1932

Abstract

Experimental advances have allowed for the exploration of nearly isolated quantum many-body systems whose coupling to an external bath is very weak. A particularly interesting class of such systems is those that do not thermalize under their own isolated quantum dynamics. In this review, we highlight the possibility for such systems to exhibit new nonequilibrium phases of matter. In particular, we focus on discrete time crystals, which are many-body phases of matter characterized by a spontaneously broken discrete time-translation symmetry. We give a definition of discrete time crystals from several points of view, emphasizing that they are a nonequilibrium phenomenon that is stabilized by many-body interactions, with no analog in noninteracting systems. We explain the theory behind several proposed models of discrete time crystals, and compare several recent realizations, in different experimental contexts.

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2020-03-10
2024-06-25
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Literature Cited

  1. 1. 
    Nandkishore R, Huse DA 2015. Annu. Rev. Condens. Matter Phys. 6:15–38
    [Google Scholar]
  2. 2. 
    Abanin DA, Altman E, Bloch I, Serbyn M 2019. Rev. Mod. Phys. 91:021001
    [Google Scholar]
  3. 3. 
    Gring M, Kuhnert M, Langen T, Kitagawa T, Rauer B et al. 2012. Science 337:1318
    [Google Scholar]
  4. 4. 
    Schreiber M, Hodgman SS, Bordia P, Lüschen HP, Fischer MH et al. 2015. Science 349:842–45
    [Google Scholar]
  5. 5. 
    Strogatz SH 2019. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (with student solutions manual). Boca Raton: FL: CRC. 2nd Ed
    [Google Scholar]
  6. 6. 
    Wilczek F 2012. Phys. Rev. Lett. 109:160401
    [Google Scholar]
  7. 7. 
    Shapere A, Wilczek F 2012. Phys. Rev. Lett. 109:160402
    [Google Scholar]
  8. 8. 
    Bruno P 2013. Phys. Rev. Lett. 110:118901
    [Google Scholar]
  9. 9. 
    Bruno P 2013. Phys. Rev. Lett. 111:029301
    [Google Scholar]
  10. 10. 
    Bruno P 2013. Phys. Rev. Lett. 111:070402
    [Google Scholar]
  11. 11. 
    Noziéres P 2013. Eur. Phys. Lett. 103:57008
    [Google Scholar]
  12. 12. 
    Watanabe H, Oshikawa M 2015. Phys. Rev. Lett. 114:251603
    [Google Scholar]
  13. 13. 
    Drummond P, McNeil K, Walls D 1980. Opt. Acta: Int. J. Opt. 27:321–35
    [Google Scholar]
  14. 14. 
    Cross MC, Hohenberg PC 1993. Rev. Mod. Phys. 65:851
    [Google Scholar]
  15. 15. 
    Yao NY, Nayak C 2018. Phys. Today 71:40–47
    [Google Scholar]
  16. 16. 
    Else DV, Bauer B, Nayak C 2016. Phys. Rev. Lett. 117:090402
    [Google Scholar]
  17. 17. 
    Else DV, Bauer B, Nayak C 2017. Phys. Rev. X 7:011026
    [Google Scholar]
  18. 18. 
    Khemani V, Lazarides A, Moessner R, Sondhi SL 2016. Phys. Rev. Lett. 116:250401
    [Google Scholar]
  19. 19. 
    Yao NY, Potter AC, Potirniche I-D, Vishwanath A 2017. Phys. Rev. Lett. 118:030401
    [Google Scholar]
  20. 20. 
    D'Alessio L, Rigol M 2014. Phys. Rev. X 4:041048
    [Google Scholar]
  21. 21. 
    Ponte P, Chandran A, Papić Z, Abanin DA 2015. Ann. Phys. 353:196–204
    [Google Scholar]
  22. 22. 
    Lazarides A, Das A, Moessner R 2014. Phys. Rev. E 90:012110
    [Google Scholar]
  23. 23. 
    Basko DM, Aleiner IL, Altshuler BL 2006. Ann. Phys. 321:1126–205
    [Google Scholar]
  24. 24. 
    Basko DM, Aleiner IL, Altshuler BL 2006. Problems of Condensed Matter Physics: Quantum Coherence Phenomena in Electron-Hole and Coupled Matter-Light Systems AL Ivanov, SG Tikhodeev50–69 Oxford, UK: Oxford Univ. Press
    [Google Scholar]
  25. 25. 
    Oganesyan V, Huse DA 2007. Phys. Rev. B 75:155111
    [Google Scholar]
  26. 26. 
    Žnidarič M, Prosen T, Prelovšek P 2008. Phys. Rev. B 77:064426
    [Google Scholar]
  27. 27. 
