Ma J Z,Richard P,Huang X C,Zhao L X,Chen G F,Matt C E,Bisti F,Strocov V N,Mesot J,Fang Z,Dai X,Qian T,Shiand M,Ding H 2015Nat.Phys.11 724
[86]Alicea J 2012 Rep.Prog.Phys.75 076501
[87]Gangadharaiah S,Braunecker B,Simon P,Loss D 2011Phys.Rev.Lett.107 036801
[88]Zhu G Y,Wang R R,Zhang G M 2017 Phys.46 154(in Chinese)[朱国毅,王瑞蕊,张广铭2017物理46 154]
[89]Lieb E,Schultz T,Mattis D 1961 Ann.Phys.16 407
[90]Dub?ek T,Kennedy C J,Lu L,Ketterle W,Solja?i?M,Buljan H 2015 Phys.Rev.Lett.114 225301
[91]Wang Y,Chen S 2017 Phys.Rev.A 95 053634
[92]Weiβe A,Wellein G,Alvermann A,Fehske H 2006 Rev.Mod.Phys.78 275
[93]Bera S,Sau J D,Roy B 2016 Phys.Rev.B 93 201302
[94]Kobayashi K,Ohtsuki T,Imura K I,Herbut I F 2014 Phys.Rev.Lett.112 016402
[95]Pixley J H,Goswami P,Das Sarma S 2015 Phys.Rev.Lett.115 076601
[96]Pixley J H,Wilson J H,Huse D A,Gopalakrishnan S 2018Phys.Rev.Lett.120 207604
[97]Yan Z,Bi R,Shen H,Lu L,Zhang S C,Wang Z 2017 Phys.Rev.B 96 041103
[98]Wang Y,Hu H,Chen S 2018 Phys.Rev.B 98 205410
[99]Kraus Y E,Lahini Y,Ringel Z,Verbin M,Zilberberg O2012 Phys.Rev.Lett.109 106402
[100]Lang L,Cai X,Chen S 2012 Phys.Rev.Lett.108 220401
[101]Madsen K,Bergholtz E J,Brouwer 2013 Phys.Rev.B 88125118
[2]Stwalley W C 1976 Phys.Rev.Lett.37 1628
[3]Bloch I,Dalibard J,Zwerger W 2008 Rev.Mod.Phys.80885
[4]Lin Y J,Jimenez-Garcia K,Spielman I B 2011 Nature 47183
[5]Wu Z,Zhang L,Sun W,Xu X T,Wang B Z,Ji S C,Deng Y J,Chen S,Liu X J,Pan J W 2016 Science 354 83
[6]Zhang L,Liu X J 2018 ar Xiv:1806.05628
[7]Cooper N R,Dalibard J,Spielman I B 2018ar Xiv:1803.00249
[8]Jian C M,Zhai H 2011 Phys.Rev.B 84 060508
[9]Hu J,Feng L,Zhang Z,Chin C,2018 ar Xiv:1807.07504
[10]Aubry S,AndréG 1980 Ann.Israel Phys.Soc 3 18
[11]Das Sarma S,He S,Xie X C 1988 Phys.Rev.Lett.61 2144
[12]Das Sarma S,He S,Xie X C 1990 Phys.Rev.B 41 5544
[13]Biddle J,Das Sarma S 2010 Phys.Rev.Lett.104 070601
[14]Biddle J,Priour Jr D J,Wang B,Das Sarma S 2011 Phys.Rev.B 83 075105
[15]Roati G,D’Errico C,Fallani L,Fattori M,Fort C,Zaccanti M,Modugno G,Modugno M,Inguscio M 2008 Nature 453895
[16]Cai X,Lang L J,Chen S,Wang Y 2013 Phys.Rev.Lett.110 176403
[17]De Gottardi W,Sen D,Vishveshwara S 2013 Phys.Rev.Lett.110 146404
[18]Wang J,Liu X J,Gao X,Hu H 2016 Phys.Rev.B 93104504
[19]Wang Y,Wang Y,Chen S 2016 Eur.Phys.J.B 89 254
[20]Iyer S,Oganesyan V,Refael G,Huse D A 2013 Phys.Rev.B 87 134202
[21]Wang Y,Hu H,Chen S 2016 Eur.Phys.J.B 89 77
[22]Setiawan F,Deng D L,Pixley J H 2017 Phys.Rev.B 96104205
