-
In recent years, there have been intensive studies on non-Hermitian physics and parity-time (PT) symmetry, due to their fundamental importance in theory and outstanding applications. A distinctive character in PT-symmetric systems is phase transition (spontaneous PT-symmetry breaking), where the energy spectrum changes from all real to complex when the non-Hermitian parameter exceeds a certain threshold. However, the conditions for PT-symmetric system with real energy spectrum to occur are rather restrictive. Generalization of PT-symmetric potentials to wider classes of non-PT-symmetric complex potentials with all-real spectra is a currently important endeavor. The simple PT-symmetric two-level Floquet quantum system is now being actively explored, because it holds potential for realization of non-unitary single-qubit quantum gate. However, studies on the evolution dynamics of non-PT-symmetric two-level non-Hermitian Floquet quantum system still remain relatively rare.
In this paper, we investigate the non-Hermitian physics of a periodically driven non-PT-symmetric two-level quantum system. By phase-space analysis, we find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions with fixed population difference and a time-dependent relative phase between the two levels. Based on these pseudo fixed points, we analytically construct the non-unitary evolution operator and then explore the dynamics of the non-PT-symmetric two-level quantum system in different parameter regions. We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system, although being non-parity-time-symmetric, still features a phase transition with the quasienergy spectrum changing from all real to complex, just as for PT symmetric systems. Furthermore, we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process. The quasi-PT symmetric dynamics is so named in our paper, in the sense that the time-evolution of population probabilities in the non-PT-symmetric two-level system respects fully the time-space symmetry (PT symmetry), while time-evolution of the quantum state (containing the phase) does not, due to the fact that time-evolution of the phases of the probability amplitudes on the two levels violates the PT symmetry requirement.-
Keywords:
- Parity-Time symmetry /
- periodically driven two-level systems /
- non-Hermitian physics /
- dynamical evolution
-
[1] Bender C M, Boettcher S 1998 Phys. Rev. Lett. 80 5243
[2] Guo A, Salamo G J, Duchesne D, Morandotti R, Volatier-Ravat M, Aimez V,Siviloglou G A, Christodoulides D N 2009 Phys. Rev. Lett. 103 093902
[3] Rüter C E, Makris K G, El-Ganainy R, Christodoulides D N, Segev M, Kip D 2010 Nat. Phys. 6 192
[4] Doppler J, Mailybaev A A, Böhm J, Kuhl U, Girschik A, Libisch F, Milburn T J, Rabl P, Moiseyev N, Rotter S 2016 Nature (London)537 76
[5] Peng B, Özdemir Ş K, Lei F, Monifi F, Gianfreda M, Long G Lu, Fan S, Nori F, Bender C M, Yang L 2014 Nat. Phys. 10 394
[6] Chang L, Jiang X, Hua S, Yang C, Wen J, Jiang L, Li G, Wang G, Xiao M 2014 Nat. Photonics 8 524
[7] Bender C M, Berntson B K, Parker D, Samuel E 2013 Am. J. Phys. 81 173
[8] Schindler J, Li A, Zheng M C, Ellis F M, Kottos T 2011 Phys. Rev. A 84 040101(R)
[9] Fleury R, Sounas D, Alù A, Nat. Commun. 2015 6 5905
[10] Liu T, Zhu X, Chen F, Liang S, Zhu J 2018 Phys. Rev. Lett. 120 124502
[11] Tang J S, Wang Y T, Yu S, He D Y, Xu J S, Liu B H, Chen G, Sun Y N, Sun K, Han Y J, Li C F, Guo G C 2016 Nat. Photonics 10 642
[12] Xiao L, Zhan X, Bian Z H, Wang K K, Zhang X, Wang X P, Li J, Mochizuki K, Kim D, Kawakami N, Yi W, Obuse H, Sanders B C, Xue P 2017 Nat. Phys. 13 1117
[13] Gao W C, Zheng C, Liu L, Wang T J, Wang C 2021 Optics Express 29 517
[14] Li J, Harter A K, Liu J, Melo L de, Joglekar Y N, Luo L 2019 Nat. Com. 10 855
[15] Zhang D K, Luo X Q, Wang Y P, Li T F, You J Q 2017 Nat.Com. 8 1368
[16] Wu Y, Liu W, Geng J, Song X, Ye X, Duan C K, Rong X, Dun J 2019 Science 364 878
[17] Zheng C, Hao L, Long G L 2013 Philos. Trans. R. Soc., A 371 20120053
[18] Wen J, Zheng C, Kong X, Wei S, Xin T, Long G 2019 Phys. Rev. A 99 062122
[19] Wang W C, Zhou Y L, Zhang H L, Zhang J, Zhang M C, Xie Y, Wu C W, Chen T, Ou B Q, Wu W, Jing H, Chen P X 2021 Phys. Rev. A 103 L020201
[20] Ding L, Shi K, Zhang Q, Shen D, Zhang X, Zhang W 2021 Phys. Rev. Lett. 126 083604
[21] Lin Z, Ramezani H, Eichelkraut T, Kottos T, Cao H, Christodoulides D N 2011 Phys. Rev. Lett. 106 213901
[22] Regensburger A, Bersch C, Miri M A, Onishchukov G, Christodoulides D N, Peschel U 2012 Nature (London)488 167
[23] Feng L, Xu Y L, Fegadolli W S, Lu M H, Oliveira J E B, Almeida V R, Chen Y F, Scherer A 2013 Nat. Mater. 12 108
[24] Sun Y, Tan W, Li H Q, Li J, Chen H 2014 Phys. Rev. Lett. 112 143903
[25] Jin L, Song Z 2018 Phys. Rev. Lett. 121 073901
[26] Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N, Khajavikhan M 2017 Nature (London)548 187
[27] Yu S, Meng Y, Tang J, Xu X, Wang Y, Yin P, Ke Z, Liu W, Li Z, Yang Y, Chen G, Han Y, Li C, Guo G 2020 Phys. Rev. Lett. 125 240506
[28] Feng L, Wong Z J, Ma R M, Wang Y, Zhang X 2014 Science 346 972
[29] Hodaei H, Miri M A, Heinrich M, Christodoulides D N, Khajavikhan M 2014 Science 346 975
[30] Assawaworrarit S, Yu X, Fan S 2017 Nature (London)546 387
[31] Xu H, Mason D, Jiang L, Harris J G E 2016 Nature (London)537 80
[32] Bender C M, Brody D C, Jones H F 2002 Phys. Rev. Lett. 27 270401
[33] Bender C M 2007 Rep. Prog. Phys. 70 947
[34] Mostafazadeh A 2002 J. Math. Phys. 43 205
[35] Mostafazadeh A 2002 J. Math. Phys. 43 2814
[36] Nixon S, Yang J 2016 Phys. Rev. A 93 031802(R)
[37] Hang C, Gabadadze G, Huang G 2017 Phys. Rev. A 95 023833
[38] Pan J, Zhou L 2020 Phys. Rev. B 102 094305
[39] Luo X B, Huang J H, Zhong H H, Qin X Z, Xie Q T, Kivshar Y S, Lee C H 2013 Phys. Rev. Lett. 110 243902
[40] Chitsazi M, Li H, Ellis F M, Kottos T 2017 Phys. Rev. Lett. 119 093901
[41] Duan L, Wang Y, Chen Q 2020 Chin. Phys. Lett 37 081101
[42] Xie Q, Rong S and Liu X 2018 Phys. Rev. A 98 052122
[43] Koutserimpas T T, Alù A, Fleury R 2018 Phys. Rev. A 97 013839
[44] Luo X B, Wu D, Luo S, Guo Y, Yu X, Hu Q 2014 J. Phys. A:Math. Theor. 47 345301
[45] Yang B, Luo X B, Hu Q, Yu X 2016 Phys. Rev. A 94 043828
[46] Luo X B, Yang B, Zhang X-F, Li L, Yu X 2017 Phys. Rev. A 95 052128
[47] Cui B, Wang L C, Yi X X 2010 Phys. Rev. A 82 062105
[48] Liu Z P, Zhang J, Özdemir Ş K, Peng B, Jing H, Lü X Y, Li C W, Yang L, Nori F, Liu Y 2016 Phys. Rev. Lett. 117 110802
[49] Bender C M, Brody D C, Jones H F, Meister B K 2007 Phys. Rev. Lett. 98 040403
Metrics
- Abstract views: 2910
- PDF Downloads: 41
- Cited By: 0
下载:
