Robust beam splitter with fast quantum state transfer through a topological interface
Jia-Ning Zhang1, Jin-Xuan Han2, Jin-Lei Wu3(), Jie Song2, Yong-Yuan Jiang1,2,4,5,6()
1. Department of Optoelectronics Science, Harbin Institute of Technology, Weihai 264209, China 2. School of Physics, Harbin Institute of Technology, Harbin 150001, China 3. School of Physics and Microelectronics, Zhengzhou University, Zhengzhou 450001, China 4. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China 5. Key Laboratory of Micro-Nano Optoelectronic Information System, Ministry of Industry and Information Technology, Harbin 150001, China 6. Key Laboratory of Micro-Optics and Photonic Technology of Heilongjiang Province, Harbin Institute of Technology, Harbin 150001, China
The Su−Schrieffer−Heeger (SSH) model, commonly used for robust state transfers through topologically protected edge pumping, has been generalized and exploited to engineer diverse functional quantum devices. Here, we propose to realize a fast topological beam splitter based on a generalized SSH model by accelerating the quantum state transfer (QST) process essentially limited by adiabatic requirements. The scheme involves delicate orchestration of the instantaneous energy spectrum through exponential modulation of nearest neighbor coupling strengths and onsite energies, yielding a significantly accelerated beam splitting process. Due to properties of topological pumping and accelerated QST, the beam splitter exhibits strong robustness against parameter disorders and losses of system. In addition, the model demonstrates good scalability and can be extended to two-dimensional crossed-chain structures to realize a topological router with variable numbers of output ports. Our work provides practical prospects for fast and robust topological QST in feasible quantum devices in large-scale quantum information processing.
. [J]. Frontiers of Physics, 2023, 18(5): 51303.
Jia-Ning Zhang, Jin-Xuan Han, Jin-Lei Wu, Jie Song, Yong-Yuan Jiang. Robust beam splitter with fast quantum state transfer through a topological interface. Front. Phys. , 2023, 18(5): 51303.
I. Cirac J., Zoller P., J. Kimble H., Mabuchi H.. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett., 1997, 78(16): 3221 https://doi.org/10.1103/PhysRevLett.78.3221
Christandl M., Datta N., Ekert A., J. Landahl A.. Perfect state transfer in quantum spin networks. Phys. Rev. Lett., 2004, 92(18): 187902 https://doi.org/10.1103/PhysRevLett.92.187902
4
Banchi L., J. G. Apollaro T., Cuccoli A., Vaia R., Verrucchi P.. Long quantum channels for high-quality entanglement transfer. New J. Phys., 2011, 13(12): 123006 https://doi.org/10.1088/1367-2630/13/12/123006
5
D. Wang Y., A. Clerk A.. Using interference for high fidelity quantum state transfer in optomechanics. Phys. Rev. Lett., 2012, 108(15): 153603 https://doi.org/10.1103/PhysRevLett.108.153603
6
Tan S., W. Bomantara R., Gong J.. High-fidelity and long-distance entangled-state transfer with Floquet topological edge modes. Phys. Rev. A, 2020, 102(2): 022608 https://doi.org/10.1103/PhysRevA.102.022608
7
Ouyang M., D. Awschalom D.. Coherent spin transfer between molecularly bridged quantum dots. Science, 2003, 301(5636): 1074 https://doi.org/10.1126/science.1086963
8
D. Greentree A., H. Cole J., R. Hamilton A., C. L. Hollenberg L.. Coherent electronic transfer in quantum dot systems using adiabatic passage. Phys. Rev. B, 2004, 70(23): 235317 https://doi.org/10.1103/PhysRevB.70.235317
9
Chen B., H. Shen Q., Fan W., Xu Y.. Long-range adiabatic quantum state transfer through a linear array of quantum dots. Sci. China Phys. Mech. Astron., 2012, 55(9): 1635 https://doi.org/10.1007/s11433-012-4841-3
10
He Y., M. He Y., J. Wei Y., Jiang X., Chen K., Y. Lu C., W. Pan J., Schneider C., Kamp M., Höfling S.. Quantum state transfer from a single photon to a distant quantum-dot electron spin. Phys. Rev. Lett., 2017, 119(6): 060501 https://doi.org/10.1103/PhysRevLett.119.060501
11
P. Kandel Y., Qiao H., Fallahi S., C. Gardner G., J. Manfra M., M. Nichol J.. Adiabatic quantum state transfer in a semiconductor quantum-dot spin chain. Nat. Commun., 2021, 12(1): 2156 https://doi.org/10.1038/s41467-021-22416-5
12
Perez-Leija A., Keil R., Kay A., Moya-Cessa H., Nolte S., C. Kwek L., M. Rodríguez-Lara B., Szameit A., N. Christodoulides D.. Coherent quantum transport in photonic lattices. Phys. Rev. A, 2013, 87(1): 012309 https://doi.org/10.1103/PhysRevA.87.012309
13
J. Chapman R., Santandrea M., Huang Z., Corrielli G., Crespi A., H. Yung M., Osellame R., Peruzzo A.. Experimental perfect state transfer of an entangled photonic qubit. Nat. Commun., 2016, 7(1): 11339 https://doi.org/10.1038/ncomms11339
14
Liu W., Wu C., Jia Y., Jia S., Chen G., Chen F.. Observation of edge-to-edge topological transport in a photonic lattice. Phys. Rev. A, 2022, 105(6): L061502 https://doi.org/10.1103/PhysRevA.105.L061502
15
F. Wei L., R. Johansson J., X. Cen L., Ashhab S., Nori F.. Controllable coherent population transfers in superconducting qubits for quantum computing. Phys. Rev. Lett., 2008, 100(11): 113601 https://doi.org/10.1103/PhysRevLett.100.113601
16
Mei F., Chen G., Tian L., L. Zhu S., Jia S.. Robust quantum state transfer via topological edge states in superconducting qubit chains. Phys. Rev. A, 2018, 98(1): 012331 https://doi.org/10.1103/PhysRevA.98.012331
17
Li X., Ma Y., Han J., Chen T., Xu Y., Cai W., Wang H., P. Song Y., Y. Xue Z., Yin Z., Sun L.. Perfect quantum state transfer in a superconducting qubit chain with parametrically tunable couplings. Phys. Rev. Appl., 2018, 10(5): 054009 https://doi.org/10.1103/PhysRevApplied.10.054009
18
M. A. Almeida G., Ciccarello F., J. G. Apollaro T., M. C. Souza A.. Quantum-state transfer in staggered coupled-cavity arrays. Phys. Rev. A, 2016, 93(3): 032310 https://doi.org/10.1103/PhysRevA.93.032310
19
Qin W., Nori F.. Controllable single-photon transport between remote coupled-cavity arrays. Phys. Rev. A, 2016, 93(3): 032337 https://doi.org/10.1103/PhysRevA.93.032337
20
Balachandran V., Gong J.. Adiabatic quantum transport in a spin chain with a moving potential. Phys. Rev. A, 2008, 77(1): 012303 https://doi.org/10.1103/PhysRevA.77.012303
21
Yang S., Bayat A., Bose S.. Spin-state transfer in laterally coupled quantum-dot chains with disorders. Phys. Rev. A, 2010, 82(2): 022336 https://doi.org/10.1103/PhysRevA.82.022336
22
M. Nikolopoulos G.. Statistics of a quantum-state-transfer Hamiltonian in the presence of disorder. Phys. Rev. A, 2013, 87(4): 042311 https://doi.org/10.1103/PhysRevA.87.042311
Niu Q., J. Thouless D., S. Wu Y.. Quantized hall conductance as a topological invariant. Phys. Rev. B, 1985, 31(6): 3372 https://doi.org/10.1103/PhysRevB.31.3372
L. Qi X., C. Zhang S.. The quantum spin Hall effect and topological insulators. Phys. Today, 2010, 63(1): 33 https://doi.org/10.1063/1.3293411
28
K. Chiu C., C. Y. Teo J., P. Schnyder A., Ryu S.. Classification of topological quantum matter with symmetries. Rev. Mod. Phys., 2016, 88(3): 035005 https://doi.org/10.1103/RevModPhys.88.035005
Ozawa T., M. Price H., Amo A., Goldman N., Hafezi M., Lu L., C. Rechtsman M., Schuster D., Simon J., Zilberberg O., Carusotto I.. Topological photonics. Rev. Mod. Phys., 2019, 91(1): 015006 https://doi.org/10.1103/RevModPhys.91.015006
34
Seo J., Roushan P., Beidenkopf H., S. Hor Y., J. Cava R., Yazdani A.. Transmission of topological surface states through surface barriers. Nature, 2010, 466(7304): 343 https://doi.org/10.1038/nature09189
35
Lang N., P. Büchler H.. Topological networks for quantum communication between distant qubits. npj Quantum Inf., 2017, 3: 47 https://doi.org/10.1038/s41534-017-0047-x
36
Dlaska C., Vermersch B., Zoller P.. Robust quantum state transfer via topologically protected edge channels in dipolar arrays. Quantum Sci. Technol., 2017, 2(1): 015001 https://doi.org/10.1088/2058-9565/2/1/015001
37
A. Lemonde M., Peano V., Rabl P., G. Angelakis D.. Quantum state transfer via acoustic edge states in a 2D optomechanical array. New J. Phys., 2019, 21(11): 113030 https://doi.org/10.1088/1367-2630/ab51f5
38
Cao J., X. Cui W., Yi X., F. Wang H.. Topological phase transition and topological quantum state transfer in periodically modulated circuit-QED lattice. Ann. Phys., 2021, 533(9): 2100120 https://doi.org/10.1002/andp.202100120
39
Y. Cheng L., N. Zheng L., Wu R., F. Wang H., Zhang S.. Change-over switch for quantum states transfer with topological channels in a circuit-QED lattice. Chin. Phys. B, 2022, 31(2): 020305 https://doi.org/10.1088/1674-1056/ac2f2e
40
Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Controllable photonic and phononic topological state transfers in a small optomechanical lattice. Opt. Lett., 2020, 45(7): 2018 https://doi.org/10.1364/OL.388835
41
Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Dissipation-induced topological phase transition and periodic-driving-induced photonic topological state transfer in a small optomechanical lattice. Front. Phys., 2021, 16(1): 12503 https://doi.org/10.1007/s11467-020-0983-3
42
Stern A., H. Lindner N.. Topological quantum computation — from basic concepts to first experiments. Science, 2013, 339(6124): 1179 https://doi.org/10.1126/science.1231473
43
D. Sarma S., Freedman M., Nayak C.. Majorana zero modes and topological quantum computation. npj Quantum Inf., 2015, 1: 15001 https://doi.org/10.1038/npjqi.2015.1
Dai T., Ao Y., Bao J., Mao J., Chi Y., Fu Z., You Y., Chen X., Zhai C., Tang B., Yang Y., Li Z., Yuan L., Gao F., Lin X., G. Thompson M., L. O’Brien J., Li Y., Hu X., Gong Q., Wang J.. Topologically protected quantum entanglement emitters. Nat. Photonics, 2022, 16(3): 248 https://doi.org/10.1038/s41566-021-00944-2
47
