Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2021, Vol. 16 Issue (1) : 12503    https://doi.org/10.1007/s11467-020-0983-3
RESEARCH ARTICLE
Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice
Lu Qi1, Guo-Li Wang1, Shutian Liu1(), Shou Zhang1,2(), Hong-Fu Wang2()
1. School of Physics, Harbin Institute of Technology, Harbin 150001, China
2. Department of Physics, College of Science, Yanbian University, Yanji 133002, China
 Download: PDF(2811 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

We propose a scheme to investigate the topological phase transition and the topological state transfer based on the small optomechanical lattice under the realistic parameters regime. We find that the optomechanical lattice can be equivalent to a topologically nontrivial Su–Schrieffer–Heeger (SSH) model via designing the effective optomechanical coupling. Especially, the optomechanical lattice experiences the phase transition between topologically nontrivial SSH phase and topologically trivial SSH phase by controlling the decay of the cavity field and the optomechanical coupling. We stress that the topological phase transition is mainly induced by the decay of the cavity field, which is counter-intuitive since the dissipation is usually detrimental to the system. Also, we investigate the photonic state transfer between the two cavity fields via the topologically protected edge channel based on the small optomechanical lattice. We find that the quantum state transfer assisted by the topological zero energy mode can be achieved via implying the external lasers with the periodical driving amplitudes into the cavity fields. Our scheme provides the fundamental and the insightful explanations towards the mapping of the photonic topological insulator based on the micro-nano optomechanical quantum optical platform.

Keywords topological phase transition      topological state transfer      optomechanical lattice     
Corresponding Author(s): Shutian Liu,Shou Zhang,Hong-Fu Wang   
Just Accepted Date: 17 August 2020   Issue Date: 10 October 2020
 Cite this article:   
Lu Qi,Guo-Li Wang,Shutian Liu, et al. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice[J]. Front. Phys. , 2021, 16(1): 12503.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-020-0983-3
https://academic.hep.com.cn/fop/EN/Y2021/V16/I1/12503
1 M. Z. Hasan and C. L. Kane, Topological insulators, Rev. Mod. Phys. 82(4), 3045 (2010)
https://doi.org/10.1103/RevModPhys.82.3045
2 X. L. Qi and S. C. Zhang, Topological insulators and superconductors, Rev. Mod. Phys. 83(4), 1057 (2011)
https://doi.org/10.1103/RevModPhys.83.1057
3 C. K. Chiu, J. C. Teo, A. P. Schnyder, and S. Ryu, Classification of topological quantum matter with symmetries, Rev. Mod. Phys. 88(3), 035005 (2016)
https://doi.org/10.1103/RevModPhys.88.035005
4 A. Bansil, H. Lin, and T. Das, Topological band theory, Rev. Mod. Phys. 88(2), 021004 (2016)
https://doi.org/10.1103/RevModPhys.88.021004
5 C. Dlaska, B. Vermersch, and P. Zoller, Robust quantum state transfer via topologically protected edge channels in dipolar arrays, Quantum Sci. Technol. 2(1), 015001 (2017)
https://doi.org/10.1088/2058-9565/2/1/015001
6 F. Mei, G. Chen, L. Tian, S. L. Zhu, and S. Jia, Robust quantum state transfer via topological edge states in superconducting qubit chains, Phys. Rev. A 98(1), 012331 (2018)
https://doi.org/10.1103/PhysRevA.98.012331
