1932

Abstract

In Floquet engineering, periodic driving is used to realize novel phases of matter that are inaccessible in thermal equilibrium. For this purpose, the Floquet theory provides us a recipe for obtaining a static effective Hamiltonian. Although many existing works have treated closed systems, it is important to consider the effect of dissipation, which is ubiquitous in nature. Understanding the interplay of periodic driving and dissipation is a fundamental problem of nonequilibrium statistical physics that is receiving growing interest because of the fact that experimental advances have allowed us to engineer dissipation in a controllable manner. In this review, we give a detailed exposition on the formalism of quantum master equations for open Floquet systems and highlight recent work investigating whether equilibrium statistical mechanics applies to Floquet states.

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2023-03-10
2024-06-18
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Literature Cited

  1. 1.
    Kubo R. 1957. J. Phys. Soc. Jpn. 12:6570–86
    [Google Scholar]
  2. 2.
    Evans DJ, Cohen EG, Morriss GP. 1993. Phys. Rev. Lett. 71:2401–4
    [Google Scholar]
  3. 3.
    Gallavotti G, Cohen EG. 1995. Phys. Rev. Lett. 74:2694–97
    [Google Scholar]
  4. 4.
    Jarzynski C. 1997. Phys. Rev. Lett. 78:2690–93
    [Google Scholar]
  5. 5.
    Bukov M, D'Alessio L, Polkovnikov A 2015. Adv. Phys. 64:2139–226
    [Google Scholar]
  6. 6.
    Eckardt A. 2017. Rev. Mod. Phys. 89:011004
    [Google Scholar]
  7. 7.
    Mori T, Kuwahara T, Saito K. 2016. Phys. Rev. Lett. 116:12120401
    [Google Scholar]
  8. 8.
    Kuwahara T, Mori T, Saito K. 2016. Ann. Phys. (N. Y.) 367:96–124
    [Google Scholar]
  9. 9.
    Abanin D, De Roeck W, Ho WW, Huveneers F. 2017. Commun. Math. Phys. 354:3809–27
    [Google Scholar]
  10. 10.
    Abanin DA, De Roeck W, Ho WW, Huveneers F. 2017. Phys. Rev. B 95:014112
    [Google Scholar]
  11. 11.
    Oka T, Kitamura S. 2019. Annu. Rev. Condens. Matter Phys. 10:387–408
    [Google Scholar]
  12. 12.
    Eckardt A, Weiss C, Holthaus M. 2005. Phys. Rev. Lett. 95:260404
    [Google Scholar]
  13. 13.
    Zenesini A, Lignier H, Ciampini D, Morsch O, Arimondo E. 2009. Phys. Rev. Lett. 102:10100403
    [Google Scholar]
  14. 14.
    Bastidas VM, Emary C, Regler B, Brandes T. 2012. Phys. Rev. Lett. 108:043003
    [Google Scholar]
  15. 15.
    Oka T, Aoki H. 2009. Phys. Rev. B 79:081406
    [Google Scholar]
  16. 16.
    Kitagawa T, Berg E, Rudner M, Demler E. 2010. Phys. Rev. B 82:235114
    [Google Scholar]
  17. 17.
    Lindner NH, Refael G, Galitski V. 2011. Nat. Phys. 7:490–95
    [Google Scholar]
  18. 18.
    Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T et al. 2014. Nature 515:237–40
    [Google Scholar]
  19. 19.
    Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro JT et al. 2015. Nat. Phys. 11:162–66
    [Google Scholar]
  20. 20.
    Aidelsburger M, Atala M, Nascimbène S, Trotzky S, Chen YA, Bloch I. 2011. Phys. Rev. Lett. 107:255301
    [Google Scholar]
  21. 21.
    Struck J, Olschläger C, Weinberg M, Hauke P, Simonet J et al. 2012. Phys. Rev. Lett. 108:225304
    [Google Scholar]
  22. 22.
    Bermudez A, Schaetz T, Porras D. 2011. Phys. Rev. Lett. 107:150501
    [Google Scholar]
  23. 23.
    Else DV, Bauer B, Nayak C. 2016. Phys. Rev. Lett. 117:090402
    [Google Scholar]
  24. 24.
    Else DV, Bauer B, Nayak C. 2017. Phys. Rev. X 7:011026
    [Google Scholar]
  25. 25.
    Yao NY, Potter AC, Potirniche ID, Vishwanath A. 2017. Phys. Rev. Lett. 118:030401
    [Google Scholar]
  26. 26.
    Tsuji N, Oka T, Aoki H. 2008. Phys. Rev. B 78:23235124
    [Google Scholar]
  27. 27.
    Tsuji N, Oka T, Aoki H. 2009. Phys. Rev. Lett. 103:047403
    [Google Scholar]
  28. 28.
    Dehghani H, Oka T, Mitra A 2014. Phys. Rev. B 90:195429
    [Google Scholar]
  29. 29.
    Dehghani H, Oka T, Mitra A 2015. Phys. Rev. B 91:155422
    [Google Scholar]
  30. 30.
    Seetharam KI, Bardyn CE, Lindner NH, Rudner MS, Refael G. 2015. Phys. Rev. X 5:041050
    [Google Scholar]
  31. 31.
    Iadecola T, Neupert T, Chamon C. 2015. Phys. Rev. B 91:235133
    [Google Scholar]
  32. 32.
    Murakami Y, Tsuji N, Eckstein M, Werner P. 2017. Phys. Rev. B 96:045125
    [Google Scholar]
  33. 33.
    McIver JW, Schulte B, Stein FU, Matsuyama T, Jotzu G et al. 2020. Nat. Phys. 16:38–41
    [Google Scholar]
  34. 34.
    Sato SA, McIver JW, Nuske M, Tang P, Jotzu G et al. 2019. Phys. Rev. B 99:214302
    [Google Scholar]
  35. 35.
    Drummond PD, Walls DF. 1980. J. Phys. A 13:725–41
    [Google Scholar]
  36. 36.
    Baumann K, Guerlin C, Brennecke F, Esslinger T. 2010. Nature 464:1301–6
    [Google Scholar]
  37. 37.
    Torre EG, Diehl S, Lukin MD, Sachdev S, Strack P. 2013. Phys. Rev. A 87: 023831.
    [Google Scholar]
  38. 38.
    Shirai T, Mori T, Miyashita S. 2014. J. Phys. B 47:025501
    [Google Scholar]
  39. 39.
    Foss-Feig M, Niroula P, Young JT, Hafezi M, Gorshkov AV et al. 2017. Phys. Rev. A 95:043826
    [Google Scholar]
  40. 40.
    Diehl S, Micheli A, Kantian A, Kraus B, Büchler HP, Zoller P. 2008. Nat. Phys. 4:878–83
    [Google Scholar]
  41. 41.
    Diehl S, Rico E, Baranov MA, Zoller P. 2011. Nat. Phys. 7:971–77
    [Google Scholar]
  42. 42.
    Vorberg D, Wustmann W, Ketzmerick R, Eckardt A. 2013. Phys. Rev. Lett. 111:240405
    [Google Scholar]
  43. 43.
    Vorberg D, Wustmann W, Schomerus H, Ketzmerick R, Eckardt A. 2015. Phys. Rev. E 92:062119
    [Google Scholar]
  44. 44.
    Schnell A, Ketzmerick R, Eckardt A. 2018. Phys. Rev. E 97:032136
    [Google Scholar]
  45. 45.
    Barreiro JT, Müller M, Schindler P, Nigg D, Monz T et al. 2011. Nature 470:7335486–91
    [Google Scholar]
  46. 46.
    Barontini G, Labouvie R, Stubenrauch F, Vogler A, Guarrera V, Ott H. 2013. Phys. Rev. Lett. 110:3035302
    [Google Scholar]
  47. 47.
    Tomita T, Nakajima S, Danshita I, Takasu Y, Takahashi Y. 2017. Sci. Adv. 3:12e1701513
    [Google Scholar]
  48. 48.
    Breuer HP, Holthaus M. 1991. Ann. Phys. (N. Y). 211:249–91
    [Google Scholar]
  49. 49.
    Breuer HP, Huber W, Petruccione F. 2000. Phys. Rev. E 61:4883–89
    [Google Scholar]
  50. 50.
    Kohn W. 2001. J. Stat. Phys. 103:417–23
    [Google Scholar]
  51. 51.
    Hone DW, Ketzmerick R, Kohn W. 2009. Phys. Rev. E 79:051129
    [Google Scholar]
  52. 52.
    Ketzmerick R, Wustmann W. 2010. Phys. Rev. E 82:021114
    [Google Scholar]
  53. 53.
    Liu DE. 2015. Phys. Rev. B 91:144301
    [Google Scholar]
  54. 54.
    Shirai T, Mori T, Miyashita S. 2015. Phys. Rev. E 91:030101
    [Google Scholar]
  55. 55.
    Shirai T, Thingna J, Mori T, Denisov S, Hänggi P, Miyashita S. 2016. New J. Phys. 18:1–13
    [Google Scholar]
  56. 56.
    Mikami T, Kitamura S, Yasuda K, Tsuji N, Oka T, Aoki H. 2016. Phys. Rev. B 93:144307
    [Google Scholar]
  57. 57.
    Blanes S, Casas F, Oteo JA, Ros J 2009. Phys. Rep. 470:151–238
    [Google Scholar]
  58. 58.
    Rahav S, Gilary I, Fishman S. 2003. Phys. Rev. A 68:013820
    [Google Scholar]
  59. 59.
    Goldman N, Dalibard J. 2014. Phys. Rev. X 4:031027
    [Google Scholar]
  60. 60.
    Eckardt A, Anisimovas E. 2015. New J. Phys. 17:9093039
    [Google Scholar]
  61. 61.
    Dunlap DH, Kenkre VM. 1986. Phys. Rev. B 34:3625–33
    [Google Scholar]
  62. 62.
    Grossmann F, Dittrich T, Jung P, Hänggi P 1991. Phys. Rev. Lett. 67:516–19
    [Google Scholar]
  63. 63.
    Lignier H, Sias C, Ciampini D, Singh Y, Zenesini A et al. 2007. Phys. Rev. Lett. 99:220403
    [Google Scholar]
  64. 64.
    Eckardt A, Holthaus M. 2007. Europhys. Lett. 80:50004
    [Google Scholar]
  65. 65.
    Goldman N, Dalibard J, Aidelsburger M, Cooper NR. 2015. Phys. Rev. A 91:033632
    [Google Scholar]
  66. 66.
    D'Alessio L, Rigol M 2014. Phys. Rev. X 4:041048
    [Google Scholar]
  67. 67.
    Lazarides A, Das A, Moessner R. 2014. Phys. Rev. E 90:012110
    [Google Scholar]
  68. 68.
    Kim H, Ikeda TN, Huse DA. 2014. Phys. Rev. E 90:5052105
    [Google Scholar]
  69. 69.
    Mori T, Ikeda TN, Kaminishi E, Ueda M. 2018. J. Phys. B 51:112001
    [Google Scholar]
  70. 70.
    Das A. 2010. Phys. Rev. B 82:172402
    [Google Scholar]
  71. 71.
    Haldar A, Moessner R, Das A. 2018. Phys. Rev. B 97:245122
    [Google Scholar]
  72. 72.
    Haldar A, Sen D, Moessner R, Das A. 2021. Phys. Rev. X 11:021008
    [Google Scholar]
  73. 73.
    Mori T. 2018. Phys. Rev. B 98:10104303
    [Google Scholar]
  74. 74.
    Rajak A, Citro R, Dalla Torre EG 2018. J. Phys. A 51:465001
    [Google Scholar]
  75. 75.
    Rajak A, Dana I, Dalla Torre EG 2019. Phys. Rev. B 100:100302(R)
    [Google Scholar]
  76. 76.
    Hodson W, Jarzynski C. 2021. Phys. Rev. Res. 3:013219
    [Google Scholar]
  77. 77.
    Bukov M, Gopalakrishnan S, Knap M, Demler E. 2015. Phys. Rev. Lett. 115:205301
    [Google Scholar]
  78. 78.
    Dalla Torre EG, Dentelski D 2021. SciPost Phys. 11:040
    [Google Scholar]
  79. 79.
    Rubio-Abadal A, Ippoliti M, Hollerith S, Wei D, Rui J et al. 2020. Phys. Rev. X 10:2021044
    [Google Scholar]
  80. 80.
    Peng P, Yin C, Huang X, Ramanathan C, Cappellaro P. 2021. Nat. Phys. 17:444
    [Google Scholar]
  81. 81.
    Mori T. 2022. Phys. Rev. Lett. 128:050604
    [Google Scholar]
  82. 82.
    Breuer HP, Petruccione F. 2002. The Theory of Open Quantum Systems Oxford, MA: Oxford Univ. Press
    [Google Scholar]
  83. 83.
    Redfield AG. 1957. IBM J. Res. Dev. 1:19–31
    [Google Scholar]
  84. 84.
    Lindblad G. 1976. Commun. Math. Phys. 48:119–30
    [Google Scholar]
  85. 85.
    Gorini V, Kossakowski A, Sudarshan ECG. 1976. J. Math. Phys. 17:821–25
    [Google Scholar]
  86. 86.
    van Kampen NG. 1992. Stochastic Processes in Physics and Chemistry Amsterdam: Elsevier
    [Google Scholar]
  87. 87.
    Kohler S, Dittrich T, Hänggi P. 1997. Phys. Rev. E 55:300–13
    [Google Scholar]
  88. 88.
    Mori T. 2014. Phys. Rev. A 89:040101
    [Google Scholar]
  89. 89.
    Mori T, Miyashita S. 2008. J. Phys. Soc. Jpn. 77:1–9
    [Google Scholar]
  90. 90.
    Suárez A, Silbey R, Oppenheim I. 1992. J. Chem. Phys. 97:5101–7
    [Google Scholar]
  91. 91.
    Gaspard P, Nagaoka M. 1999. J. Chem. Phys. 111:5668–75
    [Google Scholar]
  92. 92.
    Kohler S, Utermann R, Hänggi P, Dittrich T. 1998. Phys. Rev. E 58:7219–30
    [Google Scholar]
  93. 93.
    Van Hove L. 1957. Physica 23:441–80
    [Google Scholar]
  94. 94.
    Spohn H. 1980. Rev. Mod. Phys. 52:569–615
    [Google Scholar]
  95. 95.
    Tindall J, Buča B, Coulthard JR, Jaksch D. 2019. Phys. Rev. Lett. 123:030603
    [Google Scholar]
  96. 96.
    Prosen T. 2011. Phys. Rev. Lett. 106:217206
    [Google Scholar]
  97. 97.
    Žnidarič M. 2015. Phys. Rev. E 92:4042143
    [Google Scholar]
  98. 98.
    Sponselee K, Freystatzky L, Abeln B, Diem M, Hundt B et al. 2018. Quantum Sci. Technol. 4:14002
    [Google Scholar]
  99. 99.
    Shirai T, Mori T, Miyashita S. 2018. Eur. Phys. J. Spec. Top. 227:323–33
    [Google Scholar]
  100. 100.
    Shirai T, Mori T. 2020. Phys. Rev. E 101:042116
    [Google Scholar]
  101. 101.
    Iadecola T, Chamon C. 2015. Phys. Rev. B 91:184301
    [Google Scholar]
  102. 102.
    Iwahori K, Kawakami N. 2016. Phys. Rev. B 94:184304
    [Google Scholar]
  103. 103.
    Haddadfarshi F, Cui J, Mintert F. 2015. Phys. Rev. Lett. 114:130402
    [Google Scholar]
  104. 104.
    Dai CM, Shi ZC, Yi XX. 2016. Phys. Rev. A 93:032121
    [Google Scholar]
  105. 105.
    Hartmann M, Poletti D, Ivanchenko M, Denisov S, Hänggi P. 2017. New J. Phys. 19:083011
    [Google Scholar]
  106. 106.
    Schnell A, Eckardt A, Denisov S. 2020. Phys. Rev. B 101:100301
    [Google Scholar]
  107. 107.
    Mizuta K, Takasan K, Kawakami N. 2021. Phys. Rev. A 103:L020202
    [Google Scholar]
  108. 108.
    Schnell A, Denisov S, Eckardt A. 2021. Phys. Rev. B 104:165414
    [Google Scholar]
  109. 109.
    Ikeda T, Chinzei K, Sato M. 2021. SciPost Phys. Core 4:033
    [Google Scholar]
  110. 110.
    Wolf MM, Eisert J, Cubitt TS, Cirac JI. 2008. Phys. Rev. Lett. 101:150402
    [Google Scholar]
  111. 111.
    Li Y, Chen X, Fisher MP 2018. Phys. Rev. B 98:205136
    [Google Scholar]
  112. 112.
    Chan A, Nandkishore RM, Pretko M, Smith G. 2019. Phys. Rev. B 99:224307
    [Google Scholar]
  113. 113.
    Skinner B, Ruhman J, Nahum A 2019. Phys. Rev. X 9:031009
    [Google Scholar]
  114. 114.
    Li Y, Chen X, Fisher MP 2019. Phys. Rev. B 100:134306
    [Google Scholar]
  115. 115.
    Cao X, Tilloy A, de Luca A. 2019. SciPost Phys. 7:024
    [Google Scholar]
  116. 116.
    Bao Y, Choi S, Altman E 2020. Phys. Rev. B 101:104301
    [Google Scholar]
  117. 117.
    Gullans MJ, Huse DA. 2020. Phys. Rev. X 10:041020
    [Google Scholar]
  118. 118.
    Fuji Y, Ashida Y. 2020. Phys. Rev. B 102:054302
    [Google Scholar]
  119. 119.
    Ippoliti M, Gullans MJ, Gopalakrishnan S, Huse DA, Khemani V. 2021. Phys. Rev. X 11:011030
    [Google Scholar]
  120. 120.
    Alberton O, Buchhold M, Diehl S. 2021. Phys. Rev. Lett. 126:170602
    [Google Scholar]
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