X. Han J., L. Wu J., Wang Y., Xia Y., Y. Jiang Y., Song J.. Large-scale Greenberger−Horne−Zeilinger states through a topologically protected zero-energy mode in a superconducting qutrit-resonator chain. Phys. Rev. A, 2021, 103(3): 032402 https://doi.org/10.1103/PhysRevA.103.032402
48
X. Han J., L. Wu J., H. Yuan Z., Xia Y., Y. Jiang Y., Song J.. Fast topological pumping for the generation of large-scale Greenberger−Horne−Zeilinger states in a superconducting circuit. Front. Phys., 2022, 17(6): 62504 https://doi.org/10.1007/s11467-022-1193-y
49
Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Engineering the topological state transfer and topological beam splitter in an even-sized Su−Schrieffer−Heeger chain. Phys. Rev. A, 2020, 102(2): 022404 https://doi.org/10.1103/PhysRevA.102.022404
50
Qi L., Xing Y., D. Zhao X., Liu S., Zhang S., Hu S., F. Wang H.. Topological beam splitter via defect-induced edge channel in the Rice−Mele model. Phys. Rev. B, 2021, 103(8): 085129 https://doi.org/10.1103/PhysRevB.103.085129
51
Qi L., Yan Y., Xing Y., D. Zhao X., Liu S., X. Cui W., Han X., Zhang S., F. Wang H.. Topological router induced via long-range hopping in a Su−Schrieffer−Heeger chain. Phys. Rev. Res., 2021, 3(2): 023037 https://doi.org/10.1103/PhysRevResearch.3.023037
52
N. Zheng L., Yi X., F. Wang H.. Engineering a phase-robust topological router in a dimerized superconducting-circuit lattice with long-range hopping and chiral symmetry. Phys. Rev. Appl., 2022, 18(5): 054037 https://doi.org/10.1103/PhysRevApplied.18.054037
53
St-Jean P., Goblot V., Galopin E., Lemaȋtre A., Ozawa T., Le Gratiet L., Sagnes I., Bloch J., Amo A.. Lasing in topological edge states of a one-dimensional lattice. Nat. Photonics, 2017, 11(10): 651 https://doi.org/10.1038/s41566-017-0006-2
54
Parto M., Wittek S., Hodaei H., Harari G., A. Bandres M., Ren J., C. Rechtsman M., Segev M., N. Christodoulides D., Khajavikhan M.. Edge-mode lasing in 1D topological active arrays. Phys. Rev. Lett., 2018, 120(11): 113901 https://doi.org/10.1103/PhysRevLett.120.113901
Qi L., L. Wang G., Liu S., Zhang S., F. Wang H.. Robust interface-state laser in non-Hermitian microresonator arrays. Phys. Rev. Appl., 2020, 13(6): 064015 https://doi.org/10.1103/PhysRevApplied.13.064015
57
H. Harder T., Sun M., A. Egorov O., Vakulchyk I., Beierlein J., Gagel P., Emmerling M., Schneider C., Peschel U., G. Savenko I., Klembt S., Höfling S.. Coherent topological polariton laser. ACS Photonics, 2021, 8(5): 1377 https://doi.org/10.1021/acsphotonics.0c01958
M. D’Angelis F., A. Pinheiro F., Guéry-Odelin D., Longhi S., Impens F.. Fast and robust quantum state transfer in a topological Su-Schrieffer-Heeger chain with next-to-nearest-neighbor interactions. Phys. Rev. Res., 2020, 2(3): 033475 https://doi.org/10.1103/PhysRevResearch.2.033475
61
Brouzos I., Kiorpelidis I., K. Diakonos F., Theocharis G.. Fast, robust, and amplified transfer of topological edge modes on a time-varying mechanical chain. Phys. Rev. B, 2020, 102(17): 174312 https://doi.org/10.1103/PhysRevB.102.174312
62
E. Palaiodimopoulos N., Brouzos I., K. Diakonos F., Theocharis G.. Fast and robust quantum state transfer via a topological chain. Phys. Rev. A, 2021, 103(5): 052409 https://doi.org/10.1103/PhysRevA.103.052409
63
Hu S., Ke Y., Lee C.. Topological quantum transport and spatial entanglement distribution via a disordered bulk channel. Phys. Rev. A, 2020, 101(5): 052323 https://doi.org/10.1103/PhysRevA.101.052323
64
Guéry-Odelin D., Ruschhaupt A., Kiely A., Torrontegui E., Martínez-Garaot S., G. Muga J.. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 2019, 91(4): 045001 https://doi.org/10.1103/RevModPhys.91.045001
65
Schmidt S., Koch J.. Circuit QED lattices: Towards quantum simulation with superconducting circuits. Ann. Phys., 2013, 525(6): 395 https://doi.org/10.1002/andp.201200261
66
Frunzio L., Wallraff A., Schuster D., Majer J., Schoelkopf R.. Fabrication and characterization of superconducting circuit QED devices for quantum computation. IEEE Trans. Appl. Supercond., 2005, 15(2): 860 https://doi.org/10.1109/TASC.2005.850084
67
L. Underwood D., E. Shanks W., Koch J., A. Houck A.. Low-disorder microwave cavity lattices for quantum simulation with photons. Phys. Rev. A, 2012, 86(2): 023837 https://doi.org/10.1103/PhysRevA.86.023837
68
Peropadre B., Forn-Díaz P., Solano E., J. García-Ripoll J.. Switchable ultrastrong coupling in circuit QED. Phys. Rev. Lett., 2010, 105(2): 023601 https://doi.org/10.1103/PhysRevLett.105.023601
69
DiCarlo L., M. Chow J., M. Gambetta J., S. Bishop L., R. Johnson B., I. Schuster D., Majer J., Blais A., Frunzio L., M. Girvin S., J. Schoelkopf R.. Demonstration of two-qubit algorithms with a superconducting quantum processor. Nature, 2009, 460(7252): 240 https://doi.org/10.1038/nature08121
70
Gu X., F. Kockum A., Miranowicz A., X. Liu Y., Nori F.. Microwave photonics with superconducting quantum circuits. Phys. Rep., 2017, 1: 718 https://doi.org/10.1016/j.physrep.2017.10.002
71
He Y., Wang Y., Yan Z.. A tunable superconducting LC-resonator with a variable superconducting electrode capacitor bank for application in wireless power transfer. Supercond. Sci. Technol., 2019, 32(12): 12LT02 https://doi.org/10.1088/1361-6668/ab4c1d
72
S. Allman M., Altomare F., D. Whittaker J., Cicak K., Li D., Sirois A., Strong J., D. Teufel J., W. Simmonds R.. RF-squid-mediated coherent tunable coupling between a superconducting phase qubit and a lumped-element resonator. Phys. Rev. Lett., 2010, 104: 177004 https://doi.org/10.1103/PhysRevLett.104.177004
73
S. Allman M., D. Whittaker J., Castellanos-Beltran M., Cicak K., da Silva F., P. DeFeo M., Lecocq F., Sirois A., D. Teufel J., Aumentado J., W. Simmonds R.. Tunable resonant and nonresonant interactions between a phase qubit and LC resonator. Phys. Rev. Lett., 2014, 112(12): 123601 https://doi.org/10.1103/PhysRevLett.112.123601
74
Wulschner F., Goetz J., R. Koessel F., Hoffmann E., Baust A., Eder P., Fischer M., Haeberlein M., J. Schwarz M., Pernpeintner M., Xie E., Zhong L., W. Zollitsch C., Peropadre B., G. Ripoll J.-J., Solano E., G. Fedorov K., P. Menzel E., Deppe F., Marx A., Gross R.. Tunable coupling of transmission-line microwave resonators mediated by an RF squid. EPJ Quantum Technol., 2016, 3: 8 https://doi.org/10.1140/epjqt/s40507-016-0048-2
75
Blais A., S. Huang R., Wallraff A., M. Girvin S., J. Schoelkopf R.. Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation. Phys. Rev. A, 2004, 69(6): 062320 https://doi.org/10.1103/PhysRevA.69.062320