Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Review Article
  • Published:

Entangled states of trapped atomic ions

Abstract

To process information using quantum-mechanical principles, the states of individual particles need to be entangled and manipulated. One way to do this is to use trapped, laser-cooled atomic ions. Attaining a general-purpose quantum computer is, however, a distant goal, but recent experiments show that just a few entangled trapped ions can be used to improve the precision of measurements. If the entanglement in such systems can be scaled up to larger numbers of ions, simulations that are intractable on a classical computer might become possible.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Ions confined in a trap.
Figure 2: A CNOT-gate operation with two trapped ions.
Figure 3: A two-qubit phase gate.
Figure 4: Entanglement produced by conditional measurements.
Figure 5: Measured density matrices of Bell states.
Figure 6: Multizone trap arrays.

Similar content being viewed by others

References

  1. Ramsey, N. F. Molecular Beams (Clarendon, London, 1956).

    Google Scholar 

  2. Freedman, S. F. & Clauser, J. F. Experimental test of local hidden-variable theories. Phys. Rev. Lett. 28, 938–941 (1972).

    ADS  CAS  Google Scholar 

  3. Aspect, A., Grangier, P. & Roger, G. Experimental tests of realistic local theories via Bell's theorem. Phys. Rev. Lett. 47, 460–463 (1981).

    ADS  CAS  Google Scholar 

  4. Bell, J. S. Speakable and Unspeakable in Quantum Mechanics (Cambridge Univ. Press, Cambridge, UK, 1987).

    MATH  Google Scholar 

  5. Feynman, R. P. Simulating physics with computers. Int. J. Theoret. Phys. 21, 467–468 (1982).

    MathSciNet  Google Scholar 

  6. Deutsch, D. Quantum theory, the Church–Turing principle and the universal quantum computer. Proc. R. Soc. Lond. A 400, 97–117 (1985).

    ADS  MathSciNet  MATH  Google Scholar 

  7. Shor, P. W. Algorithms for quantum computation: discrete logarithms and factoring. In Proc. Annu. Symp. Found. Comput. Sci. 124–134 (1994).

  8. Nielsen, M. A. & Chuang, I. L. Quantum Computation and Quantum Information (Cambridge Univ. Press, Cambridge, UK, 2000).

    MATH  Google Scholar 

  9. Cirac, J. I. & Zoller, P. Quantum computations with cold trapped ions. Phys. Rev. Lett. 74, 4091–4094 (1995).

    ADS  CAS  PubMed  Google Scholar 

  10. Monroe, C. Quantum information processing with atoms and photons. Nature 416, 238–246 (2002).

    ADS  CAS  PubMed  Google Scholar 

  11. Dehmelt, H. Experiments with an isolated subatomic particle at rest. Rev. Mod. Phys. 62, 525–530 (1990).

    ADS  CAS  Google Scholar 

  12. Paul, W. Electromagnetic traps for charged and neutral particles. Rev. Mod. Phys. 62, 531–540 (1990).

    ADS  CAS  Google Scholar 

  13. Bollinger, J. J., Heinzen, D. J., Itano, W. M., Gilbert, S. L. & Wineland, D. J. A 303-MHz frequency standard based on trapped 9Be+ ions. IEEE Trans. Instrum. Meas. 40, 126–128 (1991).

    CAS  Google Scholar 

  14. Fisk, P. T. H. et al. Very high q microwave spectroscopy on trapped 171Yb+ ions: application as a frequencystandard. IEEE Trans. Instrum. Meas. 44, 113–116 (1995).

    CAS  Google Scholar 

  15. Blatt, R., Häffner, H., Roos, C., Becher, C. & Schmidt-Kaler, F. in Quantum Entanglement and Information Processing: Les Houches Session LXXIX (eds Estève, D. Raimond, J.-M. & Dalibard, J.) 223–260 (Elsevier, Amsterdam, 2004).

    Google Scholar 

  16. Wineland, D. J. in Quantum Entanglement and Information Processing: Les Houches Session LXXIX (eds Estève, D. Raimond, J.-M. & Dalibard, J.) 261–293 (Elsevier, Amsterdam, 2004).

    Google Scholar 

  17. Leibfried, D., Blatt, R., Monroe, C. & Wineland, D. Quantum dynamics of single trapped ions. Rev. Mod. Phys. 75, 281–324 (2003).

    ADS  CAS  Google Scholar 

  18. Wineland, D. J. et al. Experimental issues in coherent quantum-state manipulation of trapped atomic ions. J. Res. Natl Inst. Stand. Technol. 103, 259–328 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  19. Diedrich, F., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62, 403–406 (1989).

    ADS  CAS  PubMed  Google Scholar 

  20. Dehmelt, H. G. Mono-ion oscillator as potential ultimate laser frequency standard. IEEE Trans. Instrum. Meas. 31, 83–87 (1982).

    ADS  Google Scholar 

  21. Monroe, C., Meekhof, D. M., King, B. E., Itano, W. M. & Wineland, D. J. Demonstration of a fundamental quantum logic gate. Phys. Rev. Lett. 75, 4714–4717 (1995).

    ADS  MathSciNet  CAS  MATH  PubMed  Google Scholar 

  22. Schmidt-Kaler, F. et al. Realization of the Cirac–Zoller controlled-NOT quantum gate. Nature 422, 408–411 (2003).

    ADS  CAS  PubMed  Google Scholar 

  23. Schmidt-Kaler, F. et al. How to realize a universal quantum gate with trapped ions. Appl. Phys. B 77, 789–796 (2003).

    ADS  CAS  Google Scholar 

  24. Riebe, M. et al. Process tomography of ion trap quantum gates. Phys. Rev. Lett. 97, 220407 (2006).

    ADS  CAS  PubMed  Google Scholar 

  25. Moehring, D. L. et al. Entanglement of single-atom quantum bits at a distance. Nature 449, 68–71 (2007).

    ADS  CAS  PubMed  Google Scholar 

  26. Turchette, Q. A. et al. Deterministic entanglement of two trapped ions. Phys. Rev. Lett. 81, 3631–3634 (1998).

    ADS  CAS  Google Scholar 

  27. Rowe, M. A. et al. Experimental violation of a Bell's inequality with efficient detection. Nature 409, 791–794 (2001).

    ADS  CAS  PubMed  Google Scholar 

  28. Roos, C. F. et al. Bell states of atoms with ultralong life times and their tomographic state analysis. Phys. Rev. Lett. 92, 220402 (2004).

    ADS  CAS  PubMed  Google Scholar 

  29. Sackett, C. A. et al. Experimental entanglement of four particles. Nature 404, 256–259 (2000).

    ADS  CAS  PubMed  Google Scholar 

  30. Clauser, J. F., Horne, M. A., Shimony, A. & Holt, R. A. Proposed experiment to test local hidden-variable theories. Phys. Rev. Lett. 23, 880–884 (1969).

    ADS  MATH  Google Scholar 

  31. Moehring, D. L., Madsen, M. J., Blinov, B. B. & Monroe, C. Experimental Bell inequality violation with an atom and a photon. Phys. Rev. Lett. 93, 090410 (2004).

    ADS  CAS  PubMed  Google Scholar 

  32. Schrödinger, E. Die gegenwärtige Situation in der Quantenmechanik. Naturwissenschaften 23, 807–812 (1935).

    ADS  MATH  Google Scholar 

  33. Greenberger, D. M., Horne, M. A. & Zeilinger, A. in Going Beyond Bell's Theorem (ed. Kafatos, M.) 69–72 (Kluwer Academic, Dordrecht, 1989).

    Google Scholar 

  34. DiVincenzo, D. P. & Shor, P. W. Fault-tolerant error correction withefficient quantum codes. Phys. Rev. Lett. 77, 3260–3263 (1996).

    ADS  CAS  PubMed  Google Scholar 

  35. Steane, A. M. Error correcting codes in quantum theory. Phys. Rev. Lett. 77, 793–797 (1996).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  36. Bollinger, J. J., Itano, W. M., Wineland, D. J. & Heinzen, D. J. Optimal frequency measure-ments with maximally correlated states. Phys. Rev. A 54, R4649–R4652 (1996).

    ADS  CAS  PubMed  Google Scholar 

  37. Leibfried, D. et al. Toward Heisenberg-limited spectroscopy with multiparticle entangled states. Science 304, 1476–1478 (2004).

    ADS  CAS  PubMed  Google Scholar 

  38. Leibfried, D. et al. Creation of a six-atom 'Schrödinger cat' state. Nature 438, 639–642 (2005).

    ADS  CAS  PubMed  Google Scholar 

  39. Roos, C. F. et al. Control and measurement of three-qubit entangled states. Science 304, 1478–1480 (2004).

    ADS  CAS  PubMed  Google Scholar 

  40. Dür, W., Vidal, G. & Cirac, J. I. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A 62, 062314 (2000).

    ADS  MathSciNet  Google Scholar 

  41. Häffner, H. et al. Scalable multiparticle entanglement of trapped ions. Nature 438, 643–646 (2005).

    ADS  PubMed  Google Scholar 

  42. Deutsch, D. & Jozsa, R. Rapid solution of problems by quantum computation. Proc. R. Soc. Lond. A 439, 553–558 (1992).

    ADS  MathSciNet  MATH  Google Scholar 

  43. Chuang, I. L. et al. Experimental realization of a quantum algorithm. Nature 393, 143–146 (1998).

    ADS  CAS  Google Scholar 

  44. Gulde, S. et al. Implementation of the Deutsch–Jozsa algorithm on an ion-trap quantum computer. Nature 421, 48–50 (2003).

    ADS  CAS  PubMed  Google Scholar 

  45. Bennett, C. H. et al. Teleporting an unknown quantum state via dual classical and Einstein–Podolsky-Rosen channels. Phys. Rev. Lett. 70, 1895–1899 (1993).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  46. Barrett, M. D. et al. Deterministic quantum teleportation of atomic qubits. Nature 429, 737–739 (2004).

    ADS  CAS  PubMed  Google Scholar 

  47. Riebe, M. et al. Deterministic quantum teleportation with atoms. Nature 429, 734–737 (2004).

    ADS  CAS  PubMed  Google Scholar 

  48. Reichle, R. et al. Experimental purification of two-atom entanglement. Nature 443, 838–841 (2006).

    ADS  CAS  PubMed  Google Scholar 

  49. Chiaverini, J. et al. Realization of quantum error correction. Nature 432, 602–605 (2004).

    ADS  CAS  PubMed  Google Scholar 

  50. Chiaverini, J. et al. Implementation of the semiclassical quantum Fourier transform in a scalable system. Science 308, 997–1000 (2005).

    ADS  MathSciNet  CAS  PubMed  MATH  Google Scholar 

  51. Grover, L. K. Quantum mechanics helps in searching for a needle in a haystack. Phys. Rev. Lett. 79, 325–328 (1997).

    ADS  CAS  Google Scholar 

  52. Wineland, D. J., Bollinger, J. J., Itano, W. M., Moore, F. L. & Heinzen, D. J. Spin squeezing and reduced quantum noise in spectroscopy. Phys. Rev. A 46, R6797–R6800 (1992).

    ADS  CAS  PubMed  Google Scholar 

  53. Itano, W. M. et al. Quantum projection noise: population fluctuations in two-level systems. Phys. Rev. A 47, 3554–3570 (1993).

    ADS  CAS  PubMed  Google Scholar 

  54. Meyer, V. et al. Experimental demonstration of entanglement-enhanced rotation angle estimation using trapped ions. Phys. Rev. Lett. 86, 5870–5873 (2001).

    ADS  CAS  PubMed  Google Scholar 

  55. Leibfried, D. et al. Trapped-ion quantum simulator: experimental application to nonlinear interferometers. Phys. Rev. Lett. 89, 247901 (2002).

    ADS  CAS  PubMed  Google Scholar 

  56. Huelga, S. F. et al. Improvement of frequency standards with quantum entanglement. Phys. Rev. Lett. 79, 3865–3868 (1997).

    ADS  CAS  Google Scholar 

  57. André, A., Sørensen, A. S. & Lukin, M. D. Stability of atomic clocks based on entangled atoms. Phys. Rev. Lett. 92, 230801 (2004).

    ADS  PubMed  Google Scholar 

  58. Schaetz, T. et al. Enhanced quantum state detection efficiency through quantum information processing. Phys. Rev. Lett. 94, 010501 (2005).

    ADS  CAS  PubMed  Google Scholar 

  59. Hume, D. B., Rosenband, T. & Wineland, D. J. High-fidelity adaptive qubit detection through repetitive quantum nondemolition measurements. Phys. Rev. Lett. 99, 120502 (2007).

    ADS  CAS  PubMed  Google Scholar 

  60. Rosenband, T. et al. Frequency ratio of Al+ and Hg+ single-ion optical clocks; metrology at the 17th decimal place. Science 319, 1808–1812 (2008).

    ADS  CAS  PubMed  Google Scholar 

  61. Guerlin, C. et al. Progressive field-state collapse and quantum non-demolition photon counting. Nature 448, 889–894 (2007).

    ADS  CAS  PubMed  Google Scholar 

  62. Roos, C. F., Chwalla, M., Kim, K., Riebe, M. & Blatt, R. 'Designer atoms' for quantum metrology. Nature 443, 316–319 (2006).

    ADS  CAS  PubMed  Google Scholar 

  63. Benhelm, J., Kirchmair, G., Roos, C. F. & Blatt, R. Towards fault-tolerant quantum computing with trapped ions. Nature Phys. 4, 463–466 (2008).

    ADS  CAS  Google Scholar 

  64. Ozeri, R. et al. Errors in trapped-ion quantumgates due to spontaneous photon scattering. Phys. Rev. A 75, 042329 (2007).

    ADS  Google Scholar 

  65. Zhu, S.-L., Monroe, C. & Duan, L.-M. Arbitrary-speed quantum gates within large ion crystals through miminum control of laser beams. Europhys. Lett. 73, 485–491 (2006).

    ADS  CAS  Google Scholar 

  66. Duan, L.-M. Scaling ion trap quantum computation through fast quantum gates. Phys. Rev. Lett. 93, 100502 (2004).

    ADS  PubMed  Google Scholar 

  67. DeVoe, R. G. Elliptical ion traps and trap arrays for quantum computation. Phys. Rev. A 58, 910–914 (1998).

    ADS  CAS  Google Scholar 

  68. Cirac, J. I. & Zoller, P. A scalable quantum computer with ions in an array of microtraps. Nature 404, 579–581 (2000).

    ADS  CAS  PubMed  Google Scholar 

  69. Kielpinski, D., Monroe, C. & Wineland, D. J. Architecture for a large-scale ion-trap quantum computer. Nature 417, 709–711 (2002).

    ADS  CAS  PubMed  Google Scholar 

  70. Cirac, I., Zoller, P., Kimble, J. & Mabuchi, H. Quantum state transfer and entanglement distribution among distant nodes in a quantum network. Phys. Rev. Lett. 78, 3221–3224 (1997).

    ADS  CAS  Google Scholar 

  71. Duan, L.-M. & Kimble, H. J. Scalable photonic quantum computation through cavity-assisted interactions. Phys. Rev. Lett. 92, 127902 (2004).

    ADS  PubMed  Google Scholar 

  72. Duan, L.-M. et al. Probabilistic quantum gates between remote atoms through interference of optical frequency qubits. Phys. Rev. A 73, 062324 (2006).

    ADS  Google Scholar 

  73. Rowe, M. et al. Transport of quantum states and separation of ions in a dual rf ion trap. Quantum Inform. Comput. 2, 257–271 (2002).

    CAS  MATH  Google Scholar 

  74. Hucul, D. et al. On the transport of atomic ions in linear and multidimensional trap arrays. Preprint at <http://arxiv.org/abs/quant-ph/0702175> (2007).

    Google Scholar 

  75. Huber, G. et al. Transport of ions in a segmented linear Paul trap in printed-circuit-board technology. New J. Phys. 10, 013004 (2008).

    Google Scholar 

  76. Rohde, H. et al. Sympathetic ground-state cooling and coherent manipulation with two-ion crystals. J. Opt. Soc. Am. B 3, S34–S41 (2001).

  77. Blinov, B. B. et al. Sympathetic cooling of trapped Cd+ isotopes. Phys. Rev. A 65, 040304 (2002).

    ADS  Google Scholar 

  78. Barrett, M. D. et al. Sympathetic cooling of 9Be+ and 24Mg+ for quantum logic. Phys. Rev. A 68, 042302 (2003).

    ADS  Google Scholar 

  79. Turchette, Q. A. et al. Heating of trapped ions from the quantum ground state. Phys. Rev. A 61, 063418 (2000).

    ADS  Google Scholar 

  80. Deslauriers, L. et al. Scaling and suppression of anomalous heating in ion traps. Phys. Rev. Lett. 97, 103007 (2006).