    Pal A, Huse DA 2010. Phys. Rev. B 82:174411
    [Google Scholar]
  28. 28. 
    Bardarson JH, Pollmann F, Moore JE 2012. Phys. Rev. Lett. 109:017202
    [Google Scholar]
  29. 29. 
    Serbyn M, Papić Z, Abanin DA 2013. Phys. Rev. Lett. 110:260601
    [Google Scholar]
  30. 30. 
    Serbyn M, Papić Z, Abanin DA 2013. Phys. Rev. Lett. 111:127201
    [Google Scholar]
  31. 31. 
    Bauer B, Nayak C 2013. J. Stat. Mech: Theor. Exp. 9:09005
    [Google Scholar]
  32. 32. 
    Huse DA, Nandkishore R, Oganesyan V 2014. Phys. Rev. B 90:174202
    [Google Scholar]
  33. 33. 
    Abanin DA, Roeck WD, Huveneers F 2016. Ann. Phys. 372:5
    [Google Scholar]
  34. 34. 
    Ponte P, Papić Z, Huveneers F, Abanin DA 2015. Phys. Rev. Lett. 114:140401
    [Google Scholar]
  35. 35. 
    Lazarides A, Das A, Moessner R 2015. Phys. Rev. Lett. 115:030402
    [Google Scholar]
  36. 36. 
    Iadecola T, Santos LH, Chamon C 2015. Phys. Rev. B 92:125107
    [Google Scholar]
  37. 37. 
    von Keyserlingk CW, Sondhi SL 2016. Phys. Rev. B 93:245145
    [Google Scholar]
  38. 38. 
    Else DV, Nayak C 2016. Phys. Rev. B 93:201103
    [Google Scholar]
  39. 39. 
    Potter AC, Morimoto T, Vishwanath A 2016. Phys. Rev. X 6:041001
    [Google Scholar]
  40. 40. 
    Roy R, Harper F 2016. Phys. Rev. B 94:125105
    [Google Scholar]
  41. 41. 
    von Keyserlingk CW, Sondhi SL 2016. Phys. Rev. B 93:245146
    [Google Scholar]
  42. 42. 
    Kuwahara T, Mori T, Saito K 2016. Ann. Phys. 367:96–124
    [Google Scholar]
  43. 43. 
    Abanin D, De Roeck W, Ho WW, Huveneers F 2017. Commun. Math. Phys. 354:809–27
    [Google Scholar]
  44. 44. 
    Zhang J, Hess PW, Kyprianidis A, Becker P, Lee A et al. 2017. Nature 543:217–20
    [Google Scholar]
  45. 45. 
    Choi S, Choi J, Landig R, Kucsko G, Zhou H et al. 2017. Nature 543:221–25
    [Google Scholar]
  46. 46. 
    Rovny J, Blum RL, Barrett SE 2018. Phys. Rev. Lett. 120:180603
    [Google Scholar]
  47. 47. 
    Pal S, Nishad N, Mahesh T, Sreejith G 2018. Phys. Rev. Lett. 120:180602
    [Google Scholar]
  48. 48. 
    O'Sullivan J, Lunt O, Zollitsch CW, Thewalt M, Morton JJ, Pal A 2018. arXiv:1807.09884
  49. 49. 
    Ho WW, Choi S, Lukin MD, Abanin DA 2017. Phys. Rev. Lett. 119:010602
    [Google Scholar]
  50. 50. 
    Kucsko G, Choi S, Choi J, Maurer P, Zhou H et al. 2018. Phys. Rev. Lett. 121:023601
    [Google Scholar]
  51. 51. 
    Devoret MH, Wallraff A, Martinis JM 2004. arXiv:cond-mat/0411174
  52. 52. 
    Clarke J, Wilhelm FK 2008. Nature 453:1031
    [Google Scholar]
  53. 53. 
    Barends R, Shabani A, Lamata L, Kelly J, Mezzacapo A et al. 2016. Nature 534:222
    [Google Scholar]
  54. 54. 
    Koppens FH, Buizert C, Tielrooij K-J, Vink IT, Nowack KC et al. 2006. Nature 442:766
    [Google Scholar]
  55. 55. 
    Schirhagl R, Chang K, Loretz M, Degen CL 2014. Annu. Rev. Phys. Chem. 65:83–105
    [Google Scholar]
  56. 56. 
    Doherty MW, Manson NB, Delaney P, Jelezko F, Wrachtrup J, Hollenberg LC 2013. Phys. Rep. 528:1–45
    [Google Scholar]
  57. 57. 
    Koehl WF, Buckley BB, Heremans FJ, Calusine G, Awschalom DD 2011. Nature 479:84
    [Google Scholar]
  58. 58. 
    Harris RK 1986. Nuclear Magnetic Resonance Spectroscopy New York: John Wiley & Sons
    [Google Scholar]
  59. 59. 
    Callaghan PT 1991. Principles of Nuclear Magnetic Resonance Microscopy New York: Oxford Univ. Press
    [Google Scholar]
  60. 60. 
    Vandersypen LM, Steffen M, Breyta G, Yannoni CS, Sherwood MH, Chuang IL 2001. Nature 414:883
    [Google Scholar]
  61. 61. 
    Deutsch JM 1991. Phys. Rev. A 43:2046–49
    [Google Scholar]
  62. 62. 
    Srednicki M 1994. Phys. Rev. E 50:888–901
    [Google Scholar]
  63. 63. 
    Rigol M, Dunjko V, Olshanii M 2008. Nature 452:854–58
    [Google Scholar]
  64. 64. 
    D'Alessio L, Kafri Y, Polkovnikov A, Rigol M 2016. Adv. Phys. 65:239–362
    [Google Scholar]
  65. 65. 
    Huse DA, Nandkishore R, Oganesyan V, Pal A, Sondhi SL 2013. Phys. Rev. B 88:014206
    [Google Scholar]
  66. 66. 
    Bahri Y, Vosk R, Altman E, Vishwanath A 2013. Nat. Commun. 6:7341
    [Google Scholar]
  67. 67. 
    Abanin DA, De Roeck W, Huveneers F 2015. Phys. Rev. Lett. 115:256803
    [Google Scholar]
  68. 68. 
    Kuwahara T, Mori T, Saito K 2016. Ann. Phys. 367:96
    [Google Scholar]
  69. 69. 
    Mori T, Kuwahara T, Saito K 2016. Phys. Rev. Lett. 116:120401
    [Google Scholar]
  70. 70. 
    Bukov M, Gopalakrishnan S, Knap M, Demler E 2015. Phys. Rev. Lett. 115:205301
    [Google Scholar]
  71. 71. 
    Canovi E, Kollar M, Eckstein M 2016. Phys. Rev. E 93:012130
    [Google Scholar]
  72. 72. 
    Bukov M, Heyl M, Huse DA, Polkovnikov A 2016. Phys. Rev. B 93:155132
    [Google Scholar]
  73. 73. 
    Machado F, Meyer GD, Else DV, Nayak C, Yao NY arXiv:1708.01620
  74. 74. 
    Machado F, Else DV, Kahanamoku-Meyer GD, Nayak C, Yao NY 2019. arXiv:1908.07530
  75. 75. 
    Urbina C, Jacquinot J, Goldman M 1982. Phys. Rev. Lett. 48:206–9
    [Google Scholar]
  76. 76. 
    Autti S, Eltsov V, Volovik G 2018. Phys. Rev. Lett. 120:215301
    [Google Scholar]
  77. 77. 
    Kreil AJ, Musiienko-Shmarova HY, Bozhko DA, Pomyalov A, L'vov VS et al. 2018. Phys. Rev. B 100:020406
    [Google Scholar]
  78. 78. 
    Brown SE, Mozurkewich G, Grüner G 1984. Phys. Rev. Lett. 52:2277
    [Google Scholar]
  79. 79. 
    Brown SE, Mozurkewich G, Grüner G 1985. Solid State Commun. 54:23–26
    [Google Scholar]
  80. 80. 
    Tua P, Ruvalds J 1985. Solid State Commun. 54:471–74
    [Google Scholar]
  81. 81. 
    Sherwin M, Zettl A 1985. Phys. Rev. B 32:5536
    [Google Scholar]
  82. 82. 
    Balents L, Fisher MP 1995. Phys. Rev. Lett. 75:4270
    [Google Scholar]
  83. 83. 
    Lee HC, Newrock R, Mast D, Hebboul S, Garland J, Lobb C 1991. Phys. Rev. B 44:921
    [Google Scholar]
  84. 84. 
    Yu W, Harris E, Hebboul S, Garland J, Stroud D 1992. Phys. Rev. B 45:12624
    [Google Scholar]
  85. 85. 
    Yao NY, Nayak C, Balents L, Zaletel MP 2018. arXiv:1801.02628
  86. 86. 
    Berdanier W, Kolodrubetz M, Parameswaran S, Vasseur R 2018. Phys. Rev. B 98:174203
    [Google Scholar]
  87. 87. 
    von Keyserlingk CW, Khemani V, Sondhi SL 2016. Phys. Rev. B 94:085112
    [Google Scholar]
  88. 88. 
    Fratus KR, Srednicki M 2015. Phys. Rev. E 92:040103
    [Google Scholar]
  89. 89. 
    Mondaini R, Fratus KR, Srednicki M, Rigol M 2016. Phys. Rev. E 93:032104
    [Google Scholar]
  90. 90. 
    Fratus KR, Srednicki M 2016. arxiv:1611.03992
  91. 91. 
    Khemani V, von Keyserlingk CW, Sondhi SL 2017. Phys. Rev. B 96:115127
    [Google Scholar]
  92. 92. 
    Yu WC, Tangpanitanon J, Glaetzle AW, Jaksch D, Angelakis DG 2019. Phys. Rev. A 99:033618
    [Google Scholar]
  93. 93. 
    Nalitov A, Sigurdsson H, Morina S, Krivosenko Y, Iorsh I et al. 2019. Phys. Rev. A 99:033830
    [Google Scholar]
  94. 94. 
    Xu H-Z, Zhang S-Y, Lu Y-K, Guo G-C, Gong M 2018. arXiv:1810.08898
  95. 95. 
    Smits J, Liao L, Stoof H, van der Straten P 2018. Phys. Rev. Lett. 121:185301
    [Google Scholar]
  96. 96. 
    Cole DC, Papp SB 2018. arXiv:1811.02523
  97. 97. 
    Surace FM, Russomanno A, Dalmonte M, Silva A, Fazio R, Iemini F 2019. Phys. Rev. B 99:104303
    [Google Scholar]
  98. 98. 
    Öhberg P, Wright EM 2018. arXiv:1812.04672
  99. 99. 
    Liao L, Smits J, van der Straten P, Stoof H 2019. Phys. Rev. A 99:013625
    [Google Scholar]
  100. 100. 
    Oberreiter L, Seifert U, Barato AC 2019. Phys. Rev. E 100:012135
    [Google Scholar]
  101. 101. 
    Efetov KB 2019. arXiv:1902.07520
  102. 102. 
    Dai J, Niemi AJ, Peng X, Wilczek F 2019. Phys. Rev. A 99:023425
    [Google Scholar]
  103. 103. 
    Cai Z, Huang Y, Liu WV 2019. arXiv:1902.09747
  104. 104. 
    Gambetta F, Carollo F, Lazarides A, Lesanovsky I, Garrahan J 2019. arXiv:1905.08826
  105. 105. 
    Lazarides A, Roy S, Piazza F, Moessner R 2019. arXiv:1904.04820
  106. 106. 
    Zhu B, Marino J, Yao NY, Lukin MD, Demler EA 2019. New J. Phys 21:073028
    [Google Scholar]
  107. 107. 
    Nicolis A, Piazza F 2012. J. High Energy Phys. 2012:25
    [Google Scholar]
  108. 108. 
    Castillo E, Koch B, Palma G 2014. arXiv:1410.2261
  109. 109. 
    Thies M 2014. arXiv:1411.4236
  110. 110. 
    Volovik GE 2013. JETP Lett. 98:491
    [Google Scholar]
  111. 111. 
    Sacha K 2015. Phys. Rev. A 91:033617
    [Google Scholar]
  112. 112. 
    Mizuta K, Takasan K, Nakagawa M, Kawakami N 2018. Phys. Rev. Lett. 121:093001
    [Google Scholar]
  113. 113. 
    Matus P, Sacha K 2019. Phys. Rev. A 99:033626
    [Google Scholar]
  114. 114. 
    Pethick CJ, Smith H 2008. Bose–Einstein Condensation in Dilute Gases Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  115. 115. 
    Chandran A, Sondhi SL 2016. Phys. Rev. B 93:174305
    [Google Scholar]
  116. 116. 
    Russomanno A, Iemini F, Dalmonte M, Fazio R 2017. Phys. Rev. B 95:214307
    [Google Scholar]
  117. 117. 
    Barnes E, Nichol JM, Economou SE 2019. Phys. Rev. B 99:035311
    [Google Scholar]
  118. 118. 
    Barfknecht R, Rasmussen S, Foerster A, Zinner N 2019. Phys. Rev. B 99:144304
    [Google Scholar]
  119. 119. 
    Gong Z, Hamazaki R, Ueda M 2018. Phys. Rev. Lett. 120:040404
    [Google Scholar]
  120. 120. 
    Dicke RH 1954. Phys. Rev. 93:99
    [Google Scholar]
  121. 121. 
    Tucker K, Zhu B, Lewis-Swan R, Marino J, Jimenez F et al. 2018. New J. Phys. 20:123003
    [Google Scholar]
  122. 122. 
    Gambetta F, Carollo F, Marcuzzi M, Garrahan J, Lesanovsky I 2019. Phys. Rev. Lett. 122:015701
    [Google Scholar]
  123. 123. 
    Lledó C, Mavrogordatos T, Szymańska M 2019. Phys. Rev. B 100:054303
    [Google Scholar]
  124. 124. 
    Droenner L, Finsterhölzl R, Heyl M, Carmele A 2019. arXiv:1902.04986
  125. 125. 
    Leggett AJ, Chakravarty S, Dorsey AT, Fisher MPA, Garg A, Zwerger W 1987. Rev. Mod. Phys. 59:1–85
    [Google Scholar]
  126. 126. 
    Gács P 2001. J. Stat. Phys. 103:45–267
    [Google Scholar]
  127. 127. 
    Choi J, Zhou H, Choi S, Landig R, Ho WW et al. 2019. Phys. Rev. Lett. 122:043603
    [Google Scholar]
  128. 128. 
    Yao NY, Laumann CR, Gopalakrishnan S, Knap M, Mueller M et al. 2014. Phys. Rev. Lett. 113:243002
    [Google Scholar]
  129. 129. 
    Islam R, Edwards E, Kim K, Korenblit S, Noh C et al. 2011. Nat. Commun. 2:377–84
    [Google Scholar]
  130. 130. 
    Bohnet JG, Sawyer BC, Britton JW, Wall ML, Rey AM et al. 2016. Science 352:1297–301
    [Google Scholar]
  131. 131. 
    Leibfried D, Blatt R, Monroe C, Wineland D 2003. Rev. Mod. Phys. 75:281–324
    [Google Scholar]
  132. 132. 
    Porras D, Cirac JI 2004. Phys. Rev. Lett. 92:207901
    [Google Scholar]
  133. 133. 
    Smith J, Lee A, Richerme P, Neyenhuis B, Hess PW et al. 2016. Nat. Phys. 12:907–11
    [Google Scholar]
  134. 134. 
    Korenblit S, Kafri D, Campbell WC, Islam R, Edwards EE et al. 2012. New J. Phys. 14:095024
    [Google Scholar]
  135. 135. 
    Deng X-L, Porras D, Cirac JI 2005. Phys. Rev. A 72:063407
    [Google Scholar]
  136. 136. 
    Taylor JM, Calarco T 2008. Phys. Rev. A 78:062331
    [Google Scholar]
  137. 137. 
    Islam R, Senko C, Campbell W, Korenblit S, Smith J et al. 2013. Science 340:583–87
    [Google Scholar]
  138. 138. 
    Khemani V, Moessner R, Sondhi SL 2019. arXiv:1910.10745
  139. 139. 
    Doherty MW, Manson NB, Delaney P, Jelezko F, Wrachtrup J, Hollenberg LC 2013. Phys. Rep. 528:1–45
    [Google Scholar]
  140. 140. 
    Nandkishore RM, Sondhi SL 2017. Phys. Rev. X 7:041021
    [Google Scholar]
  141. 141. 
    Rovny J, Blum RL, Barrett SE 2018. Phys. Rev. B 97:184301
    [Google Scholar]
  142. 142. 
    Luitz DJ, Moessner R, Sondhi SL, Khemani V 2019. arXiv:1908.10371
  143. 143. 
    Else DV, Ho WW, Dumitrescu PT 2019. arXiv:1910.03584
  144. 144. 
    Dumitrescu PT, Vasseur R, Potter AC 2018. Phys. Rev. Lett. 120:070602
    [Google Scholar]
  145. 145. 
    Po HC, Fidkowski L, Morimoto T, Potter AC, Vishwanath A 2017. Phys. Rev. X 6:041070
    [Google Scholar]
  146. 146. 
    Harper F, Roy R 2017. Phys. Rev. Lett. 118:115301
    [Google Scholar]
  147. 147. 
    Roy R, Harper F 2017. Phys. Rev. B 95:195128
    [Google Scholar]
  148. 148. 
    Po HC, Fidkowski L, Vishwanath A, Potter AC 2017. Phys. Rev. B 96:245116
    [Google Scholar]
  149. 149. 
    Potirniche I-D, Potter AC, Schleier-Smith M, Vishwanath A, Yao NY 2017. Phys. Rev. Lett. 119:123601
    [Google Scholar]
  150. 150. 
    Haah J, Fidkowski L, Hastings MB arXiv:1812.01625
  151. 151. 
    Else DV 2018. Time crystals and space crystals: strongly correlated phases of matter with space-time symmetries PhD Thesis, Univ. Calif., Santa Barbara
    [Google Scholar]
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