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Applied Physics B

, 122:89 | Cite as

A quantum repeater node with trapped ions: a realistic case example

  • A. D. Pfister
  • M. Salz
  • M. Hettrich
  • U. G. Poschinger
  • F. Schmidt-Kaler
Article
Part of the following topical collections:
  1. Quantum Repeaters: From Components to Strategies

Abstract

We evaluate the feasibility of the implementation of two quantum repeater protocols with an existing experimental platform based on a \(^{40}\hbox {Ca}^+\)-ion in a segmented microtrap, and a third one that requires small changes to the platform. A fiber cavity serves as an ion–light interface. Its small mode volume allows for a large coupling strength of \(g_c = 2 \pi \times 20\) MHz despite comparatively large losses \(\kappa = 2\pi \times 18.3\) MHz. With a fiber diameter of \(125\,\upmu \hbox {m}\), the cavity is integrated into the microstructured ion trap, which in turn is used to transport single ions in and out of the interaction zone in the fiber cavity. We evaluate the entanglement generation rate for a given fidelity using parameters from the experimental setup. The DLCZ protocol (Duan et al. in 414:413–418, 2001) and the hybrid protocol (van Loock et al. in 96:240501, 2006) outperform the EPR protocol (Sangouard et al. in 15(8):085004, 2013). We calculate rates of more than \(100\,\hbox {s}^{-1}\) for non-local Bell state fidelities larger than 0.95 with the existing platform. We identify parameters which mainly limit the attainable rates, and conclude that entanglement generation rates of \(750\,\hbox {s}^{-1}\) at fidelities of 0.95 are within reach with current technology.

Keywords

Success Probability Bell State Stationary Qubit Mode Match Hybrid Protocol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank Peter van Loock, Denis Gonta and Pascal Eich for helpful discussions. We acknowledge financial support by the European commission within the IP SIQS and by the Bundesministerium für Bildung und Forschung via IKT 2020 (Q.com).