    ADS  CAS  PubMed  Google Scholar 

  81. Leibrandt, D., Yurke, B. & Slusher, R. Modeling ion trap thermal noise decoherence. Quant. Inform. Comput. 7, 52–72 (2007).

    MathSciNet  CAS  MATH  Google Scholar 

  82. Labaziewicz, J. et al. Suppression of heating rates in cryogenic surface-electrode ion traps. Phys. Rev. Lett. 100, 013001 (2008).

    ADS  PubMed  Google Scholar 

  83. Stick, D. et al. Ion trap in a semiconductor chip. Nature Phys. 2, 36–39 (2006).

    ADS  CAS  Google Scholar 

  84. Chiaverini, J. et al. Surface-electrode architecture for ion-trap quantum information processing. Quantum Inform. Comput. 5, 419–439 (2005).

    MathSciNet  CAS  MATH  Google Scholar 

  85. Seidelin, S. et al. Microfabricated surface-electrode ion trap for scalable quantum information processing. Phys. Rev. Lett. 96, 253003 (2006).

    ADS  CAS  PubMed  Google Scholar 

  86. Kim, J. et al. System design for large-scale ion trap quantum information processor. Quant. Inform. Comput. 5, 515–537 (2005).

    CAS  MATH  Google Scholar 

  87. Leibfried, D., Knill, E., Ospelkaus, C. & Wineland, D. J. Transport quantum logic gates for trapped ions. Phys. Rev. A 76, 032324 (2007).

    ADS  Google Scholar 

  88. Wunderlich, C. & Balzer, C. Quantum measurements and new concepts for experiments with trapped ions. Adv. At. Mol. Opt. Phys. 49, 293–376 (2003).

    ADS  CAS  Google Scholar 

  89. Porras, D. & Cirac, J. I. Quantum manipulation of trapped ions in two dimensional Coulomb crystals. Phys. Rev. Lett. 96, 250501 (2006).

    ADS  CAS  PubMed  Google Scholar 

  90. Taylor, J. M. & Calarco, T. Wigner crystals of ions as quantum hard drives. Preprint at <http://arxiv.org/abs/0706.1951> (2007).

  91. Chiaverini, J. & Lybarger Jr, W. E. Laserless trapped-ion quantum simulations without spontaneous scattering using microtrap arrays. Phys. Rev. A 77, 022324 (2008).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

  93. Milburn, G. J., Schneider, S. & James, D. F. Ion trap quantum computing with warm ions. Fortschr. Physik 48, 801–810 (2000).

    ADS  CAS  Google Scholar 

  94. Solano, E., de Matos Filho, R. L. & Zagury, N. Mesoscopic superpositions of vibronic collective states of N trapped ions. Phys. Rev. Lett. 87, 060402 (2001).

    ADS  CAS  PubMed  Google Scholar 

  95. Leibfried, D. et al. Experimental demonstration of a robust, high-fidelity geometric two ion-qubit phase gate. Nature 422, 412–415 (2003).

    ADS  CAS  PubMed  Google Scholar 

  96. Haljan, P. C. et al. Entanglement of trapped-ion clock states. Phys. Rev. A 72, 062316 (2005).

    ADS  Google Scholar 

  97. Home, J. P. et al. Deterministic entanglement and tomography of ion spin qubits. New J. Phys. 8, 188 (2006).

    ADS  Google Scholar 

  98. Matsukevich, D. N., Maunz, P., Moehring, D. L., Olmschenk, S. & Monroe, C. Bell inequality violation with two remote atomic qubits. Phys. Rev. Lett. 100, 150404 (2008).

    ADS  CAS  PubMed  Google Scholar 

  99. Hensinger, W. K. et al. T-junction ion trap array for two-dimensional ion shuttling storage, and manipulation. Appl. Phys. Lett. 88, 034101 (2006).

    ADS  Google Scholar 

Download references

Acknowledgements

We thank H. Häffner, J. Home, E. Knill, D. Leibfried, C. Roos and P. Schmidt for comments on the manuscript.

Author information

Authors and Affiliations

Authors

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Correspondence should be addressed to R.B. (Rainer.Blatt@uibk.ac.at).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blatt, R., Wineland, D. Entangled states of trapped atomic ions. Nature 453, 1008–1015 (2008). https://doi.org/10.1038/nature07125

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07125

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing