Skip to main content

Advertisement

Springer Nature Link
Log in

Generation of distributed steady entangled state between two solid-state spins

  • Published:
Quantum Information Processing Aims and scope Submit manuscript

Abstract

The generation of distributed entangled states among solid-state spins is key to the development of large-scale quantum networks and quantum computation. We propose a dissipative scheme for generating stable entanglement between the electron-spin states of two separated nitrogen-vacancy centers, each coupled to a microtoroidal resonator and separated in space. An optical fiber-taper waveguide links the two microtoroidal resonators. Numerical simulations show that spontaneous emission from the NV centers and the collective decay of delocalized field modes can act as effective resources to generate stationary singlet-like states without the need for initialization and precise control of the evolution of the system over time. Results indicate that the proposed scheme can reach high-fidelity and purity of states, and is resilient against small parameter fluctuations. We also discuss how the pure spin dephasing that arises from longitudinal magnetic-near-field noise affects the fidelity of the target state.

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
$34.99 /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 excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

Explore related subjects

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

References

  1. Calderbank, A.R., Shor, P.W.: Good quantum error-correcting codes exist. Phys. Rev. A 54, 1098 (1996)

    ADS  Google Scholar 

  2. Bennett, C.H., DiVincenzo, D.P., Smolin, J.A., Wootters, W.K.: Mixed-state entanglement and quantum error correction. Phys. Rev. A 54, 3824 (1996)

    ADS  MathSciNet  MATH  Google Scholar 

  3. Kosut, R.L., Shabani, A., Lidar, D.A.: Robust quantum error correction via convex optimization. Phys. Rev. Lett. 100, 020502 (2008)

    ADS  Google Scholar 

  4. Moussa, O., Baugh, J., Ryan, C.A., Laflamme, R.: Demonstration of sufficient control for two rounds of quantum error correction in a solid state ensemble quantum information processor. Phys. Rev. Lett. 107, 160501 (2011)

    ADS  Google Scholar 

  5. Reed, M.D., DiCarlo, L., Nigg, S.E., Sun, L., Frunzio, L., Girvin, S.M., Schoelkopf, R.J.: Realization of three-qubit quantum error correction with superconducting circuits. Nature (London) 482, 382 (2012)

    ADS  Google Scholar 

  6. Lidar, D.A., Chuang, I.L., Whaley, K.B.: Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594 (1998)

    ADS  Google Scholar 

  7. Beige, A., Braun, D., Tregenna, B., Knight, P.L.: Quantum computing using dissipation to remain in a decoherence-free subspace. Phys. Rev. Lett. 85, 1762 (2000)

    ADS  Google Scholar 

  8. Kempe, J., Bacon, D., Lidar, D.A., Whaley, K.B.: Theory of decoherence-free fault-tolerant universal quantum computation. Phys. Rev. A 63, 042307 (2001)

    ADS  Google Scholar 

  9. Steane, A.M.: Efficient fault-tolerant quantum computing. Nature (London) 399, 124 (1999)

    ADS  Google Scholar 

  10. Verstraete, F., Wolf, M.M., Cirac, J.I.: Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633 (2009)

    Google Scholar 

  11. Vollbrecht, K.G.H., Muschik, C.A., Cirac, J.I.: Entanglement distillation by dissipation and continuous quantum repeaters. Phys. Rev. Lett. 107, 120502 (2011)

    ADS  Google Scholar 

  12. Pastawski, F., Clemente, L., Cirac, J.I.: Quantum memories based on engineered dissipation. Phys. Rev. A 83, 012304 (2011)

    ADS  Google Scholar 

  13. Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777 (1935)

    ADS  MATH  Google Scholar 

  14. Schrödinger, E.: Die gegenwärtige situation in der quantenmechanik. Naturwissenschaften 23, 823 (1935)

    ADS  MATH  Google Scholar 

  15. Lin, J., Shen, L.-T., Wu, H.-Z., Yang, Z.-B.: Stabilizing a Bell state by engineering collective photon decay. Quantum Inf. Process. 15, 185 (2015)

    ADS  MathSciNet  MATH  Google Scholar 

  16. Plenio, M.B., Huelga, S.F., Beige, A., Knight, P.L.: Cavity-loss-induced generation of entangled atoms. Phys. Rev. A 59, 2468 (1999)

    ADS  Google Scholar 

  17. Clark, S., Peng, A., Gu, M., Parkins, S.: Unconditional preparation of entanglement between atoms in cascaded optical cavities. Phys. Rev. Lett. 91, 177901 (2003)

    ADS  Google Scholar 

  18. Reiter, F., Kastoryano, M.J.S., Sørensen, A.: Driving two atoms in an optical cavity into an steady entangled state using engineered decay. New J. Phys. 14, 053022 (2012)

    ADS  Google Scholar 

  19. Kastoryano, M.J., Reiter, F., Sørensen, A.S.: Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011)

    ADS  Google Scholar 

  20. Busch, J., De, S., Ivanov, S.S., Torosov, B.T., Spiller, T.P., Beige, A.: Cooling atom-cavity systems into entangled states. Phys. Rev. A 84, 022316 (2011)

    ADS  Google Scholar 

  21. Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Steady-state entanglement for distant atoms by dissipation in coupled cavities. Phys. Rev. A 84, 064302 (2011)

    ADS  Google Scholar 

  22. Shen, L.T., Chen, X.Y., Yang, Z.B., Wu, H.Z., Zheng, S.B.: Distributed entanglement induced by dissipative bosonic media. Europhys. Lett. 99, 20003 (2012)

    ADS  Google Scholar 

  23. Su, S.L., Shao, X.Q., Wang, H.F., Zhang, S.: Scheme for entanglement generation in an atom-cavity system via dissipation. Phys. Rev. A 90, 054302 (2014)

    ADS  Google Scholar 

  24. Li, D.X., Shao, X.Q., Wu, J.H., Yi, X.X.: Noise-induced distributed entanglement in atom-cavity-fiber system. Opt. Express 25, 33359 (2017)

    ADS  Google Scholar 

  25. Li, D.X., Shao, X.Q., Wu, J.H., Yi, X.X.: Engineering steady-state entanglement via dissipation and quantum Zeno dynamics, in an optical cavity. Opt. Lett. 42, 3904 (2017)

    ADS  Google Scholar 

  26. Wang, Y., Hu, C.S., Shi, Z.C., Huang, B.H., Song, J., Xia, Y.: Accelerated and noise-resistant protocol of dissipation-based Knill–Laflamme–Milburn state generation with Lyapunov control. Ann. Phys. (Berlin) 531, 1900006 (2019)

    ADS  MathSciNet  Google Scholar 

  27. Borjans, F., Croot, X.G., Mi, X., Gullans, M.J., Petta, J.R.: Resonant microwave-mediated interactions between distant electron spins. Nature 577, 195 (2020)

    ADS  Google Scholar 

  28. Bernien, H., Hensen, B., Pfaff, W., Koolstra, G., Blok, M.S., Robledo, L., Taminiau, T.H., Markham, M., Twitchen, D.J., Childress, L., Hanson, R.: Heralded entanglement between solid-state qubits separated by 3 meters. Nature 497, 86 (2013)

    ADS  Google Scholar 

  29. Maurer, P.C., Kucsko, G., Latta, C., Jiang, L., Yao, N.Y., Bennett, S.D., Pastawski, F., Hunger, D., Chisholm, N., Markham, M., Twitchen, D.J., Cirac, J.I., Lukin, M.D.: Room-temperature quantum bit memory exceeding one second. Science 336, 1283 (2012)

    ADS  Google Scholar 

  30. 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 (London) 466, 730 (2010)

    ADS  Google Scholar 

  31. 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, 383 (2009)

    Google Scholar 

  32. Buckley, B.B., Fuchs, G.D., Bassett, L.C., Awschalom, D.D.: Spin-light coherence for single-spin measurement and control in diamond. Science 330, 1212 (2010)

    ADS  Google Scholar 

  33. Fuchs, G.D., Dobrovitski, V.V., Toyli, D.M., Heremans, F.J., Awschalom, D.D.: Gigahertz dynamics of a strongly driven single quantum spin. Science 326, 1520 (2009)

    ADS  Google Scholar 

  34. Gaebel, T., Domhan, M., Popa, I., Wittmann, C., Neumann, P., Jelezko, F., Rabeau, J.R., Stavrias, N., Greentree, A.D., Prawer, S., Meijer, J., Twamley, J., Hemmer, P.R., Wrachtrup, J.: Room-temperature coherent coupling of single spins in diamond. Nat. Phys. 2, 408 (2006)

    Google Scholar 

  35. Waldherr, G., Wang, Y., Zaiser, S., Jamali, M., SchulteHerbruggen, T., Abe, H., Ohshima, T., Isoya, J., Du, J.F., Neumann, P., Wrachtrup, J.: Quantum error correction in a solid-state hybrid spin register. Nature (London) 506, 204 (2014)

    ADS  Google Scholar 

  36. Robledo, L., Childress, L., Bernien, H., Hensen, B., Alkemade, P.F., Hanson, R.: High-fidelity projective read-out of a solid-state spin quantum register. Nature (London) 477, 574 (2011)

    ADS  Google Scholar 

  37. Neumann, P., Beck, J., Steiner, M., Rempp, F., Fedder, H., Hemmer, P.R., Wrachtrup, J., Jelezko, F.: Single-shot readout of a single nuclear spin. Science 329, 542 (2010)

    ADS  Google Scholar 

  38. Fuchs, G.D., Burkard, G., Klimov, P.V., Awschalom, D.D.: A quantum memory intrinsic to single nitrogen-vacancy centres in diamond. Nat. Phys. 7, 789 (2011)

    Google Scholar 

  39. Shim, J.H., Niemeyer, I., Zhang, J., Suter, D.: Room-temperature high-speed nuclear-spin quantum memory in diamond. Phys. Rev. A 87, 012301 (2013)

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  41. Ren, B.C., Wang, G.Y., Deng, F.G.: Universal hyperparallel hybrid photonic quantum gates with the dipole induced transparency in weak-coupling regime. Phys. Rev. A 91, 032328 (2015)

    ADS  Google Scholar 

  42. Zhou, J., Liu, B.J., Hong, Z.P., Xue, Z.Y.: Fast holonomic quantum computation based on solid-state spins with all-optical control. Sci. China Phys. Mech. Astron. 61, 010312 (2018)

    ADS  Google Scholar 

  43. Doherty, M.W., Manson, N.B., Delaney, P., Hollenberg, L.C.L.: The negatively charged nitrogen-vacancy centre in diamond: the electronic solution. New J. Phys. 13, 025019 (2011)

    ADS  Google Scholar 

  44. Hensen, B., Bernien, H., Dréau, A.E., Reiserer, A., Kalb, N., Blok, M.S., Ruitenberg, J., Vermeulen, R.F.L., Schouten, R.N., Abellán, C., Amaya, W., Pruneri, V., Mitchell, M.W., Markham, M., Twitchen, D.J., Elkouss, D., Wehner, S., Taminiau, T.H., Hanson, R.: Loophole-free Bell inequality violation using electron spins separated by 1.3 kilometres. Nature 526, 682 (2015)

    ADS  Google Scholar 

  45. Park, Y.S., Cook, A.K., Wang, H.: Cavity QED with diamond nanocrystals and silica microspheres. Nano Lett. 6, 2075 (2006)

    ADS  Google Scholar 

  46. Larsson, M., Dinyari, K.N., Wang, H.: Composite optical microcavity of diamond nanopillar and silica microsphere. Nano Lett. 9, 1447 (2009)

    ADS  Google Scholar 

  47. Cheng, L.Y., Wang, H.F., Zhang, S., Yeon, K.H.: Quantum state engineering with nitrogen-vacancy centers coupled to low-Q microresonator. Opt. Express 21, 5988 (2013)

    ADS  Google Scholar 

  48. Barclay, P.E., Fu, K.M.C., Santori, C., Beausoleil, R.G.: Chip-based microcavities coupled to nitrogenvacancy centers in single crystal diamond. Appl. Phys. Lett. 95, 191115 (2009)

    ADS  Google Scholar 

  49. McCutcheon, M.W., Lončar, M.: Design of a silicon nitride photonic crystal nanocavity with a Quality factor of one million for coupling to a diamond nanocrystal. Opt. Express 16, 19136 (2008)

    ADS  Google Scholar 

  50. Acharyya, N., Kozyreff, G.: Large Q factor with very small whispering-gallery-mode resonators. Phys. Rev. Appl. 12, 014060 (2019)

    ADS  Google Scholar 

  51. Armani, D.K., Kippenberg, T.J., Spillane, S.M., Vahala, K.J.: Ultra-high-Q toroid microcavity on a chip. Nature 421, 925 (2003)

    ADS  Google Scholar 

  52. Kippenberg, T.J., Spillane, S.M., Vahala, K.J.: Demonstration of ultra-high-Q small mode volume toroid microcavities on a chip. Appl. Phys. Lett. 85, 61115 (2004)

    Google Scholar 

  53. Gramotnev, D.K., Bozhevolnyi, S.I.: Plasmonics beyond the diffraction limit. Nat. Photon. 4, 91 (2010)

    ADS  Google Scholar 

  54. Shen, Z., Zhou, Z.H., Zou, C.L., Sun, F.W., Guo, G.P., Dong, C.H., Guo, G.C.: Observation of high-Q optomechanical modes in the mounted silica microspheres. Photon. Res. 3, 243 (2015)

    Google Scholar 

  55. Jiang, X.F., Shao, L.B., Zhang, S.X., Yi, X., Wiersig, J., Wang, L., Gong, Q.H., Lončar, M., Yang, L., Xiao, Y.F.: Chaos-assisted broadband momentum transformation in optical microresonators. Science 358, 344 (2017)

    ADS  Google Scholar 

  56. Suh, M.G., Yang, Q.F., Yang, K.Y., Yi, X., Vahala, K.J.: Microresonator soliton dual-comb spectroscopy. Science 354, 600 (2016)

    ADS  Google Scholar 

  57. Tian, Z., Li, S.L., Kiravittaya, S., Xu, B.R., Tang, S.W., Zhen, H.L., Lu, W., Mei, Y.F.: Selected and enhanced single whispering-gallery mode emission from a mesostructured nanomembrane microcavity. Nano Lett. 18, 8035 (2018)

    ADS  Google Scholar 

  58. 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, 042306 (2012)

    ADS  Google Scholar 

  59. Yang, W.L., Yin, Z.Q., Xu, Z.Y., Feng, M., Oh, C.H.: Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities. Phys. Rev. A 84, 043849 (2011)

    ADS  Google Scholar 

  60. Jin, Z., Su, S.L., Zhang, S.: Preparation of a steady entangled state of two nitrogen-vacancy centers by simultaneously utilizing two dissipative factors. Phys. Rev. A 100, 052332 (2019)

    ADS  Google Scholar 

  61. Li, P.B., Gao, S.Y., Li, F.L.: Quantum information transfer with nitrogen-vacancy centers coupled to a whispering-gallery microresonator. Phys. Rev. A 83, 054306 (2011)

    ADS  Google Scholar 

  62. Yi, X., Xiao, Y.F., Liu, Y.C., Li, B.B., Chen, Y.L., Li, Y., Gong, Q.: Multiple-Rayleigh–Scatterer-induced mode splitting in a high-Q whispering-gallery-mode microresonator. Phys. Rev. A 83, 023803 (2011)

    ADS  Google Scholar 

  63. Yale, C.G., Buckley, B.B., Christle, D.J., Burkard, G., Heremans, F.J., Bassett, L.C., Awschalom, D.D.: All-optical control of a solid-state spin using coherent dark states. Proc. Natl. Acad. Sci. USA 110, 7595 (2013)

    ADS  Google Scholar 

  64. Santori, C., Tamarat, P., Neumann, P., Wrachtrup, J., Fattal, D., Beausoleil, J.R., Olivero, P., Greentree, A., Prawer, S., Jelezko, F., Hemmer, P.: Coherent population trapping of single spins in diamond under optical excitation. Phys. Rev. Lett. 97, 247401 (2006)

    ADS  Google Scholar 

  65. Manson, N.B., Harrison, J.P., Sellars, M.J.: Nitrogen-vacancy center in diamond: model of the electronic structure and associated dynamics. Phys. Rev. B 74, 104303 (2006)

    ADS  Google Scholar 

  66. Serafini, A., Mancini, S., Bose, S.: Distributed quantum computation via optical fibers. Phys. Rev. Lett. 96, 010503 (2006)

    ADS  Google Scholar 

  67. Reiter, F., Sørensen, A.S.: Effective operator formalism for open quantum systems. Phys. Rev. A 85, 032111 (2012)

    ADS  Google Scholar 

  68. Knill, E., Laflamme, R., Milburn, G.J.: A scheme for efficient quantum computation with linear optics. Nature 409, 46 (2001)

    ADS  Google Scholar 

  69. Shen, C.P., Gao, Y., Su, S.L., Liang, E., Mao, Y., Chen, S.: Mutual conversions between Knill–Laflamme–Milburn and W states. Ann. Phys. (Berlin) 530, 1800114 (2018)

    ADS  Google Scholar 

  70. Shen, C.P., Xiu, X.-M., Dong, L., Zhu, X.-Y., Chen, L., Liang, E., Yan, L.-L., Su, S.L.: Conversion of Knill–Laflamme–Milburn entanglement to Greenberger–Horne–Zeilinger entanglement. Ann. Phys. (Berlin) 531, 1900160 (2019)

    ADS  Google Scholar 

  71. Park, Y.S., Cook, A.K., Wang, H.: Cavity QED with diamond nanocrystals and silica microspheres. Nano Lett. 6, 2075 (2006)

    ADS  Google Scholar 

  72. Dayan, B., Parkins, A.S., Aoki, T., Ostby, E.P., Vahala, K.I., Kimble, H.J.: A photon turnstile dynamically regulated by one atom. Science 319, 1062 (2008)

    ADS  Google Scholar 

  73. Yin, Z.Q., Xu, Z.Y., Feng, M., Du, J.F.: One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity. Appl. Phys. Lett. 96, 241113 (2010)

    ADS  Google Scholar 

  74. Spillane, S.M., Kippenberg, T.J., Painter, O.J., Vahala, K.J.: Ideality in a fiber-taper-coupled microresonator system for application to cavity quantum electrodynamics. Phys. Rev. Lett. 91, 043902 (2003)

    ADS  Google Scholar 

  75. Spillane, S.M., Kippenberg, T.J., Vahala, K.J., Goh, K.W., Wilcut, E., Kimble, H.J.: Ultrahigh-Q toroidal microresonators for cavity quantum electrodynamics. Phys. Rev. A 71, 013817 (2005)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Sciences, Northeastern University, Shenyang, 110819, China

    Zhao Jin

  2. Department of Physics, College of Science, Yanbian University, Yanji, 133002, Jilin, China

    Ai-Dong Zhu & Shou Zhang

  3. School of Materials Science and Engineering, State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang, 110819, China

    Yang Qi

  4. School of Physics, Zhengzhou University, Zhengzhou, 450001, China

    S.-L. Su

Authors
  1. Zhao Jin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ai-Dong Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shou Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yang Qi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S.-L. Su
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhao Jin.

Additional information

Publisher's Note

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

This work was supported by the National Natural Science Foundations of China under Grants Nos. 11804308, 11747096, China Postdoctoral Science Foundation under Grant No. 2018T110735, and Basal Research Fund under Grant No. 02060022120009.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Jin, Z., Zhu, AD., Zhang, S. et al. Generation of distributed steady entangled state between two solid-state spins. Quantum Inf Process 19, 318 (2020). https://doi.org/10.1007/s11128-020-02812-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11128-020-02812-4

Keywords

Search

Navigation