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.

  • Letter
  • Published:

Squeezing and entanglement in a Bose–Einstein condensate

Nature volume 455, pages 1216–1219 (2008)Cite this article

This article has been updated

Abstract

Entanglement, a key feature of quantum mechanics, is a resource that allows the improvement of precision measurements beyond the conventional bound attainable by classical means1. This results in the standard quantum limit, which is reached in today’s best available sensors of various quantities such as time2 and position3,4. Many of these sensors are interferometers in which the standard quantum limit can be overcome by using quantum-entangled states (in particular spin squeezed states5,6) at the two input ports. Bose–Einstein condensates of ultracold atoms are considered good candidates to provide such states involving a large number of particles. Here we demonstrate spin squeezed states suitable for atomic interferometry by splitting a condensate into a few parts using a lattice potential. Site-resolved detection of the atoms allows the measurement of the atom number difference and relative phase, which are conjugate variables. The observed fluctuations imply entanglement between the particles7,8,9, a resource that would allow a precision gain of 3.8 dB over the standard quantum limit for interferometric measurements.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Observing spin squeezing in a Bose–Einstein condensate confined in a double- or six-well trap.
Figure 2: Number squeezing and phase coherence as a criterion for quantum metrology and entanglement.
Figure 3: Systematics of number squeezing and phase coherence during the splitting of a condensate.
Figure 4: Random loss restores Poissonian fluctuations.

Similar content being viewed by others

Change history

  • 30 October 2008

    The AOP version of this paper contained inaccuracies in the main text. This was corrected for print on 30 October 2008.

References

  1. Giovannetti, V., Lloyd, S. & Maccone, L. Quantum-enhanced measurements: Beating the standard quantum limit. Science 306, 1330–1336 (2004)

    Article  ADS  CAS  Google Scholar 

  2. Santarelli, G. et al. Quantum projection noise in an atomic fountain: A high stability cesium frequency standard. Phys. Rev. Lett. 82, 4619–4622 (1999)

    Article  ADS  CAS  Google Scholar 

  3. Goda, K. et al. A quantum-enhanced prototype gravitational-wave detector. Nature Phys. 4, 472–476 (2008)

    Article  ADS  CAS  Google Scholar 

  4. Arcizet, O. et al. High-sensitivity optical monitoring of a micromechanical resonator with a quantum-limited optomechanical sensor. Phys. Rev. Lett. 97, 133601 (2006)

    Article  ADS  CAS  Google Scholar 

  5. Kitagawa, M. & Ueda, M. Squeezed spin states. Phys. Rev. A 47, 5138–5143 (1993)

    Article  ADS  CAS  Google Scholar 

  6. Wineland, D. J., Bollinger, J. J., Itano, W. M. & Heinzen, D. J. Squeezed atomic states and projection noise in spectroscopy. Phys. Rev. A 50, 67–88 (1994)

    Article  ADS  CAS  Google Scholar 

  7. Sorensen, A., Duan, L., Cirac, J. & Zoller, P. Many-particle entanglement with Bose–Einstein condensates. Nature 409, 63–66 (2001)

    Article  ADS  CAS  Google Scholar 

  8. Wang, X. & Sanders, B. C. Spin squeezing and pairwise entanglement for symmetric multiqubit states. Phys. Rev. A 68, 012101 (2003)

    Article  ADS  Google Scholar 

  9. Korbicz, J. K., Cirac, J. I. & Lewenstein, M. Spin squeezing inequalities and entanglement of N qubit states. Phys. Rev. Lett. 95, 120502 (2005)

    Article  ADS  CAS  Google Scholar 

  10. Hald, J., Sørensen, J. L., Schori, C. & Polzik, E. S. Spin squeezed atoms: A macroscopic entangled ensemble created by light. Phys. Rev. Lett. 83, 1319–1322 (1999)

    Article  ADS  Google Scholar 

  11. Kuzmich, A., Mandel, L. & Bigelow, N. P. Generation of spin squeezing via continuous quantum nondemolition measurement. Phys. Rev. Lett. 85, 1594–1597 (2000)

    Article  ADS  CAS  Google Scholar 

  12. Julsgaard, B., Kozhekin, A. & Polzik, E. S. Experimental long-lived entanglement of two macroscopic objects. Nature 413, 400–403 (2001)

    Article  ADS  CAS  Google Scholar 

  13. Chaudhury, S. et al. Quantum control of the hyperfine spin of a Cs atom ensemble. Phys. Rev. Lett. 99, 163002 (2007)

    Article  ADS  Google Scholar 

  14. Fernholz, T. et al. Spin squeezing of atomic ensembles via nuclear-electronic spin entanglement. Preprint at 〈http://arxiv.org/abs/0802.2876〉 (2008)

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  18. Orzel, C., Tuchman, A., Fenselau, M., Yasuda, M. & Kasevich, M. Squeezed states in a Bose-Einstein condensate. Science 291, 2386–2389 (2001)

    Article  ADS  CAS  Google Scholar 

  19. Greiner, M., Mandel, O., Hansch, T. & Bloch, I. Collapse and revival of the matter wave field of a Bose–Einstein condensate. Nature 419, 51–54 (2002)

    Article  ADS  CAS  Google Scholar 

  20. Gerbier, F., Fölling, S., Widera, A., Mandel, O. & Bloch, I. Probing number squeezing of ultracold atoms across the superfluid-Mott insulator transition. Phys. Rev. Lett. 96, 090401 (2006)

    Article  ADS  Google Scholar 

  21. Sebby-Strabley, J. et al. Preparing and probing atomic number states with an atom interferometer. Phys. Rev. Lett. 98, 200405 (2007)

    Article  ADS  CAS  Google Scholar 

  22. Jo, G.-B. et al. Long phase coherence time and number squeezing of two Bose-Einstein condensates on an atom chip. Phys. Rev. Lett. 98, 030407 (2007)

    Article  ADS  Google Scholar 

  23. Li, W., Tuchman, A. K., Chien, H.-C. & Kasevich, M. A. Extended coherence time with atom-number squeezed states. Phys. Rev. Lett. 98, 040402 (2007)

    Article  ADS  Google Scholar 

  24. Sørensen, A. S. & Mølmer, K. Entanglement and extreme spin squeezing. Phys. Rev. Lett. 86, 4431–4434 (2001)

    Article  ADS  Google Scholar 

  25. Korbicz, J. K. et al. Generalized spin-squeezing inequalities in N-qubit systems: Theory and experiment. Phys. Rev. A 74, 052319 (2006)

    Article  ADS  Google Scholar 

  26. Javanainen, J. Phonon approach to an array of traps containing Bose-Einstein condensates. Phys. Rev. A 60, 4902–4909 (1999)

    Article  ADS  CAS  Google Scholar 

  27. Gati, R., Hemmerling, B., Folling, J., Albiez, M. & Oberthaler, M. K. Noise thermometry with two weakly coupled Bose-Einstein condensates. Phys. Rev. Lett. 96, 130404 (2006)

    Article  ADS  Google Scholar 

  28. Reinaudi, G., Lahaye, T., Wang, Z. & Guéry-Odelin, D. Strong saturation absorption imaging of dense clouds of ultracold atoms. Opt. Lett. 32, 3143–3145 (2007)

    Article  ADS  CAS  Google Scholar 

  29. Estève, J. et al. Experimental observations of density fluctuations in an elongated Bose gas: Ideal gas and quasi-condensate regimes. Phys. Rev. Lett. 96, 130403 (2005)

    Article  Google Scholar 

Download references

Acknowledgements

We gratefully acknowledge support from the DFG, GIF and EC (MIDAS STREP). J.E. acknowledges support from the EC Marie-Curie program. C.G. acknowledges support from the Landesgraduiertenförderung Baden-Württemberg.

Author information

Authors and Affiliations

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

    J. Estève, C. Gross, A. Weller, S. Giovanazzi & M. K. Oberthaler

Authors
  1. J. Estève
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. Gross
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Weller
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. Giovanazzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. M. K. Oberthaler
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. K. Oberthaler.

Supplementary information

Supplementary Information

This file contains a discussion of experimental techniques: (I) Calculation of the Number Squeezing Factor; (II) Atom Number Measurement and Calibration; (III) Measuring the Phase Coherence; and Supplementary Figures I and II with Legends (PDF 395 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Estève, J., Gross, C., Weller, A. et al. Squeezing and entanglement in a Bose–Einstein condensate. Nature 455, 1216–1219 (2008). https://doi.org/10.1038/nature07332

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature07332

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

Advanced 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