Letter | Published:

Atomic homodyne detection of continuous-variable entangled twin-atom states

Nature volume 480, pages 219223 (08 December 2011) | Download Citation

Abstract

Historically, the completeness of quantum theory has been questioned using the concept of bipartite continuous-variable entanglement1. The non-classical correlations (entanglement) between the two subsystems imply that the observables of one subsystem are determined by the measurement choice on the other, regardless of the distance between the subsystems. Nowadays, continuous-variable entanglement is regarded as an essential resource, allowing for quantum enhanced measurement resolution2, the realization of quantum teleportation3,4,5 and quantum memories3,6, or the demonstration of the Einstein–Podolsky–Rosen paradox1,7,8,9. These applications rely on techniques to manipulate and detect coherences of quantum fields, the quadratures. Whereas in optics coherent homodyne detection10 of quadratures is a standard technique, for massive particles a corresponding method was missing. Here we report the realization of an atomic analogue to homodyne detection for the measurement of matter-wave quadratures. The application of this technique to a quantum state produced by spin-changing collisions in a Bose–Einstein condensate11,12 reveals continuous-variable entanglement, as well as the twin-atom character of the state13. Our results provide a rare example of continuous-variable entanglement of massive particles6,14. The direct detection of atomic quadratures has applications not only in experimental quantum atom optics, but also for the measurement of fields in many-body systems of massive particles15.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.

from$8.99

All prices are NET prices.

References

  1. 1.

    , & Can quantum-mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935)

  2. 2.

    , & Quantum-enhanced measurements: beating the standard quantum limit. Science 306, 1330–1336 (2004)

  3. 3.

    & Quantum information with continuous variables. Rev. Mod. Phys. 77, 513–577 (2005)

  4. 4.

    & Teleportation of continuous quantum variables. Phys. Rev. Lett. 80, 869–872 (1998)

  5. 5.

    & Matter-wave entanglement and teleportation by molecular dissociation and collisions. Phys. Rev. Lett. 86, 3180–3183 (2001)

  6. 6.

    , & Quantum interface between light and atomic ensembles. Rev. Mod. Phys. 82, 1041–1093 (2010)

  7. 7.

    et al. The Einstein-Podolsky-Rosen paradox: from concepts to applications. Rev. Mod. Phys. 81, 1727–1751 (2009)

  8. 8.

    , , & Realization of the Einstein- Podolsky-Rosen paradox for continuous variables. Phys. Rev. Lett. 68, 3663–3666 (1992)

  9. 9.

    Demonstration of the Einstein-Podolsky-Rosen paradox using nondegenerate parametric amplification. Phys. Rev. A 40, 913–923 (1989)

  10. 10.

    & Quantum Optics (Springer, 2008)

  11. 11.

    , , & Squeezing and entanglement of atomic beams. Phys. Rev. Lett. 85, 3991–3994 (2000)

  12. 12.

    & Creating macroscopic atomic Einstein-Podolsky-Rosen states from Bose-Einstein condensates. Phys. Rev. Lett. 85, 3987–3990 (2000)

  13. 13.

    , , & Separability criterion for separate quantum systems. Phys. Rev. A 67, 052104 (2003)

  14. 14.

    , & Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400–403 (2001)

  15. 15.

    , & Many-body physics with ultracold gases. Rev. Mod. Phys. 80, 885–964 (2008)

  16. 16.

    et al. Amplification of fluctuations in a spinor Bose-Einstein condensate. Phys. Rev. A 79, 043631 (2009)

  17. 17.

    et al. Parametric amplification of vacuum fluctuations in a spinor condensate. Phys. Rev. Lett. 104, 195303 (2010)

  18. 18.

    et al. Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein condensates. Phys. Rev. Lett. 92, 140403 (2004)

  19. 19.

    et al. Dynamics of F = 2 spinor Bose-Einstein condensates. Phys. Rev. Lett. 92, 040402 (2004)

  20. 20.

    & New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states. Phys. Rev. A 31, 3068–3092 (1985)

  21. 21.

    , , , & Nonlinear atom interferometer surpasses classical precision limit. Nature 464, 1165–1169 (2010)

  22. 22.

    , & Quantum spins mixing in spinor Bose-Einstein condensates. Phys. Rev. Lett. 81, 5257–5261 (1998)

  23. 23.

    , , , & Magnetically tuned spin dynamics resonance. Phys. Rev. Lett. 97, 110404 (2006)

  24. 24.

    , , , & Resonant control of spin dynamics in ultracold quantum gases by microwave dressing. Phys. Rev. A 73, 041602 (2006)

  25. 25.

    & Quantum spin dynamics of spin-1 Bose gas. Preprint at 〈〉 (2006)

  26. 26.

    , , & Detection of continuous variable entanglement without coherent local oscillators. Phys. Rev. A 78, 060104 (2008)

  27. 27.

    et al. Sub-Poissonian number differences in four-wave mixing of matter waves. Phys. Rev. Lett. 105, 190402 (2010)

  28. 28.

    et al. Twin-atom beams. Nature Phys. 7, 608–611 (2011)

  29. 29.

    , & Strong quantum spin correlations observed in atomic spin mixing. Preprint at 〈〉 (2011)

  30. 30.

    et al. Twin matter waves for interferometry beyond the classical limit. Science doi:10.1126/science.1208798 (published online 13 October 2011)

Download references

Acknowledgements

We acknowledge discussions with P. Grangier, A. Aspect, A. J. Ferris, M. J. Davis and B. C. Sanders. This work was supported by the Forschergruppe FOR760, the Deutsche Forschungsgemeinschaft, the German–Israeli Foundation, the Heidelberg Center for Quantum Dynamics, Landesstiftung Baden-Württemberg, the ExtreMe Matter Institute and the European Commission Future and Emerging Technologies Open Scheme project MIDAS (Macroscopic Interference Devices for Atomic and Solid-State Systems). G.K. acknowledges support from the Humboldt-Meitner Award and the Deutsche-Israelische Projektgruppe (DIP).

Author information

Author notes

    • N. Bar-Gill

    Present address: Harvard-Smithsonian CfA, Harvard University Department of Physics, Cambridge, Massachusetts 02138, USA.

Affiliations

  1. Kirchhoff-Institut für Physik, Universität Heidelberg, Im Neuenheimer Feld 227, 69120 Heidelberg, Germany

    • C. Gross
    • , H. Strobel
    • , E. Nicklas
    • , T. Zibold
    •  & M. K. Oberthaler
  2. Weizmann Institute of Science, Rehovot 76100, Israel

    • N. Bar-Gill
    •  & G. Kurizki

Authors

  1. Search for C. Gross in:

  2. Search for H. Strobel in:

  3. Search for E. Nicklas in:

  4. Search for T. Zibold in:

  5. Search for N. Bar-Gill in:

  6. Search for G. Kurizki in:

  7. Search for M. K. Oberthaler in:

Contributions

N.B.-G. and G.K. contributed to the formulation of the problem. C.G., H.S., E.N., T.Z. and M.K.O. contributed equally to the study. All authors discussed the results and commented on the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to M. K. Oberthaler.

Supplementary information

PDF files

  1. 1.

    Supplementary Information

    The file contains Supplementary Text and Data, Supplementary Figures 1-2 with legends and additional references.

About this article

Publication history

Received

Accepted

Published

DOI

https://doi.org/10.1038/nature10654

Further reading

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.