Generation of multiparticle entangled states of nitrogen-vacancy centers with carbon nanotubes | Quantum Information Processing Skip to main content

Advertisement

Springer Nature Link
Log in

Generation of multiparticle entangled states of nitrogen-vacancy centers with carbon nanotubes

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

We propose an efficient scheme for generating multiparticle entangled states between two arrays of nitrogen-vacancy centers that interact with two magnetically coupled carbon nanotubes, respectively. We show that through adjusting the external driving microwave fields and the dc currents flowing through the nanotube mechanical resonators, the multiparticle entanglement between the separated arrays of NV centers can be engineered and tuned dynamically. The experimental feasibility of this scheme is analyzed, as well as the method to produce the NOON states of phonon modes is presented using the generated multiparticle entangled states. This scheme may have interesting applications for quantum information processing.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
¥17,985 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Japan)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Tao, Y., Boss, J.M., Moores, B.A., Degen, C.L.: Single-crystal diamond nanomechanical resonators with quality factors exceeding one million. Nat. Commun. 5, 3638 (2014)

    ADS  Google Scholar 

  2. Burek, M.J., Ramos, D., Patel, P., Frank, I.W., Lončar, M.: Nanomechanical resonant structures in single-crystal diamond. Appl. Phys. Lett. 103(13), 131904 (2013)

    ADS  Google Scholar 

  3. Ovartchaiyapong, P., Pascal, L.M.A., Myers, B.A., Lauria, P., Jayich, A.C.B.: High quality factor single-crystal diamond mechanical resonator. Appl. Phys. Lett. 101(16), 163505 (2012)

    ADS  Google Scholar 

  4. Sohn, Y.I., Burek, M.J., Kara, V., Kearns, R., Lončar, M.: Dynamic actuation of single-crystal diamond nanobeams. Appl. Phys. Lett. 107(24), 243106 (2015)

    ADS  Google Scholar 

  5. Ovartchaiyapong, P., Lee, K.W., Myers, B.A., Jayich, A.C.B.: Dynamic strain-mediated coupling of a single diamond spin to a mechanical resonator. Nat. Commun. 5, 4429 (2014)

    ADS  Google Scholar 

  6. Sazonova, V., Yaish, Y., Üstünel, H., Roundy, D., Arias, T.A., McEuen, P.L.: A tunable carbon nanotube electromechanical oscillator. Nature 431(7006), 284–287 (2004)

    ADS  Google Scholar 

  7. Witkamp, B., Poot, M., van der Zant, H.S.J.: Bending-mode vibration of a suspended nanotube resonator. Nano Lett. 6(12), 2904–2908 (2006)

    ADS  Google Scholar 

  8. Moser, J., Eichler, A., Güttinger, J., Dykman, M.I., Bachtold, A.: Nanotube mechanical resonators with quality factors of up to 5 million. Nat. Nanotechnol. 9(12), 1007–1011 (2014)

    ADS  Google Scholar 

  9. Aykol, M., Hou, B.Y., Dhall, R., Chang, S.W., Branham, W., Qiu, J., Cronin, S.B.: Clamping instability and van der Waals forces in carbon nanotube mechanical resonators. Nano Lett. 14(5), 2426–2430 (2014)

    ADS  Google Scholar 

  10. Wang, X., Miranowicz, A., Li, H.R., Nori, F.: Hybrid quantum device with a carbon nanotube and a flux qubit for dissipative quantum engineering. Phys. Rev. B 95(20), 205415 (2017)

    ADS  Google Scholar 

  11. Pályi, A., Struck, P.R., Rudner, M., Flensberg, K., Burkard, G.: Spin-orbit-induced strong coupling of a single spin to a nanomechanical resonator. Phys. Rev. Lett. 108(20), 206811 (2012)

    ADS  Google Scholar 

  12. Chang, K., Eichler, A., Rhensius, J., Lorenzelli, L., Degen, C.L.: Nanoscale imaging of current density with a single-spin magnetometer. Nano Lett. 17(4), 2367–2373 (2017)

    ADS  Google Scholar 

  13. Eichler, A., Ruiz, M.D., Plaza, J.A., Bachtold, A.: Strong coupling between mechanical modes in a nanotube resonator. Phys. Rev. Lett. 109(2), 025503 (2012)

    ADS  Google Scholar 

  14. Darázs, Z., Kurucz, Z., Kálmán, O., Kiss, T., Fortágh, J., Domokos, P.: Parametric amplification of the mechanical vibrations of a suspended nanowire by magnetic coupling to a Bose–Einstein condensate. Phys. Rev. Lett. 112(13), 133603 (2014)

    ADS  Google Scholar 

  15. Muschik, C.A., Moulieras, S., Bachtold, A., Koppens, F.H.L., Lewenstein, M., Chang, D.E.: Harnessing vacuum forces for quantum sensing of graphene motion. Phys. Rev. Lett. 112(22), 223601 (2014)

    ADS  Google Scholar 

  16. Stadler, P., Belzig, W., Rastelli, G.: Ground-state cooling of a carbon nanomechanical resonator by spin-polarized current. Phys. Rev. Lett. 113(4), 047201 (2014)

    ADS  Google Scholar 

  17. Li, P.B., Xiang, Z.L., Rabl, P., Nori, F.: Hybrid quantum device with nitrogen-vacancy centers in diamond coupled to carbon nanotubes. Phys. Rev. Lett. 117(1), 015502 (2016)

    ADS  Google Scholar 

  18. Kálmán, O., Kiss, T., Fortágh, J., Domokos, P.: Quantum galvanometer by interfacing a vibrating nanowire and cold atoms. Nano Lett. 12(1), 435–439 (2012)

    ADS  Google Scholar 

  19. Deng, G.W., Zhu, D., Wang, X.H., Zou, C.L., Wang, J.T., Li, H.O., Cao, G., Liu, D., Li, Y., Xiao, M., Guo, G.C., Jiang, K.L., Dai, X.C., Guo, G.P.: Strongly coupled nanotube electromechanical resonators. Nano Lett. 16(9), 5456–5462 (2016)

    ADS  Google Scholar 

  20. Zhu, D., Wang, X.H., Kong, W.C., Deng, G.W., Wang, J.T., Li, H.O., Cao, G., Xiao, M., Jiang, K.L., Dai, X.C., Guo, G.C., Nori, F., Guo, G.P.: Coherent phonon rabi oscillations with a high-frequency carbon nanotube phonon cavity. Nano Lett. 17(2), 915–921 (2017)

    ADS  Google Scholar 

  21. Bunch, J.S., van der Zande, A.M., Verbridge, S.S., Frank, I.W., Tanenbaum, D.M., Parpia, J.M., Craighead, H.G., McEuen, P.L.: Electromechanical resonators from graphene sheets. Science 315(5811), 490–493 (2007)

    ADS  Google Scholar 

  22. Weber, P., Güttinger, J., Tsioutsios, I., Chang, D.E., Bachtold, A.: Coupling graphene mechanical resonators to superconducting microwave cavities. Nano Lett. 14(5), 2854–2860 (2014)

    ADS  Google Scholar 

  23. Singh, V., Bosman, S.J., Schneider, B.H., Blanter, Y.M., Castellanos-Gomez, A., Steele, G.A.: Optomechanical coupling between a multilayer graphene mechanical resonator and a superconducting microwave cavity. Nat. Nanotechnol. 9(10), 820–824 (2014)

    ADS  Google Scholar 

  24. Bar-Gill, N., Pham, L.M., Jarmola, A., Budker, D., Walsworth, R.L.: Solid-state electronic spin coherence time approaching one second. Nat. Commun. 4, 1743 (2013)

    ADS  Google Scholar 

  25. Hong, S.K., Grinolds, M.S., Maletinsky, P., Walsworth, R.L., Lukin, M.D., Yacoby, A.: Coherent, mechanical control of a single electronic spin. Nano Lett. 12(8), 3920–3924 (2012)

    ADS  Google Scholar 

  26. Doherty, M.W., Manson, N.B., Delaney, P., Jelezko, F., Wrachtrup, J., Hollenberg, L.C.L.: The nitrogen-vacancy colour centre in diamond. Phys. Rep.-Rev. Sect. Phys. Lett. 528(1), 1–45 (2013)

    Google Scholar 

  27. Hanson, R., Awschalom, D.D.: Coherent manipulation of single spins in semiconductors. Nature 453(7198), 1043–1049 (2008)

    ADS  Google Scholar 

  28. Brenneis, A., Gaudreau, L., Seifert, M., Karl, H., Brandt, M.S., Huebl, H., Garrido, J.A., Koppens, F.H.L., Holleitner, A.W.: Ultrafast electronic readout of diamond nitrogen-vacancy centres coupled to graphene. Nat. Nanotechnol. 10(2), 135–139 (2015)

    ADS  Google Scholar 

  29. Childress, L., Dutt, M.V.G., Taylor, J.M., Zibrov, A.S., Jelezko, F., Wrachtrup, J., Hemmer, P.R., Lukin, M.D.: Coherent dynamics of coupled electron and nuclear spin qubits in diamond. Science 314(5797), 281–285 (2006)

    ADS  Google Scholar 

  30. Bourgeois, E., Jarmola, A., Siyushev, P., Gulka, M., Hruby, J., Jelezko, F., Budker, D., Nesladek, M.: Photoelectric detection of electron spin resonance of nitrogen-vacancy centres in diamond. Nat. Commun. 6, 8577 (2015)

    ADS  Google Scholar 

  31. Reserbat-Plantey, A., Schädler, K.G., Gaudreau, L., Navickaite, G., Güttinger, J., Chang, D., Toninelli, C., Bachtold, A., Koppens, F.H.L.: Electromechanical control of nitrogen-vacancy defect emission using graphene NEMS. Nat. Commun. 7, 10218 (2016)

    ADS  Google Scholar 

  32. Ajoy, A., Bissbort, U., Poletti, D., Cappellaro, P.: Selective decoupling and hamiltonian engineering in dipolar spin networks. Phys. Rev. Lett. 122(1), 013205 (2019)

    ADS  Google Scholar 

  33. Steinert, S., Dolde, F., Neumann, P., Aird, A., Naydenov, B., Balasubramanian, G., Jelezko, F., Wrachtrup, J.: High sensitivity magnetic imaging using an array of spins in diamond. Rev. Sci. Instrum. 81(4), 043705 (2010)

    ADS  Google Scholar 

  34. Appel, P., Neu, E., Ganzhorn, M., Barfuss, A., Batzer, M., Gratz, M., Tschöpe, A., Maletinsky, P.: Fabrication of all diamond scanning probes for nanoscale magnetometry. Rev. Sci. Instrum. 87(6), 063703 (2016)

    ADS  Google Scholar 

  35. Togan, E., Chu, Y., Trifonov, A.S., Jiang, L., Maze, J., Childress, L., Dutt, M.V.G., Sørensen, A.S., Hemmer, P.R., Zibrov, A.S., Lukin, M.D.: Quantum entanglement between an optical photon and a solid-state spin qubit. Nature 466(7307), 730–734 (2010)

    ADS  Google Scholar 

  36. Li, P.B., Li, F.L.: Deterministic generation of multiparticle entanglement in a coupled cavity-fiber system. Opt. Express 19(2), 1207–1216 (2011)

    ADS  Google Scholar 

  37. Li, P.B., Gao, S.Y., Li, H.R., Ma, S.L., Li, F.L.: Dissipative preparation of entangled states between two spatially separated nitrogen-vacancy centers. Phys. Rev. A 85(4), 042306 (2012)

    ADS  Google Scholar 

  38. Zhou, Y., Ma, S.L., Li, B., Li, X.X., Li, F.L., Li, P.B.: Simulating the Lipkin–Meshkov–Glick model in a hybrid quantum system. Phys. Rev. A 96(6), 062333 (2017)

    ADS  Google Scholar 

  39. Chen, Q., Yang, W.L., Feng, M., Du, J.F.: Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators. Phys. Rev. A 83(5), 054305 (2011)

    ADS  Google Scholar 

  40. Li, X.X., Li, P.B., Ma, S.L., Li, F.L.: Preparing entangled states between two NV centers via the damping of nanomechanical resonators. Sci. Rep.-UK 7(1), 14116 (2017)

    ADS  Google Scholar 

  41. Dong, Y., Chen, X.-D., Guo, G.-C., Sun, F.-W.: Robust scalable architecture for a hybrid spin-mechanical quantum entanglement system. Phys. Rev. B 100(21), 214103 (2019)

    ADS  Google Scholar 

  42. Chen, X.Y., Yin, Z.Q.: Universal quantum gates between nitrogen-vacancy centers in a levitated nanodiamond. Phys. Rev. A 99(2), 022319 (2019)

    ADS  MathSciNet  Google Scholar 

  43. Cao, P.H., Betzholz, R., Zhang, S.L., Cai, J.M.: Entangling distant solid-state spins via thermal phonons. Phys. Rev. B 96(24), 245418 (2017)

    ADS  Google Scholar 

  44. Dong, L.H., Rong, X., Geng, J.P., Shi, F.Z., Li, Z.K., Duan, C.K., Du, J.F.: Scalable quantum computation scheme based on quantum-actuated nuclear-spin decoherence-free qubits. Phys. Rev. B 96(20), 205149 (2017)

    ADS  Google Scholar 

  45. Li, T., Miranowicz, A., Hu, X., Xia, K., Nori, F.: Quantum memory and gates using a \(\Lambda \)-type quantum emitter coupled to a chiral waveguide. Phys. Rev. A 97(6), 062318 (2018)

    ADS  Google Scholar 

  46. Xu, X.K., Wang, Z.X., Duan, C.K., Huang, P., Wang, P.F., Wang, Y., Xu, N.Y., Kong, X., Shi, F.Z., Rong, X., Du, J.F.: Coherence-protected quantum gate by continuous dynamical decoupling in diamond. Phys. Rev. Lett. 109(7), 070502 (2012)

    ADS  Google Scholar 

  47. Zu, C., Wang, W.B., He, L., Zhang, W.G., Dai, C.Y., Wang, F., Duan, L.M.: Experimental realization of universal geometric quantum gates with solid-state spins. Nature 514(7520), 72 (2014)

    ADS  Google Scholar 

  48. Yang, W.L., An, J.H., Zhang, C.J., Feng, M., Oh, C.H.: Preservation of quantum correlation between separated nitrogen-vacancy centers embedded in photonic-crystal cavities. Phys. Rev. A 87(2), 022312 (2013)

    ADS  Google Scholar 

  49. Lü, X.Y., Xiang, Z.L., Cui, W., You, J.Q., Nori, F.: Quantum memory using a hybrid circuit with flux qubits and nitrogen-vacancy centers. Phys. Rev. A 88(1), 012329 (2013)

    ADS  Google Scholar 

  50. Li, P.-B., Liu, Y.-C., Gao, S.Y., Xiang, Z.-L., Rabl, P., Xiao, Y.-F., Li, F.-L.: Hybrid quantum device based on NV centers in diamond nanomechanical resonators plus superconducting waveguide cavities. Phys. Rev. Appl. 4(4), 044003 (2015)

    ADS  Google Scholar 

  51. Li, B., Li, P.B., Zhou, Y., Liu, J., Li, H.R., Li, F.L.: Interfacing a topological qubit with a spin qubit in a hybrid quantum system. Phys. Rev. Appl. 11(4), 044026 (2019)

    ADS  Google Scholar 

  52. Rabl, P., Cappellaro, P., Dutt, M.V.G., Jiang, L., Maze, J.R., Lukin, M.D.: Strong magnetic coupling between an electronic spin qubit and a mechanical resonator. Phys. Rev. B 79(4), 041302 (2009)

    ADS  Google Scholar 

  53. Rabl, P., Kolkowitz, S.J., Koppens, F.H.L., Harris, J.G.E., Zoller, P., Lukin, M.D.: A quantum spin transducer based on nanoelectromechanical resonator arrays. Nat. Phys. 6(8), 602–608 (2010)

    Google Scholar 

  54. Sørensen, A., Mølmer, K.: Quantum computation with ions in thermal motion. Phys. Rev. Lett. 82(9), 1971–1974 (1999)

    ADS  Google Scholar 

  55. Raussendorf, R., Briegel, H.J.: A one-way quantum computer. Phys. Rev. Lett. 86(22), 5188–5191 (2001)

    ADS  Google Scholar 

  56. Dakić, B., Radonjić, M.: Macroscopic superpositions as quantum ground states. Phys. Rev. Lett. 119(9), 090401 (2017)

    ADS  Google Scholar 

  57. Horodecki, R., Horodecki, P., Horodecki, M., Horodecki, K.: Quantum entanglement. Rev. Mod. Phys. 81(2), 865–942 (2009)

    ADS  MathSciNet  MATH  Google Scholar 

  58. Vedral, V.: The role of relative entropy in quantum information theory. Rev. Mod. Phys. 74(1), 197–234 (2002)

    ADS  MathSciNet  MATH  Google Scholar 

  59. Zhou, L.G., Wei, L.F., Gao, M., Wang, X.B.: Strong coupling between two distant electronic spins via a nanomechanical resonator. Phys. Rev. A 81(4), 042323 (2010)

    ADS  Google Scholar 

  60. Mølmer, K., Sørensen, A.: Multiparticle entanglement of hot trapped ions. Phys. Rev. Lett. 82(9), 1835–1838 (1999)

    ADS  Google Scholar 

  61. Møller, D., Madsen, L.B., Mølmer, K.: Quantum gates and multiparticle entanglement by rydberg excitation blockade and adiabatic passage. Phys. Rev. Lett. 100(17), 170504 (2008)

    ADS  Google Scholar 

  62. Zhang, Z., Duan, L.M.: Generation of massive entanglement through an adiabatic quantum phase transition in a spinor condensate. Phys. Rev. Lett. 111(18), 180401 (2013)

    ADS  Google Scholar 

  63. Duan, L.M., Monroe, C.: Colloquium: quantum networks with trapped ions. Rev. Mod. Phys. 82(2), 1209–1224 (2010)

    ADS  Google Scholar 

  64. Reiter, F., Reeb, D., Sørensen, A.S.: Scalable dissipative preparation of many-body entanglement. Phys. Rev. Lett. 117(4), 040501 (2016)

    ADS  Google Scholar 

  65. Zheng, S.B.: Generation of entangled states for many multilevel atoms in a thermal cavity and ions in thermal motion. Phys. Rev. A 68(3), 035801 (2003)

    ADS  Google Scholar 

  66. Zheng, S.B.: One-step synthesis of multiatom Greenberger–Horne–Zeilinger states. Phys. Rev. Lett. 87(23), 230404 (2001)

    ADS  Google Scholar 

  67. Zhu, S.L., Wang, Z.D., Zanardi, P.: Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity. Phys. Rev. Lett. 94(10), 100502 (2005)

    ADS  MathSciNet  Google Scholar 

  68. Morrison, S., Parkins, A.S.: Dynamical quantum phase transitions in the dissipative Lipkin–Meshkov–Glick model with proposed realization in optical cavity QED. Phys. Rev. Lett. 100(4), 040403 (2008)

    ADS  Google Scholar 

  69. Armata, F., Calajo, G., Jaako, T., Kim, M.S., Rabl, P.: Harvesting multiqubit entanglement from ultrastrong interactions in circuit quantum electrodynamics. Phys. Rev. Lett. 119(18), 183602 (2017)

    ADS  Google Scholar 

  70. Zheng, S.B.: Quantum-information processing and multiatom-entanglement engineering with a thermal cavity. Phys. Rev. A 66(6), 060303 (2002)

    ADS  Google Scholar 

  71. Yang, C.P., Su, Q.P., Zheng, S.B., Han, S.Y.: Generating entanglement between microwave photons and qubits in multiple cavities coupled by a superconducting qutrit. Phys. Rev. A 87(2), 022320 (2013)

    ADS  Google Scholar 

  72. Xia, K.Y., Twamley, J.: Generating spin squeezing states and Greenberger–Horne–Zeilinger entanglement using a hybrid phonon-spin ensemble in diamond. Phys. Rev. B 94(20), 205118 (2016)

    ADS  Google Scholar 

  73. Ashhab, S., Niskanen, A.O., Harrabi, K., Nakamura, Y., Picot, T., de Groot, P.C., Harmans, C.J.P.M., Mooij, J.E., Nori, F.: Interqubit coupling mediated by a high-excitation-energy quantum object. Phys. Rev. B 77(1), 014510 (2008)

    ADS  Google Scholar 

  74. Zhou, Y., Li, B., Li, X.X., Li, F.L., Li, P.B.: Preparing multiparticle entangled states of nitrogen-vacancy centers via adiabatic ground-state transitions. Phys. Rev. A 98(5), 052346 (2018)

    ADS  Google Scholar 

  75. Balasubramanian, G., Neumann, P., Twitchen, D., Markham, M., Kolesov, R., Mizuochi, N., Isoya, J., Achard, J., Beck, J., Tissler, J., Jacques, V., Hemmer, P.R., Jelezko, F., Wrachtrup, J.: Ultralong spin coherence time in isotopically engineered diamond. Nat. Mater. 8(5), 383–387 (2009)

    ADS  Google Scholar 

  76. Kapale, K.T., Dowling, J.P.: Bootstrapping approach for generating maximally path-entangled photon states. Phys. Rev. Lett. 99(5), 053602 (2007)

    ADS  Google Scholar 

  77. Qin, W., Miranowicz, A., Long, G., You, J.Q., Nori, F.: Proposal to test quantum wave-particle superposition on massive mechanical resonators. NPJ Quantum Inf. 5(1), 58 (2019)

    ADS  Google Scholar 

  78. Sørensen, A., Mølmer, K.: Entanglement and quantum computation with ions in thermal motion. Phys. Rev. A 62(2), 022311 (2000)

    ADS  Google Scholar 

  79. Sapmaz, S., Blanter, Y.M., Gurevich, L., van der Zant, H.S.J.: Carbon nanotubes as nanoelectromechanical systems. Phys. Rev. B 67(23), 235414 (2003)

    ADS  Google Scholar 

  80. Poot, M., van der Zant, H.S.J.: Mechanical systems in the quantum regime. Phys. Rep.-Rev. Sect. Phys. Lett. 511(5), 273–335 (2012)

    Google Scholar 

  81. Frank, S., Poncharal, P., Wang, Z.L., de Heer, W.A.: Carbon nanotube quantum resistors. Science 280(5370), 1744–1746 (1998)

    ADS  Google Scholar 

  82. Tsutsui, M., Taninouchi, Y., Kurokawa, S., Sakai, A.: Electrical breakdown of short multiwalled carbon nanotubes. J. Appl. Phys. 100(9), 094302 (2006)

    ADS  Google Scholar 

  83. Yao, Z., Kane, C.L., Dekker, C.: High-field electrical transport in single-wall carbon nanotubes. Phys. Rev. Lett. 84(13), 2941–2944 (2000)

    ADS  Google Scholar 

  84. Collins, P.G., Hersam, M., Arnold, M., Martel, R., Avouris, P.: Current saturation and electrical breakdown in multiwalled carbon nanotubes. Phys. Rev. Lett. 86(14), 3128–3131 (2001)

    ADS  Google Scholar 

  85. Johansson, J.R., Nation, P.D., Nori, F.: QuTiP: an open-source Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 183(8), 1760–1772 (2012)

    ADS  Google Scholar 

  86. Johansson, J.R., Nation, P.D., Nori, F.: QuTiP 2: a Python framework for the dynamics of open quantum systems. Comput. Phys. Commun. 184(4), 1234–1240 (2013)

    ADS  Google Scholar 

  87. Ma, Y., Ding, Q., Wu, E.: Entanglement of two nitrogen-vacancy ensembles via a nanotube. Phys. Rev. A 101(2), 022311 (2020)

    ADS  Google Scholar 

  88. Ohashi, K., Rosskopf, T., Watanabe, H., Loretz, M., Tao, Y., Hauert, R., Tomizawa, S., Ishikawa, T., Ishi-Hayase, J., Shikata, S., Degen, C.L., Itoh, K.M.: Negatively charged nitrogen-vacancy centers in a 5 nm thin 12C diamond film. Nano Lett. 13(10), 4733–4738 (2013)

    ADS  Google Scholar 

  89. Luo, G., Zhang, Z.Z., Deng, G.W., li, H.O., Cao, G., Xiao, M., Guo, G.C., Tian, L., Guo, G.P.: Strong indirect coupling between graphene-based mechanical resonators via a phonon cavity. Nat. Commun. 9, 383 (2018)

  90. Zhang, Z.Z., Song, X.X., Luo, G., Su, Z.J., Wang, K.L., Cao, G., Li, H.O., Xiao, M., Guo, G.C., Tian, L., Deng, G.W., Guo, G.P.: Coherent phonon dynamics in spatially separated graphene mechanical resonators. PNAS 117(11), 5582–5587 (2020)

    ADS  Google Scholar 

  91. Hong, S.W., Banks, T., Rogers, J.A.: Improved density in aligned arrays of single-walled carbon nanotubes by sequential chemical vapor deposition on quartz. Adv. Mater. 22(16), 1826–1830 (2010)

    Google Scholar 

  92. Farrokhabadi, A., Abadian, N., Rach, R., Abadyan, M.: Theoretical modeling of the Casimir force-induced instability in freestanding nanowires with circular cross-section. Physica E 63, 67–80 (2014)

    ADS  Google Scholar 

Download references

Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants No. 11774285, as well as the Fundamental Research Funds for the Central Universities. Part of the simulations are coded in PYTHON using the QuTiP library [85, 86].

Author information

Authors and Affiliations

  1. Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, Department of Applied Physics, Xi’an Jiaotong University, Xi’an, 710049, China

    Bo-Long Wang, Bo Li, Xiao-Xiao Li, Fu-Li Li & Peng-Bo Li

Authors
  1. Bo-Long Wang
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Bo Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Xiao-Xiao Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Fu-Li Li
    View author publications

    You can also search for this author inPubMed Google Scholar

  5. Peng-Bo Li
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Peng-Bo Li.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Wang, BL., Li, B., Li, XX. et al. Generation of multiparticle entangled states of nitrogen-vacancy centers with carbon nanotubes. Quantum Inf Process 19, 223 (2020). https://doi.org/10.1007/s11128-020-02714-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02714-5

Keywords