| ATOMIC AND MOLECULAR PHYSICS |
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Dynamics of Quantum State and Effective Hamiltonian with Vector Differential Form of Motion Method |
| Long Xiong1, Wei-Feng Zhuang1, and Ming Gong1,2* |
1CAS Key Lab of Quantum Information, School of Physics, University of Science and Technology of China, Hefei 230026, China
2Synergetic Innovation Center of Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei 230026, China
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| Cite this article: |
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Long Xiong, Wei-Feng Zhuang, and Ming Gong 2022 Chin. Phys. Lett. 39 073101 |
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Abstract Effective Hamiltonians in periodically driven systems have received widespread attention for realization of novel quantum phases, non-equilibrium phase transition, and Majorana mode. Recently, the study of effective Hamiltonian using various methods has gained great interest. We consider a vector differential equation of motion to derive the effective Hamiltonian for any periodically driven two-level system, and the dynamics of the spin vector are an evolution under the Bloch sphere. Here, we investigate the properties of this equation and show that a sudden change of the effective Hamiltonian is expected. Furthermore, we present several exact relations, whose expressions are independent of the different starting points. Moreover, we deduce the effective Hamiltonian from the high-frequency limit, which approximately equals the results in previous studies. Our results show that the vector differential equation of motion is not affected by a convergence problem, and thus, can be used to numerically investigate the effective models in any periodic modulating system. Finally, we anticipate that the proposed method can be applied to experimental platforms that require time-periodic modulation, such as ultracold atoms and optical lattices.
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Received: 08 April 2022
Published: 29 June 2022
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| PACS: |
31.30.jy
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(Higher-order effective Hamiltonians)
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71.10.Fd
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(Lattice fermion models (Hubbard model, etc.))
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02.60.Lj
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(Ordinary and partial differential equations; boundary value problems)
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64.60.-i
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(General studies of phase transitions)
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| [1] | Hauke P, Lewenstein M, and Eckardt A 2014 Phys. Rev. Lett. 113 045303 |
| [2] | Miyake H, Siviloglou G A, Kennedy C J, Burton W C, and Ketterle W 2013 Phys. Rev. Lett. 111 185302 |
| [3] | Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B, and Bloch I 2013 Phys. Rev. Lett. 111 185301 |
| [4] | Zheng W and Zhai H 2014 Phys. Rev. A 89 061603 |
| [5] | Zhang S L and Zhou Q 2014 Phys. Rev. A 90 051601 |
| [6] | Mei F, You J B, Zhang D W, Yang X C, Fazio R, Zhu S L, and Kwek L C 2014 Phys. Rev. A 90 063638 |
| [7] | Gómez-León A and Platero G 2013 Phys. Rev. Lett. 110 200403 |
| [8] | Fläschner N, Rem B, Tarnowski M, Vogel D, Lühmann D S, Sengstock K, and Weitenberg C 2016 Science 352 1091 |
| [9] | Verdeny A and Mintert F 2015 Phys. Rev. A 92 063615 |
| [10] | Xiong T S, Gong J, and An J H 2016 Phys. Rev. B 93 184306 |
| [11] | Rechtsman M C, Zeuner J M, Plotnik Y, Lumer Y, Podolsky D, Dreisow F, Nolte S, Segev M, and Szameit A 2013 Nature 496 196 |
| [12] | Lindner N H, Refael G, and Galitski V 2011 Nat. Phys. 7 490 |
| [13] | Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T, Nascimbene S, Cooper N, Bloch I, and Goldman N 2015 Nat. Phys. 11 162 |
| [14] | Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D, and Esslinger T 2014 Nature 515 237 |
| [15] | Galitski V and Spielman I B 2013 Nature 494 49 |
| [16] | Zhang W and Yi W 2013 Nat. Commun. 4 2711 |
| [17] | Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J, and Pan J W 2016 Science 354 83 |
| [18] | Kinoshita T, Wenger T, and Weiss D S 2006 Nature 440 900 |
| [19] | Schreiber M, Hodgman S S, Bordia P, Lüschen H P, Fischer M H, Vosk R, Altman E, Schneider U, and Bloch I 2015 Science 349 842 |
| [20] | Baumann K, Guerlin C, Brennecke F, and Esslinger T 2010 Nature 464 1301 |
| [21] | Deng S, Shi Z Y, Diao P, Yu Q, Zhai H, Qi R, and Wu H 2016 Science 353 371 |
| [22] | Kaufman A M, Tai M E, Lukin A, Rispoli M, Schittko R, Preiss P M, and Greiner M 2016 Science 353 794 |
| [23] | Russomanno A, Iemini F, Dalmonte M, and Fazio R 2017 Phys. Rev. B 95 214307 |
| [24] | Moessner R and Sondhi S 2017 Nat. Phys. 13 424 |
| [25] | Zhang J, Hess P, Kyprianidis A et al. 2017 Nature 543 217 |
| [26] | Else D V, Bauer B, and Nayak C 2016 Phys. Rev. Lett. 117 090402 |
| [27] | Yao N Y, Potter A C, Potirniche I D, and Vishwanath A 2017 Phys. Rev. Lett. 118 030401 |
| [28] | Blanes S, Casas F, Oteo J A, and Ros J 2009 Phys. Rep. 470 151 |
| [29] | Lefebvre R 1999 Int. J. Quantum Chem. 72 261 |
| [30] | Eckardt A and Anisimovas E 2015 New J. Phys. 17 093039 |
| [31] | Faisal F H M and Kamiński J Z 1997 Phys. Rev. A 56 748 |
| [32] | Bukov M, D'Alessio L, and Polkovnikov A 2015 Adv. Phys. 64 139 |
| [33] | Itin A P and Katsnelson M I 2015 Phys. Rev. Lett. 115 075301 |
| [34] | Hemmerich A 2010 Phys. Rev. A 81 063626 |
| [35] | Wells J, Simbotin I, and Gavrila M 1997 Phys. Rev. A 56 3961 |
| [36] | Casas F, Oteo J, and Ros J 2001 J. Phys. A 34 3379 |
| [37] | Mananga E S 2017 J. Phys. Chem. A 121 6063 |
| [38] | Rahav S, Gilary I, and Fishman S 2003 Phys. Rev. A 68 013820 |
| [39] | Kundu A, Fertig H, and Seradjeh B 2014 Phys. Rev. Lett. 113 236803 |
| [40] | Goldman N and Dalibard J 2014 Phys. Rev. X 4 031027 |
| [41] | Ramesh R and Krishnan M S 2001 J. Chem. Phys. 114 5967 |
| [42] | Zhao X G 1994 Phys. Rev. B 49 16753 |
| [43] | Angelo R M and Wreszinski W F 2005 Phys. Rev. A 72 034105 |
| [44] | Barata J A C A and Cortez D A 2002 Phys. Lett. A 301 350 |
| [45] | Gentile G 2003 Commun. Math. Phys. 242 221 |
| [46] | Blekher P, Jauslin H, and Lebowitz J 1992 J. Stat. Phys. 68 271 |
| [47] | Scott W R 2012 Group Theory (Massachusetts: Courier) |
| [48] | Zel'Dovich Y B 1967 Sov. Phys.-JETP 24 1006 |
| [49] | Ritus V 1967 Sov. Phys.-JETP 24 1041 |
| [50] | Shirley J H 1965 Phys. Rev. 138 B979 |
| [51] | Moskalets M and Büttiker M 2002 Phys. Rev. B 66 205320 |
| [52] | Gammaitoni L, Hänggi P, Jung P, and Marchesoni F 1998 Rev. Mod. Phys. 70 223 |
| [53] | Barone S R, Narcowich M A, and Narcowich F J 1977 Phys. Rev. A 15 1109 |
| [54] | Simmendinger C, Wunderlin A, and Pelster A 1999 Phys. Rev. E 59 5344 |
| [55] | Dai C, Shi Z, and Yi X 2016 Phys. Rev. A 93 032121 |
| [56] | Traversa F L, Di Ventra M, and Bonani F 2013 Phys. Rev. Lett. 110 170602 |
| [57] | Sambe H 1973 Phys. Rev. A 7 2203 |
| [58] | Lazarides A, Das A, and Moessner R 2014 Phys. Rev. Lett. 112 150401 |
| [59] | Tong Q J, An J H, Gong J, Luo H G, and Oh C 2013 Phys. Rev. B 87 201109 |
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