References

  1. 1.
    L.-M. Duan, M.D. Lukin, J.I. Cirac, P. Zoller, Long-distance quantum communication and with atomic ensembles and linear optics. Nature 414, 413–418 (2001)ADSCrossRefGoogle Scholar
  2. 2.
    P. van Loock, T.D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W.J. Munro, Y. Yamamoto, Hybrid quantum repeater using bright coherent light. Phys. Rev. Lett. 96, 240501 (2006)CrossRefGoogle Scholar
  3. 3.
    N. Sangouard, J.-D. Bancal, P. Müller, J. Ghosh, J. Eschner, Heralded mapping of photonic entanglement into single atoms in free space: proposal for a loophole-free Bell test. New J. Phys. 15(8), 085004 (2013)ADSCrossRefGoogle Scholar
  4. 4.
    W.K. Wooters, W.H. Zurek, A single quantum cannot be cloned. Nature 229, 802–803 (1982)ADSCrossRefGoogle Scholar
  5. 5.
    C.H. Bennett, G. Brassard, Quantum cryptography: Public key distribution and coin tossing, in Proceedings of the IEEE International Conference on Computers, Systems, and Signal Processing (1984), p. 175Google Scholar
  6. 6.
    A.K. Ekert, Quantum cryptography based on Bell’s theorem. Phys. Rev. Lett. 67, 661–663 (1991)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
  8. 8.
    MagiQ Technologies. http://www.magiqtech.com/
  9. 9.
    X.-S. Ma, T. Herbst, T. Scheidl, D. Wang, S. Kropatschek, W. Naylor, B. Wittmann, A. Mech, J. Kofler, E. Anisimova, V. Makarov, T. Jennewein, R. Ursin, A. Zeilinger, Quantum teleportation over 143 kilometres using active feed-forward. Nature 489(7415), 269–273 (2012)ADSCrossRefGoogle Scholar
  10. 10.
    G. Vallone, D. Bacco, D. Dequal, S. Gaiarin, V. Luceri, G. Bianco, P. Villoresi, Experimental satellite quantum communications. Phys. Rev. Lett. 115, 040502 (2015)ADSCrossRefGoogle Scholar
  11. 11.
    H.-J. Briegel, W. Dür, J.I. Cirac, P. Zoller, Quantum repeaters: the role of imperfect local operations in quantum communication. Phys. Rev. Lett. 81, 5932–5935 (1998)ADSCrossRefGoogle Scholar
  12. 12.
    C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, W.K. Wootters, Purification of noisy entanglement and faithful teleportation via noisy channels. Phys. Rev. Lett. 76, 722–725 (1996)ADSCrossRefGoogle Scholar
  13. 13.
    A.R. Calderbank, P.W. Shor, Good quantum error-correcting codes exist. Phys. Rev. A 54(2), 1098–1105 (1996)ADSCrossRefGoogle Scholar
  14. 14.
    R. Reichle, D. Leibfried, E. Knill, J. Britton, R.B. Blakestad, J.D. Jost, C. Langer, R. Ozeri, S. Seidelin, D.J. Wineland, Experimental purification of two-atom entanglement. Nature 443(7113), 838–841 (2006)ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    B.M. Terhal, Quantum error correction for quantum memories. Rev. Mod. Phys. 87(2), 307–346 (2015)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    W.J. Munro, A.M. Stephens, S.J. Devitt, K.A. Harrison, K. Nemoto, Quantum communication without the necessity of quantum memories. Nat. Photonics 6(11), 777–781 (2012)ADSCrossRefGoogle Scholar
  17. 17.
    S. Pirandola, J. Eisert, C. Weedbrook, A. Furusawa, S.L. Braunstein, Advances in quantum teleportation. ArXiv e-prints arxiv:1505.07831 (2015)
  18. 18.
    A. Kuzmich, W.P. Bowen, A.D. Boozer, A. Boca, C.W. Chou, L.-M. Duan, H.J. Kimble, Generation of nonclassical photon pairs for scalable quantum communication with atomic ensembles. Nature 423(6941), 731–734 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    L.-M. Duan, C. Monroe, Colloquium: quantum networks with trapped ions. Rev. Mod. Phys. 82(2), 1209–1224 (2010)ADSCrossRefGoogle Scholar
  20. 20.
    S. Ritter, C. Nolleke, C. Hahn, A. Reiserer, A. Neuzner, M. Uphoff, M. Mucke, E. Figueroa, J. Bochmann, G. Rempe, An elementary quantum network of single atoms in optical cavities. Nature 484(7393), 195–200 (2012)ADSCrossRefGoogle Scholar
  21. 21.
    D. Hucul, I.V. Inlek, G. Vittorini, C. Crocker, S. Debnath, S.M. Clark, C. Monroe, Modular entanglement of atomic qubits using photons and phonons. Nat. Phys. 11(1), 37–42 (2014)CrossRefGoogle Scholar
  22. 22.
    D. Press, T.D. Ladd, B. Zhang, Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses. Nature 456(7219), 218–221 (2008)ADSCrossRefGoogle Scholar
  23. 23.
    M. Gschrey, A. Thoma, P. Schnauber, M. Seifried, R. Schmidt, B.Wohlfeil, L. Kruger, J.-H. Schulze, T. Heindel, S. Burger, F.Schmidt, A. Strittmatter, S. Rodt, S. Reitzenstein, Highly indistinguishable photons from deterministic quantum-dot microlenses utilizing three-dimensional in situ electron-beam lithography. Nat. Commun. 6, 8662 (1976)Google Scholar
  24. 24.
    A.B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, R. Blatt, Coupling a single atomic quantum bit to a high finesse optical cavity. Phys. Rev. Lett. 89, 103001 (2002)ADSCrossRefGoogle Scholar
  25. 25.
    M. Steiner, H.M. Meyer, J. Reichel, M. Köhl, Photon emission and absorption of a single ion coupled to an optical-fiber cavity. Phys. Rev. Lett. 113, 263003 (2014)ADSCrossRefGoogle Scholar
  26. 26.
    B. Casabone, K. Friebe, B. Brandstätter, K. Schüppert, R. Blatt, T.E. Northup, Enhanced quantum interface with collective ion-cavity coupling. Phys. Rev. Lett. 114, 023602 (2015)ADSCrossRefGoogle Scholar
  27. 27.
    R. Ikuta, Y. Kusaka, T. Kitano, H. Kato, T. Yamamoto, M. Koashi, N. Imoto, Wide-band quantum interface for visible-to-telecommunication wavelength conversion. Nat. Commun. 2, 1544 (2011)CrossRefGoogle Scholar
  28. 28.
    S. Zaske, A. Lenhard, C.A. Keßler, J. Kettler, C. Hepp, C. Arend, R. Albrecht, W.-M. Schulz, M. Jetter, P. Michler, C. Becher, Visible-to-telecom quantum frequency conversion of light from a single quantum emitter. Phys. Rev. Lett. 109, 147404 (2012)ADSCrossRefGoogle Scholar
  29. 29.
    G. Brassard, L. Salvail, Secret-key reconciliation by public discussion. in Advances in Cryptology—EUROCRYPT’93, ed. by T. Helleseth (Springer, 1994), pp. 410–423Google Scholar
  30. 30.
    C.H. Bennett, G. Brassard, J.-M. Robert, Privacy amplification by public discussion. SIAM J. Comput. 17(2), 210–229 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, A. Sanpera, Quantum privacy amplification and the security of quantum cryptography over noisy channels. Phys. Rev. Lett. 77, 2818–2821 (1996)ADSCrossRefGoogle Scholar
  32. 32.
    S. Lloyd, M.S. Shahriar, J.H. Shapiro, P.R. Hemmer, Long distance, unconditional teleportation of atomic states via complete Bell state measurements. Phys. Rev. Lett. 87, 167903 (2001)ADSCrossRefGoogle Scholar
  33. 33.
    C. Cabrillo, J.I. Cirac, P. Garcia-Fernandez, P. Zoller, Creation of entangled states of distant atoms by interference. Phys. Rev. A 59, 1025–1033 (1999)ADSCrossRefGoogle Scholar
  34. 34.
    C. Simon, W.T.M. Irvine, Robust long-distance entanglement and a loophole-free Bell test with ions and photons. Phys. Rev. Lett. 91, 110405 (2003)ADSCrossRefGoogle Scholar
  35. 35.
    C. Kurz, M. Schug, P. Eich, J. Huwer, P. Müller, J. Eschner, Experimental protocol for high-fidelity heralded photon-to-atom quantum state transfer. Nat. Commun. 5, 5527 (2014)ADSCrossRefGoogle Scholar
  36. 36.
    M. Schug, C. Kurz, P. Eich, J. Huwer, P. Müller, J. Eschner, Quantum interference in the absorption and emission of single photons by a single ion. Phys. Rev. A 90, 023829 (2014)ADSCrossRefGoogle Scholar
  37. 37.
    A. Stute, B. Casabone, P. Schindler, T. Monz, P.O. Schmidt, B. Brandstätter, T.E. Northup, R. Blatt, Tunable ion-photon entanglement in an optical cavity. Nature 485(7399), 482–485 (2012)ADSCrossRefGoogle Scholar
  38. 38.
    S. Zippilli, G.A. Olivares-Rentera, G. Morigi, C. Schuck, F. Rohde, J. Eschner, Entanglement of distant atoms by projective measurement: the role of detection efficiency. New J. Phys. 10(10), 103003 (2008)ADSCrossRefGoogle Scholar
  39. 39.
    T.D. Ladd, P. van Loock, K. Nemoto, W.J. Munro, Y. Yamamoto, Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light. New J. Phys. 8(9), 184 (2006)ADSCrossRefGoogle Scholar
  40. 40.
    P. van Loock, N. Lütkenhaus, W.J. Munro, K. Nemoto, Quantum repeaters using coherent-state communication. Phys. Rev. A 78, 062319 (2008)ADSCrossRefGoogle Scholar
  41. 41.
    C.H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, W.K. Wootters, Teleporting an unknown quantum state via dual classical and Einstein–Podolsky–Rosen channels. Phys. Rev. Lett. 70(13), 1895–1899 (1993)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    M. Riebe, T. Monz, K. Kim, A.S. Villar, P. Schindler, M. Chwalla, M. Hennrich, R. Blatt, Deterministic entanglement swapping with an ion-trap quantum computer. Nat. Phys. 4(11), 839–842 (2008)CrossRefGoogle Scholar
  43. 43.
    S.A. Schulz, U. Poschinger, F. Ziesel, F. Schmidt-Kaler, Sideband cooling and coherent dynamics in a microchip multi-segmented ion trap. New J. Phys. 10(4), 045007 (2008)ADSCrossRefGoogle Scholar
  44. 44.
    U.G. Poschinger, G. Huber, F. Ziesel, M. Deiss, M. Hettrich, S.A. Schulz, G. Poulsen, M. Drewsen, R.J. Hendricks, K. Singer, F. Schmidt-Kaler, Coherent manipulation of a \(^{40}\)Ca\(^+\) spin qubit in a micro ion trap. J. Phys. B 42, 154013 (2009)ADSCrossRefGoogle Scholar
  45. 45.
    S. Schulz, U. Poschinger, K. Singer, F. Schmidt-Kaler, Optimization of segmented linear Paul traps and transport of stored particles. Fortschr. Phys. 54(8–10), 648–665 (2006)CrossRefGoogle Scholar
  46. 46.
    D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T.W. Hänsch, J. Reichel, A fiber Fabry–Pérot cavity with high finesse. New J. Phys. 12(6), 065038 (2010)ADSCrossRefGoogle Scholar
  47. 47.
    A. Walther, F. Ziesel, T. Ruster, S.T. Dawkins, K. Ott, M. Hettrich, K. Singer, F. Schmidt-Kaler, U. Poschinger, Controlling fast transport of cold trapped ions. Phys. Rev. Lett. 109, 080501 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    R. Bowler, J. Gaebler, Y. Lin, T.R. Tan, D. Hanneke, J.D. Jost, J.P. Home, D. Leibfried, D.J. Wineland, Coherent diabatic ion transport and separation in a multizone trap array. Phys. Rev. Lett. 109, 080502 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    H. Kaufmann, T. Ruster, C.T. Schmiegelow, F. Schmidt-Kaler, U.G. Poschinger, Dynamics and control of fast ion crystal splitting in segmented paul traps. New J. Phys. 16(7), 073012 (2014)ADSCrossRefGoogle Scholar
  50. 50.
    T. Ruster, C. Warschburger, H. Kaufmann, C.T. Schmiegelow, A. Walther, M. Hettrich, A. Pfister, V. Kaushal, F. Schmidt-Kaler, U.G. Poschinger, Experimental realization of fast ion separation in segmented paul traps. Phys. Rev. A 90, 033410 (2014)ADSCrossRefGoogle Scholar
  51. 51.
    P. Schindler, D. Nigg, T. Monz, J.T. Barreiro, E. Martinez, S.X. Wang, S. Quint, M.F. Brandl, V. Nebendahl, C.F. Roos, M. Chwalla, M. Hennrich, R. Blatt, A quantum information processor with trapped ions. New J. Phys. 15(12), 123012 (2013)ADSCrossRefGoogle Scholar
  52. 52.
    D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W.M. Itano, B. Jelenkovic, C. Langer, T. Rosenband, D.J. Wineland, Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422(6930), 412–415 (2003)ADSCrossRefGoogle Scholar
  53. 53.
    Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, J. Reichel, Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip. Nature 450(7167), 272–276 (2007)ADSCrossRefGoogle Scholar
  54. 54.
    B. Brandstätter, A. McClung, K. Schüppert, B. Casabone, K. Friebe, A. Stute, P.O. Schmidt, C. Deutsch, J. Reichel, R. Blatt, T.E. Northup, Integrated fiber-mirror ion trap for strong ion-cavity coupling. Rev. Sci. Instrum. 84, 123104 (2013)ADSCrossRefGoogle Scholar
  55. 55.
    M. Harlander, M. Brownnutt, W. Hänsel, R. Blatt, Trapped-ion probing of light-induced charging effects on dielectrics. New J. Phys. 12(9), 093035 (2010)ADSCrossRefGoogle Scholar
  56. 56.
    P.F. Herskind, S.X. Wang, M. Shi, Y. Ge, M. Cetina, I.L. Chuang, Microfabricated surface ion trap on a high-finesse optical mirror. Opt. Lett. 36(16), 3045 (2011)ADSCrossRefGoogle Scholar
  57. 57.
    M. Brownnutt, M. Kumph, P. Rabl, R. Blatt, Ion-trap measurements of electric-field noise near surface. ArXiv e-prints arXiv:1409.6572 (2014)
  58. 58.
    J. Gallego, S. Ghosh, S.K. Alavi, W. Alt, M. Martinez-Dorantes, D. Meschede, L. Ratschbacher, High finesse fiber Fabry-Perot cavities: stabilization and mode matching analysis. arxiv:1508.05289 (2015)
  59. 59.
    D. Meschede, Optik, Licht und Laser (Lehrbuch Physik, Teubner, 2005)CrossRefGoogle Scholar
  60. 60.
    C.J. Hood, H.J. Kimble, J. Ye, Characterization of high-finesse mirrors: loss, phase shifts, and mode structure in an optical cavity. Phys. Rev. A 64, 033804 (2001)ADSCrossRefGoogle Scholar
  61. 61.
    C. Schuck, F. Rohde, N. Piro, M. Almendros, J. Huwer, M.W. Mitchell, M. Hennrich, A. Haase, F. Dubin, J. Eschner, Resonant interaction of a single atom with single photons from a down-conversion source. Phys. Rev. A 81, 011802 (2010)ADSCrossRefGoogle Scholar
  62. 62.
    J. Huwer, J. Ghosh, N. Piro, M. Schug, F. Dubin, J. Eschner, Photon entanglement detection by a single atom. New J. Phys. 15(2), 025033 (2013)ADSCrossRefGoogle Scholar
  63. 63.
    C. Kurz, Quantum networking with single ions and single photons interfaced in free space. Ph.D. thesis, Universität des Saarlandes, Saarbrücken (2015)Google Scholar
  64. 64.
    H.G. Barros, A. Stute, T.E. Northup, C. Russo, P.O. Schmidt, R. Blatt, Deterministic single-photon source from a single ion. New J. Phys. 11(10), 103004 (2009)ADSCrossRefGoogle Scholar
  65. 65.
    R.H. Hadfield, Single-photon detectors for optical quantum information applications. Nat. Photonics 3(12), 696–705 (2009)ADSCrossRefGoogle Scholar
  66. 66.
    M. Dusek, M. Jahma, N. Lütkenhaus, Unambiguous state discrimination in quantum cryptography with weak coherent states. Phys. Rev. A 62, 022306 (2000)ADSCrossRefGoogle Scholar
  67. 67.
    N. Sangouard, C. Simon, H. de Riedmatten, N. Gisin, Quantum repeaters based on atomic ensembles and linear optics. Rev. Mod. Phys. 83, 33–80 (2011)ADSCrossRefGoogle Scholar
  68. 68.
    L.-S. Ma, P. Jungner, J. Ye, J.L. Hall, Delivering the same optical frequency at two places: accurate cancellation of phase noise introduced by an optical fiber or other time-varying path. Opt. Lett. 19(21), 1777 (1994)ADSCrossRefGoogle Scholar
  69. 69.
    J. Minàř, H. de Riedmatten, C. Simon, H. Zbinden, N. Gisin, Phase-noise measurements in long-fiber interferometers for quantum-repeater applications. Phys. Rev. A 77, 052325 (2008)ADSCrossRefGoogle Scholar
  70. 70.
    H. Jiang, F. Kflian, S. Crane, O. Lopez, M. Lours, J. Millo, D. Holleville, P. Lemonde, C. Chardonnet, A. Amy-Klein et al., Long-distance frequency transfer over an urban fiber link using optical phase stabilization. J. Opt. Soc. Am. B 25(12), 2029 (2008)ADSCrossRefGoogle Scholar
  71. 71.
    L.-M. Duan, G. Giedke, J.I. Cirac, P. Zoller, Entanglement purification of Gaussian continuous variable quantum states. Phys. Rev. Lett. 84, 4002–4005 (2000)ADSCrossRefzbMATHGoogle Scholar
  72. 72.
    J.-W. Pan, C. Simon, C. Brukner, A. Zeilinger, Entanglement purification for quantum communication. Nature 410(6832), 1067–1070 (2001)ADSCrossRefGoogle Scholar
  73. 73.
    H. Häffner, F. Schmidt-Kaler, W. Hänsel, C. Roos, T. Körber, M. Chwalla, M. Riebe, J. Benhelm, U. Rapol, C. Becher, R. Blatt, Robust entanglement. Appl. Phys. B 81(2–3), 151–153 (2005)ADSCrossRefGoogle Scholar
  74. 74.
    P. Schindler, J.T. Barreiro, T. Monz, V. Nebendahl, D. Nigg, M. Chwalla, M. Hennrich, R. Blatt, Experimental repetitive quantum error correction. Science 332(6033), 1059–1061 (2011)ADSCrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.QUANTUM, Institut für PhysikJohannes Gutenberg UniversitätMainzGermany

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