Atom-chip-based generation of entanglement for quantum metrology

Abstract

Atom chips provide a versatile quantum laboratory for experiments with ultracold atomic gases1. They have been used in diverse experiments involving low-dimensional quantum gases2, cavity quantum electrodynamics3, atom–surface interactions4,5, and chip-based atomic clocks6 and interferometers7,8. However, a severe limitation of atom chips is that techniques to control atomic interactions and to generate entanglement have not been experimentally available so far. Such techniques enable chip-based studies of entangled many-body systems and are a key prerequisite for atom chip applications in quantum simulations9, quantum information processing10 and quantum metrology11. Here we report the experimental generation of multi-particle entanglement on an atom chip by controlling elastic collisional interactions with a state-dependent potential12. We use this technique to generate spin-squeezed states of a two-component Bose–Einstein condensate13; such states are a useful resource for quantum metrology. The observed reduction in spin noise of -3.7 ± 0.4 dB, combined with the spin coherence, implies four-partite entanglement between the condensate atoms14; this could be used to improve an interferometric measurement by -2.5 ± 0.6 dB over the standard quantum limit15. Our data show good agreement with a dynamical multi-mode simulation16 and allow us to reconstruct the Wigner function17 of the spin-squeezed condensate. The techniques reported here could be directly applied to chip-based atomic clocks, currently under development18.

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Figure 1: Spin squeezing and entanglement through controlled interactions on an atom chip.
Figure 2: Spin noise tomography and reconstructed Wigner function of the spin-squeezed BEC.

References

  1. 1

    Fortágh, J. & Zimmermann, C. Magnetic microtraps for ultracold atoms. Rev. Mod. Phys. 79, 235–289 (2007)

    ADS  Article  Google Scholar 

  2. 2

    Hofferberth, S., Lesanovsky, I., Fischer, B., Schumm, T. & Schmiedmayer, J. Non-equilibrium coherence dynamics in one-dimensional Bose gases. Nature 449, 324–327 (2007)

    ADS  CAS  Article  Google Scholar 

  3. 3

    Colombe, Y. et al. Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip. Nature 450, 272–276 (2007)

    ADS  CAS  Article  Google Scholar 

  4. 4

    Lin, Y., Teper, I., Chin, C. & Vuletić, V. Impact of the Casimir-Polder potential and Johnson noise on Bose-Einstein condensate stability near surfaces. Phys. Rev. Lett. 92, 050404 (2004)

    ADS  Article  Google Scholar 

  5. 5

    Aigner, S. et al. Long-range order in electronic transport through disordered metal films. Science 319, 1226–1229 (2008)

    ADS  CAS  Article  Google Scholar 

  6. 6

    Treutlein, P., Hommelhoff, P., Steinmetz, T., Hänsch, T. W. & Reichel, J. Coherence in microchip traps. Phys. Rev. Lett. 92, 203005 (2004)

    ADS  Article  Google Scholar 

  7. 7

    Wang, Y.-J. et al. Atom Michelson interferometer on a chip using a Bose-Einstein condensate. Phys. Rev. Lett. 94, 090405 (2005)

    ADS  Article  Google Scholar 

  8. 8

    Schumm, T. et al. Matter-wave interferometry in a double well on an atom chip. Nature Phys. 1, 57–62 (2005)

    ADS  CAS  Article  Google Scholar 

  9. 9

    Lloyd, S. Universal quantum simulators. Science 273, 1073–1078 (1996)

    ADS  MathSciNet  CAS  Article  Google Scholar 

  10. 10

    DiVincenzo, D. The physical implementation of quantum computation. Fortschr. Phys. 48, 771–783 (2000)

    Article  Google Scholar 

  11. 11

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

    ADS  CAS  Article  Google Scholar 

  12. 12

    Böhi, P. et al. Coherent manipulation of Bose-Einstein condensates with state-dependent microwave potentials on an atom chip. Nature Phys. 5, 592–597 (2009)

    ADS  Article  Google Scholar 

  13. 13

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

    ADS  Article  Google Scholar 

  14. 14

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

    ADS  Article  Google Scholar 

  15. 15

    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)

    ADS  CAS  Article  Google Scholar 

  16. 16

    Li, Y., Treutlein, P., Reichel, J. & Sinatra, A. Spin squeezing in a bimodal condensate: spatial dynamics and particle losses. Eur. Phys. J. B 68, 365–381 (2009)

    ADS  CAS  Article  Google Scholar 

  17. 17

    Wigner, E. On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759 (1932)

    ADS  CAS  Article  Google Scholar 

  18. 18

    Rosenbusch, P. Magnetically trapped atoms for compact atomic clocks. Appl. Phys. B 95, 227–235 (2009)

    ADS  CAS  Article  Google Scholar 

  19. 19

    Estève, J., Gross, C., Weller, A., Giovanazzi, S. & Oberthaler, M. K. Squeezing and entanglement in a Bose-Einstein condensate. Nature 455, 1216–1219 (2008)

    ADS  Article  Google Scholar 

  20. 20

    Appel, J. et al. Mesoscopic atomic entanglement for precision measurements beyond the standard quantum limit. Proc. Natl Acad. Sci. USA 106, 10960–10965 (2009)

    ADS  CAS  Article  Google Scholar 

  21. 21

    Schleier-Smith, M. H., Leroux, I. D. & Vuletić, V. States of an ensemble of two-level atoms with reduced quantum uncertainty. Phys. Rev. Lett. 104, 073604 (2010)

    ADS  Article  Google Scholar 

  22. 22

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

    ADS  CAS  Article  Google Scholar 

  23. 23

    Vogel, A. et al. Bose-Einstein condensates in microgravity. Appl. Phys. B 84, 663–671 (2006)

    ADS  CAS  Article  Google Scholar 

  24. 24

    Calarco, T. et al. Quantum gates with neutral atoms: controlling collisional interactions in time-dependent traps. Phys. Rev. A 61, 022304 (2000)

    ADS  Article  Google Scholar 

  25. 25

    Treutlein, P. et al. Microwave potentials and optimal control for robust quantum gates on an atom chip. Phys. Rev. A 74, 022312 (2006)

    ADS  Article  Google Scholar 

  26. 26

    Charron, E., Cirone, M. A., Negretti, A., Schmiedmayer, J. & Calarco, T. Theoretical analysis of a realistic atom-chip quantum gate. Phys. Rev. A 74, 012308 (2006)

    ADS  Article  Google Scholar 

  27. 27

    Zhao, B., Chen, Z., Pan, J. & Schmiedmayer, J. High-fidelity entanglement via molecular dissociation in integrated atom optics. Phys. Rev. A 75, 042312 (2007)

    ADS  Article  Google Scholar 

  28. 28

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

    ADS  CAS  Article  Google Scholar 

  29. 29

    Li, Y., Castin, Y. & Sinatra, A. Optimum spin squeezing in Bose-Einstein condensates with particle losses. Phys. Rev. Lett. 100, 210401 (2008)

    ADS  Article  Google Scholar 

  30. 30

    Poulsen, U. & Mølmer, K. Quantum beam splitter for atoms. Phys. Rev. A 65, 033613 (2002)

    ADS  Article  Google Scholar 

  31. 31

    Gross, C., Zibold, T., Nicklas, E., Estève, J. & Oberthaler, M. K. Nonlinear atom interferometer surpasses classical precision limit. Nature 10.1038/nature08919 (this issue)

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Acknowledgements

We thank K. Mølmer, J. Reichel, A. Smerzi and A. Sørensen for discussions and J. Halimeh for reading the manuscript. This work was supported by the Nanosystems Initiative Munich and by the European Community's Seventh Framework Programme under grant agreement no. 247687 (Integrating Project AQUTE). T.W.H. acknowledges support by the Max Planck Foundation.

Author Contributions A.S. and P.T. jointly conceived the study. M.F.R., P.B. and P.T. performed the experiment and analysed the data. Y.L. and A.S. carried out the simulations. All authors discussed the results and contributed to the manuscript.

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Correspondence to Alice Sinatra or Philipp Treutlein.

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The authors declare no competing financial interests.

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Supplementary Information

This Supplementary Information file comprises: Experimental Setup; Imaging System; Data evaluation; Phase noise; Depth of Entanglement; Wigner Function reconstruction; Using the squeezed state in an atomic clock. It also contains Supplementary Figures 1-8 with legends and Supplementary References. (PDF 362 kb)

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Riedel, M., Böhi, P., Li, Y. et al. Atom-chip-based generation of entanglement for quantum metrology. Nature 464, 1170–1173 (2010). https://doi.org/10.1038/nature08988

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