[23]Schreiber M,Hodgman S S,Bordia P,Lüschen H P,Fischer M H,Vosk R,Altman E,Schneider U,Bloch I 2015 Science349 842
[24]Anderson P W 1958 Phys.Rev.109 1492
[25]Thouless D J 1974 Phys.Rep.13 93
[26]Schreiber M 1985 J.Phys.C 18 2493
[27]Hashimoto Y,Niizeki K,Okabe Y 1992 J.Phys.A 25 5211
[28]Modugno M 2009 New J.Phys.11 033023
[29]Lang L J 2014 Ph.D.Dissertation(Beijing:University of Chinese Academy of Sciences)(in Chinese)[郎利君2014博士学位论文(北京:中国科学院大学)]
[30]Li X,Li X,Das Sarma S 2017 Phys.Rev.B 96 085119
[31]Lüschen H P,Scherg S,Kohlert T,Schreiber M,Bordia P,Li X,Das Sarma S,Bloch I 2018 Phys.Rev.Lett.120160404
[32]Basko D,Aleiner I,Altshuler B 2006 Ann.Phys.321 1126
[33]Nandkishore R,Huse D A 2015 Annu.Rev.Condens.Matter Phys.6 15
[34]Pal A,Huse D A 2010 Phys.Rev.B 82 174411
[35]Vosk R,Huse D A,Altman E 2015 Phys.Rev.X 5 031032
[36]Agarwal K,Gopalakrishnan S,Knap M,Müller,Demler E2015 Phys.Rev.Lett.114 160401
[37]Fan R,Zhang P,Shen H,Zhai H 2017 Sci.Bull.62 707
[38]Else D V,Bauer B,Nayak C 2016 Phys.Rev.Lett.117090402
[39]Oganesyan V,Huse D A 2007 Phys.Rev.B 75 155111
[40]Vosk R,Altman E 2013 Phys.Rev.Lett.110 067204
[41]Bauer B,Nayak C 2013 J.Stat.Mech.2013 P09005
[42]Wang Y 2018 Ph.D.Dissertation(Beijing:University of Chinese Academy of Sciences)(in Chinese)[王玉成2018博士学位论文(北京:中国科学院大学)]
[43]Serbyn M,Papi?,Abanin D A 2013 Phys.Rev.Lett.111127201
[44]Bardarson J H,Pollmann F,Moore J E 2012 Phys.Rev.Lett.109 017202
[45]Serbyn M,Papi?Z,Abanin D A 2013 Phys.Rev.Lett.110260601
[46]Bordia P,Lüschen H P,Scherg S,Gopalakrishnan S,Knap M,Schneider U,Bloch I 2017 Phys.Rev.X 7 041047
[47]Kohlert T,Scherg S,Li X,Lüschen H P,Das Sarma S,Bloch I,Aidelsburger M 2018 ar Xiv:1809.04055
[48]Hiramoto H,Abe S 1988 J.Phys.Soc.Jpn.57 230
[49]Hiramoto H,Abe S 1988 J.Phys.Soc.Jpn.57 1365
[50]Metzler R,Klafter J 2000 Phys.Rep.339 1
[51]Battiato M,Carva K,Oppeneer P M 2012 Phys.Rev.B 86024404
[52]Foster S,Thesberg M,Neophytou N 2017 Phys.Rev.B 96195425
[53]Ketzmerick R,Petschel G,Geisel T 1992 Phys.Rev.Lett.69 695
[54]Ketzmerick R,Kruse K,Kraut S,Geisel T 1997 Phys.Rev.Lett.79 1959
[55]Qin P,Yin C,Chen S 2014 Phys.Rev.B 90 054303
[56]Floquet G 1883 Ann.ENS 12 47
[57]Grifoni M,H?nggi P 1998 Phys.Rep.304 229
[58]Blümel R,Smilansky U 1984 Phys.Rev.Lett.52 137
[59]Izrailev F M 1988 Phys.Lett.A 134 13
[60]Amico L,Fazio R,Osterloh A,Vedral V 2008 Rev.Mod.Phys.80 517
[61]Wilcox R M 1967 J.Math.Phys.8 962
[62]Heyl M,Polkovnikov A,Kehrein S 2013 Phys.Rev.Lett.110 135704
[63]Heyl M 2014 Phys.Rev.Lett.113 205701
[64]Heyl M 2015 Phys.Rev.Lett.115 140602
[65]Heyl M 2018 Rep.Prog.Phys.81 054001
[66]Yang C,Wang Y,Wang P,Gao X,Chen S 2017 Phys.Rev.B 95 184201
[67]Jalabert R A,Pastawski H M 2001 Phys.Rev.Lett.86 2490
[68]Cucchietti F M,Dalvit D A R,Paz J P,Zurek W H 2003Phys.Rev.Lett.91 210403
[69]Gorin T,Prosen T,Seligman T H,Znidaric M 2006 Phys.Rep.435 33
[70]Quan H T,Song Z,Liu X F,Zanardi P,Sun C P 2006Phys.Rev.Lett.96 140604
[71]Jafari R,Johannesson H 2017 Phys.Rev.Lett.118 015701
[72]Yang B J,Nagaosa N 2014 Nat.Commun.5 4898
[73]Hassan M Z,Kane C L 2010 Rev.Mod.Phys.82 3045
[74]Qi X L,Zhang S C 2011 Rev.Mod.Phys.83 1057
[75]Fang C,Weng H,Dai X,Fang Z 2016 Chin.Phys.B 25117106
[76]Su W P,Schrieffer J R,Heeger A J 1979 Phys.Rev.Lett.42 1698
[77]Guo H,Chen S 2015 Phys.Rev.B 91 041402
[78]Thouless D J 1983 Phys.Rev.B 27 6083
[79]Wang L,Troyer M,Dai X 2013 Phys.Rev.Lett.111 026802
[80]Nakajima S,Tomita T,Taie S,Ichinose T,Ozawa H,Wang L,Troyer M,Takahashi Y 2016 Nat.Phys.12 296
[81]Xu Z,Zhang Y,Chen S 2017 Phys.Rev.A 96 013606
[82]Kitaev A Y 2001 Phys.Usp.44 131
[83]Wan X,Turner A M,Vishwanath A,Savrasov S Y 2011Phys.Rev.B 83 205101
[84]Xu G,Weng H,Wang Z,Dai X,Fang Z 2011 Phys.Rev.Lett.107 186806
[85]Lv B Q,Xu N,Weng H M,Ma J Z,Richard P,Huang X C,Zhao L X,Chen G F,Matt C E,Bisti F,Strocov V N,Mesot J,Fang Z,Dai X,Qian T,Shiand M,Ding H 2015Nat.Phys.11 724
[86]Alicea J 2012 Rep.Prog.Phys.75 076501
[87]Gangadharaiah S,Braunecker B,Simon P,Loss D 2011Phys.Rev.Lett.107 036801
[88]Zhu G Y,Wang R R,Zhang G M 2017 Phys.46 154(in Chinese)[朱国毅,王瑞蕊,张广铭2017物理46 154]
[89]Lieb E,Schultz T,Mattis D 1961 Ann.Phys.16 407
[90]Dub?ek T,Kennedy C J,Lu L,Ketterle W,Solja?i?M,Buljan H 2015 Phys.Rev.Lett.114 225301
[91]Wang Y,Chen S 2017 Phys.Rev.A 95 053634
[92]Weiβe A,Wellein G,Alvermann A,Fehske H 2006 Rev.Mod.Phys.78 275
[93]Bera S,Sau J D,Roy B 2016 Phys.Rev.B 93 201302
[94]Kobayashi K,Ohtsuki T,Imura K I,Herbut I F 2014 Phys.Rev.Lett.112 016402
[95]Pixley J H,Goswami P,Das Sarma S 2015 Phys.Rev.Lett.115 076601
[96]Pixley J H,Wilson J H,Huse D A,Gopalakrishnan S 2018Phys.Rev.Lett.120 207604
[97]Yan Z,Bi R,Shen H,Lu L,Zhang S C,Wang Z 2017 Phys.Rev.B 96 041103
[98]Wang Y,Hu H,Chen S 2018 Phys.Rev.B 98 205410
[99]Kraus Y E,Lahini Y,Ringel Z,Verbin M,Zilberberg O2012 Phys.Rev.Lett.109 106402
[100]Lang L,Cai X,Chen S 2012 Phys.Rev.Lett.108 220401
[101]Madsen K,Bergholtz E J,Brouwer 2013 Phys.Rev.B 88125118