7 L. Qi, G. L. Wang, S. Liu, S. Zhang, and H. F. Wang, Controllable photonic and phononic topological state transfers in a small optomechanical lattice, Opt. Lett. 45(7), 2018 (2020)
https://doi.org/10.1364/OL.388835
8 D. Aasen, M. Hell, R. V. Mishmash, A. Higginbotham, J. Danon, M. Leijnse, T. S. Jespersen, J. A. Folk, C. M. Marcus, K. Flensberg, and J. Alicea, Milestones toward Majorana-based quantum computing, Phys. Rev. X 6(3), 031016 (2016)
https://doi.org/10.1103/PhysRevX.6.031016
9 S. D. Sarma, M. Freedman, and C. Nayak, Majorana zero modes and topological quantum computation, npj Quantum Inf. 1, 15001 (2015)
https://doi.org/10.1038/npjqi.2015.1
10 G. Harari, M. A. Bandres, Y. Lumer, M. C. Rechtsman, Y. D. Chong, M. Khajavikhan, D. N. Christodoulides, and M. Segev, Topological insulator laser: Theory, Science 359, eaar4003 (2018)
https://doi.org/10.1126/science.aar4003
11 M. A. Bandres, S. Wittek, G. Harari, M. Parto, J. Ren, M. Segev, D. N. Christodoulides, and M. Khajavikhan, Topological insulator laser: Experiments, Science 359, eaar4005 (2018)
https://doi.org/10.1126/science.aar4005
12 A. B. Khanikaev, S. Hossein Mousavi, W. K. Tse, M. Kargarian, A. H. MacDonald, and G. Shvets, Photonic topological insulators, Nat. Mater. 12(3), 233 (2013)
https://doi.org/10.1038/nmat3520
13 M. C. Rechtsman, J. M. Zeuner, Y. Plotnik, Y. Lumer, D. Podolsky, F. Dreisow, S. Nolte, M. Segev, and A. Szameit, Photonic floquet topological insulators, Nature 496(7444), 196 (2013)
https://doi.org/10.1038/nature12066
14 P. Yan, R. Lin, H. Chen, H. Zhang, A. Liu, H. Yang, and S. Ruan, Topological insulator solution filled in photonic crystal fiber for passive mode-locked fiber laser, IEEE Photonics Technol. Lett. 27, 264 (2014)
https://doi.org/10.1109/LPT.2014.2361915
15 L. Lu, C. Fang, L. Fu, S. G. Johnson, J. D. Joannopoulos, and M. Soljačić, Symmetry-protected topological photonic crystal in three dimensions, Nat. Phys. 12(4), 337 (2016)
https://doi.org/10.1038/nphys3611
16 L. Gao, T. Zhu, W. Huang, and Z. Luo, Stable, ultrafast pulse mode-locked by topological insulator Bi2Se3 nanosheets interacting with photonic crystal fiber: From anomalous dispersion to normal dispersion, IEEE Photonics J. 7, 1 (2015)
https://doi.org/10.1109/JPHOT.2015.2402594
17 M. I. Shalaev, W. Walasik, A. Tsukernik, Y. Xu, and N. M. Litchinitser, Robust topologically protected transport in photonic crystals at telecommunication wavelengths, Nat. Nanotechnol. 14(1), 31 (2019)
https://doi.org/10.1038/s41565-018-0297-6
18 S. A. Skirlo, L. Lu, Y. Igarashi, Q. Yan, J. Joannopoulos, and M. Soljačić, Experimental observation of large Chern numbers in photonic crystals, Phys. Rev. Lett. 115(25), 253901 (2015)
https://doi.org/10.1103/PhysRevLett.115.253901
19 L. Xu, H. X. Wang, Y. D. Xu, H. Y. Chen, and J. H. Jiang, Accidental degeneracy in photonic bands and topological phase transitions in two-dimensional core-shell dielectric photonic crystals, Opt. Express 24(16), 18059 (2016)
https://doi.org/10.1364/OE.24.018059
20 L. H. Wu and X. Hu, Scheme for achieving a topological photonic crystal by using dielectric material, Phys. Rev. Lett. 114(22), 223901 (2015)
https://doi.org/10.1103/PhysRevLett.114.223901
21 A. Tomita and R. Y. Chiao, Observation of Berry’s topological phase by use of an optical fiber, Phys. Rev. Lett. 57(8), 937 (1986)
https://doi.org/10.1103/PhysRevLett.57.937
22 W. J. Chen, S. J. Jiang, X. D. Chen, B. Zhu, L. Zhou, J. W. Dong, and C. T. Chan, Experimental realization of photonic topological insulator in a uniaxial metacrystal waveguide, Nat. Commun. 5(1), 5782 (2014)
https://doi.org/10.1038/ncomms6782
23 S. Ke, D. Zhao, J. Liu, Q. Liu, Q. Liao, B. Wang, and P. Lu, Topological bound modes in anti-PT-symmetric optical waveguide arrays, Opt. Express 27(10), 13858 (2019)
https://doi.org/10.1364/OE.27.013858
24 S. Longhi, Zak phase of photons in optical waveguide lattices, Opt. Lett. 38(19), 3716 (2013)
https://doi.org/10.1364/OL.38.003716
25 A. Blanco-Redondo, I. Andonegui, M. J. Collins, G. Harari, Y. Lumer, M. C. Rechtsman, B. J. Eggleton, and M. Segev, Topological optical waveguiding in silicon and the transition between topological and trivial defect states, Phys. Rev. Lett. 116(16), 163901 (2016)
https://doi.org/10.1103/PhysRevLett.116.163901
26 G. Liang and Y. Chong, Optical resonator analog of a two-dimensional topological insulator, Phys. Rev. Lett. 110(20), 203904 (2013)
https://doi.org/10.1103/PhysRevLett.110.203904
27 F. Mivehvar, H. Ritsch, and F. Piazza, Superradiant topological Peierls insulator inside an optical cavity, Phys. Rev. Lett. 118(7), 073602 (2017)
https://doi.org/10.1103/PhysRevLett.118.073602
28 G. Liang and Y. Chong, Optical resonator analog of a photonic topological insulator: A finite-difference timedomain study, Int. J. Mod. Phys. B 28(02), 1441007 (2014)
https://doi.org/10.1142/S0217979214410070
29 C. Poli, M. Bellec, U. Kuhl, F. Mortessagne, and H. Schomerus, Selective enhancement of topologically induced interface states in a dielectric resonator chain, Nat. Commun. 6(1), 6710 (2015)
https://doi.org/10.1038/ncomms7710
30 C. He, Z. Li, X. Ni, X. C. Sun, S. Y. Yu, M. H. Lu, X. P. Liu, and Y. F. Chen, Topological phononic states of underwater sound based on coupled ring resonators, Appl. Phys. Lett. 108(3), 031904 (2016)
https://doi.org/10.1063/1.4940403
31 D. Leykam, S. Mittal, M. Hafezi, and Y. D. Chong, Reconfigurable topological phases in next-nearest-neighbor coupled resonator lattices, Phys. Rev. Lett. 121(2), 023901 (2018)
https://doi.org/10.1103/PhysRevLett.121.023901
32 J. Tangpanitanon, V. M. Bastidas, S. Al-Assam, P. Roushan, D. Jaksch, and D. G. Angelakis, Topological pumping of photons in nonlinear resonator arrays, Phys. Rev. Lett. 117(21), 213603 (2016)
https://doi.org/10.1103/PhysRevLett.117.213603
33 M. Hafezi, S. Mittal, J. Fan, A. Migdall, and J. Taylor, Imaging topological edge states in silicon photonics, Nat. Photonics 7(12), 1001 (2013)
https://doi.org/10.1038/nphoton.2013.274
34 T. Ma and G. Shvets, All-Si valley-Hall photonic topological insulator, New J. Phys. 18(2), 025012 (2016)
https://doi.org/10.1088/1367-2630/18/2/025012
35 X. T. He, E. T. Liang, J. J. Yuan, H. Y. Qiu, X. D. Chen, F. L. Zhao, and J. W. Dong, A silicon-on-insulator slab for topological valley transport, Nat. Commun. 10(1), 872 (2019)
https://doi.org/10.1038/s41467-019-08881-z
36 F. Mei, Z. Y. Xue, D. W. Zhang, L. Tian, C. Lee, and S. L. Zhu, Witnessing topological Weyl semimetal phase in a minimal circuit-QED lattice, Quantum Sci. Technol. 1(1), 015006 (2016)
https://doi.org/10.1088/2058-9565/1/1/015006
37 Y. Huang, Z. Q. Yin, and W. Yang, Realizing a topological transition in a non-Hermitian quantum walk with circuit QED, Phys. Rev. A 94(2), 022302 (2016)
https://doi.org/10.1103/PhysRevA.94.022302
38 F. Mei, J. B. You, W. Nie, R. Fazio, S. L. Zhu, and L. C. Kwek, Simulation and detection of photonic Chern insulators in a one-dimensional circuit-QED lattice, Phys. Rev. A 92(4), 041805 (2015)
https://doi.org/10.1103/PhysRevA.92.041805
39 L. Qi, Y. Xing, J. Cao, X. X. Jiang, C. S. An, A. D. Zhu, S. Zhang, and H. F. Wang, Simulation and detection of the topological properties of a modulated Ricemele model in a one-dimensional circuit-QED lattice, Sci. China Phys. Mech. Astron. 61(8), 080313 (2018)
https://doi.org/10.1007/s11433-018-9212-4
40 X. Tan, Y. Zhao, Q. Liu, G. Xue, H. F. Yu, Z. Wang, and Y. Yu, Simulation and manipulation of tunable Weyl semimetal bands using superconducting quantum circuits, Phys. Rev. Lett. 122(1), 010501 (2019)
https://doi.org/10.1103/PhysRevLett.122.010501
41 M. Aspelmeyer, T. J. Kippenberg, and F. Marquardt, Cavity optomechanics, Rev. Mod. Phys. 86(4), 1391 (2014)
https://doi.org/10.1103/RevModPhys.86.1391
42 T. J. Kippenberg and K. J. Vahala, Cavity optomechanics: Back-action at the mesoscale, Science 321(5893), 1172 (2008)
https://doi.org/10.1126/science.1156032
43 M. Eichenfield, J. Chan, R. M. Camacho, K. J. Vahala, and O. Painter, Optomechanical crystals, Nature 462, 78 (2009)
https://doi.org/10.1038/nature08524
44 T. J. Kippenberg and K. J. Vahala, Cavity optomechanics, Opt. Express 15(25), 17172 (2007)
https://doi.org/10.1364/OE.15.017172
45 T. Wang, M. H. Zheng, C. H. Bai, D. Y. Wang, A. D. Zhu, H. F. Wang, and S. Zhang, Normal-mode splitting and optomechanically induced absorption, amplification, and transparency in a hybrid optomechanical system, Ann. Phys. 530(10), 1800228 (2018)
https://doi.org/10.1002/andp.201800228
46 J. M. Dobrindt, I. Wilson-Rae, and T. J. Kippenberg, Parametric normal-mode splitting in cavity optomechanics, Phys. Rev. Lett. 101(26), 263602 (2008)
https://doi.org/10.1103/PhysRevLett.101.263602
47 Y. C. Liu, Y. F. Xiao, X. Luan, and C. W. Wong, Dynamic dissipative cooling of a mechanical resonator in strong coupling optomechanics, Phys. Rev. Lett. 110(15), 153606 (2013)
https://doi.org/10.1103/PhysRevLett.110.153606
48 D. Vitali, S. Gigan, A. Ferreira, H. Böhm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Optomechanical entanglement between a movable mirror and a cavity field, Phys. Rev. Lett. 98(3), 030405 (2007)
https://doi.org/10.1103/PhysRevLett.98.030405
49 R. Ghobadi, S. Kumar, B. Pepper, D. Bouwmeester, A. Lvovsky, and C. Simon, Optomechanical micro-macro entanglement, Phys. Rev. Lett. 112(8), 080503 (2014)
https://doi.org/10.1103/PhysRevLett.112.080503
50 C. H. Bai, D. Y. Wang, S. Zhang, S. Liu, and H. F. Wang, Engineering of strong mechanical squeezing via the joint effect between Duffing nonlinearity and parametric pump driving, Photon. Res. 7(11), 1229 (2019)
https://doi.org/10.1364/PRJ.7.001229
51 T. P. Purdy, P. L. Yu, R. Peterson, N. Kampel, and C. Regal, Strong optomechanical squeezing of light, Phys. Rev. X 3(3), 031012 (2013)
https://doi.org/10.1103/PhysRevX.3.031012
52 C. H. Bai, D. Y. Wang, S. Zhang, and H. F. Wang, Qubitassisted squeezing of mirror motion in a dissipative cavity optomechanical system, Sci. China Phys. Mech. Astron. 62(7), 970311 (2019)
https://doi.org/10.1007/s11433-018-9327-8
53 A. Nunnenkamp, K. Børkje, J. G. E. Harris, and S. M. Girvin, Cooling and squeezing via quadratic optomechanical coupling, Phys. Rev. A 82(2), 021806 (2010)
https://doi.org/10.1103/PhysRevA.82.021806
54 D. Y. Wang, C. H. Bai, S. Liu, S. Zhang, and H. F. Wang, Optomechanical cooling beyond the quantum back-action limit with frequency modulation, Phys. Rev. A 98(2), 023816 (2018)
https://doi.org/10.1103/PhysRevA.98.023816
55 G. Heinrich, M. Ludwig, J. Qian, B. Kubala, and F. Marquardt, Collective dynamics in optomechanical arrays, Phys. Rev. Lett. 107(4), 043603 (2011)
https://doi.org/10.1103/PhysRevLett.107.043603
56 M. Ludwig and F. Marquardt, Quantum many-body dynamics in optomechanical arrays, Phys. Rev. Lett. 111(7), 073603 (2013)
https://doi.org/10.1103/PhysRevLett.111.073603
57 A. Xuereb, C. Genes, and A. Dantan, Strong coupling and long-range collective interactions in optomechanical arrays, Phys. Rev. Lett. 109(22), 223601 (2012)
https://doi.org/10.1103/PhysRevLett.109.223601
58 U. Akram, W. Munro, K. Nemoto, and G. Milburn, Photon–phonon entanglement in coupled optomechanical arrays, Phys. Rev. A 86(4), 042306 (2012)
https://doi.org/10.1103/PhysRevA.86.042306
59 H. Xiong, L. G. Si, X. Yang, and Y. Wu, Asymmetric optical transmission in an optomechanical array, Appl. Phys. Lett. 107(9), 091116 (2015)
https://doi.org/10.1063/1.4930166
60 L. Qi, Y. Yan, G. L. Wang, S. Zhang, and H. F. Wang, Bosonic Kitaev phase in a frequency-modulated optomechanical array, Phys. Rev. A 100(6), 062323 (2019)
https://doi.org/10.1103/PhysRevA.100.062323
61 A. Tomadin, S. Diehl, M. D. Lukin, P. Rabl, and P. Zoller, Reservoir engineering and dynamical phase transitions in optomechanical arrays, Phys. Rev. A 86(3), 033821 (2012)
https://doi.org/10.1103/PhysRevA.86.033821
62 J. H. Gan, H. Xiong, L. G. Si, X. Y. Lü, and Y. Wu, Solitons in optomechanical arrays, Opt. Lett. 41(12), 2676 (2016)
https://doi.org/10.1364/OL.41.002676
63 L. Qi, Y. Xing, H. F. Wang, A. D. Zhu, and S. Zhang, Simulating Z2 topological insulators via a onedimensional cavity optomechanical cells array, Opt. Express 25(15), 17948 (2017)
https://doi.org/10.1364/OE.25.017948
64 T. F. Roque, V. Peano, O. M. Yevtushenko, and F. Marquardt, Anderson localization of composite excitations in disordered optomechanical arrays, New J. Phys. 19(1), 013006 (2017)
https://doi.org/10.1088/1367-2630/aa52e2
65 S. Raeisi and F. Marquardt, Quench dynamics in onedimensional optomechanical arrays, Phys. Rev. A 101(2), 023814 (2020)
https://doi.org/10.1103/PhysRevA.101.023814
66 D. Obana, F. Liu, and K. Wakabayashi, Topological edge states in the Su–Schrieffer–Heeger model, Phys. Rev. B 100(7), 075437 (2019)
https://doi.org/10.1103/PhysRevB.100.075437
67 T. Liu and H. Guo, Topological phase transition in the quasiperiodic disordered Su–Schriffer–Heeger chain, Phys. Lett. A 382(45), 3287 (2018)
https://doi.org/10.1016/j.physleta.2018.09.023
68 F. L. J. Vos, D. P. Aalberts, and W. Saarloos, Su– Schrieffer–Heeger model applied to chains of finite length, Phys. Rev. B 53(22), 14922 (1996)
https://doi.org/10.1103/PhysRevB.53.14922
69 S. R. Barone, M. A. Narcowich, and F. J. Narcowich, Floquet theory and applications, Phys. Rev. A 15(3), 1109 (1977)
https://doi.org/10.1103/PhysRevA.15.1109
70 W. Berdanier, M. Kolodrubetz, R. Vasseur, and J. E. Moore, Floquet dynamics of boundary-driven systems at criticality, Phys. Rev. Lett. 118(26), 260602 (2017)
https://doi.org/10.1103/PhysRevLett.118.260602
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed