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Comparison of the Hanbury Brown–Twiss effect for bosons and fermions

Nature volume 445, pages 402–405 (2007)Cite this article

Abstract

Fifty years ago, Hanbury Brown and Twiss (HBT) discovered photon bunching in light emitted by a chaotic source1, highlighting the importance of two-photon correlations2 and stimulating the development of modern quantum optics3. The quantum interpretation of bunching relies on the constructive interference between amplitudes involving two indistinguishable photons, and its additive character is intimately linked to the Bose nature of photons. Advances in atom cooling and detection have led to the observation and full characterization of the atomic analogue of the HBT effect with bosonic atoms4,5,6. By contrast, fermions should reveal an antibunching effect (a tendency to avoid each other). Antibunching of fermions is associated with destructive two-particle interference, and is related to the Pauli principle forbidding more than one identical fermion to occupy the same quantum state. Here we report an experimental comparison of the fermionic and bosonic HBT effects in the same apparatus, using two different isotopes of helium: 3He (a fermion) and 4He (a boson). Ordinary attractive or repulsive interactions between atoms are negligible; therefore, the contrasting bunching and antibunching behaviour that we observe can be fully attributed to the different quantum statistics of each atomic species. Our results show how atom–atom correlation measurements can be used to reveal details in the spatial density7,8 or momentum correlations9 in an atomic ensemble. They also enable the direct observation of phase effects linked to the quantum statistics of a many-body system, which may facilitate the study of more exotic situations10.

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Figure 1: The experimental set-up.
Figure 2: Normalized correlation functions for 4 He* (bosons) in the upper plot, and 3 He* (fermions) in the lower plot.
Figure 3: Effect of demagnifying the source size.

References

  1. Hanbury Brown, R. & Twiss, R. Q. Correlation between photons in two coherent beams of light. Nature 177, 27–29 (1956)

    Article  ADS  Google Scholar 

  2. Scully, M. O. & Zubairy, M. S. Quantum Optics (Cambridge Univ. Press, Cambridge, UK, 1997)

    Book  Google Scholar 

  3. Glauber, R. J. in Quantum Optics and Electronics (eds DeWitt, C., Blandin, A. & Cohen-Tannoudji, C.) 63–185 (Gordon and Breach, New York, 1965)

    Google Scholar 

  4. Yasuda, M. & Shimizu, F. Observation of two-atom correlation of an ultracold neon atomic beam. Phys. Rev. Lett. 77, 3090–3093 (1996)

    Article  ADS  CAS  Google Scholar 

  5. Schellekens, M. et al. Hanbury Brown Twiss effect for ultracold quantum gases. Science 310, 648–651 (2005); published online 15 September 2005 (doi:10.1126/science.1118024).

    Article  ADS  CAS  Google Scholar 

  6. Öttl, A., Ritter, S., Köhl, M. & Esslinger, T. Correlations and counting statistics on an atom laser. Phys. Rev. Lett. 95, 090404 (2005)

    Article  ADS  Google Scholar 

  7. Fölling, S. et al. Spatial quantum noise interferometry in expanding condensates. Nature 434, 481–484 (2005)

    Article  ADS  Google Scholar 

  8. Spielman, I. B., Phillips, W. D. & Porto, J. V. The Mott insulator transition in two dimensions. Preprint at 〈http://arxiv.org/cond-mat/0606216〉 (2006)

  9. Greiner, M., Regal, C. A., Stewart, J. T. & Jin, D. S. Probing pair-correlated fermionic atoms through correlations in atom shot noise. Phys. Rev. Lett. 94, 110401 (2005)

    Article  ADS  CAS  Google Scholar 

  10. Altman, E., Demler, E. & Lukin, M. D. Probing many-body states of ultracold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004)

    Article  ADS  Google Scholar 

  11. Grondalski, J., Alsing, P. M. & Deutsch, I. H. Spatial correlation diagnostics for atoms in optical lattices. Opt. Express 5, 249–261 (1999)

    Article  ADS  CAS  Google Scholar 

  12. Hellweg, D. et al. Measurement of the spatial correlation function of phase fluctuating Bose-Einstein condensates. Phys. Rev. Lett. 91, 010406 (2003)

    Article  ADS  CAS  Google Scholar 

  13. Estève, J. et al. Observations of density fluctuations in an elongated Bose gas: ideal gas and quasicondensate regimes. Phys. Rev. Lett. 96, 130403 (2006)

    Article  ADS  Google Scholar 

  14. Loudon, R. The Quantum Theory of Light 3rd edn (Oxford Univ. Press, Oxford, 2000)

    MATH  Google Scholar 

  15. Fano, U. Quantum theory of interference effects in the mixing of light from phase independent sources. Am. J. Phys. 29, 539–545 (1961)

    Article  ADS  Google Scholar 

  16. Hanbury Brown, R. & Twiss, R. Q. A test of a new stellar interferometer on Sirius. Nature 178, 1046–1048 (1956)

    Article  ADS  Google Scholar 

  17. Baym, G. The physics of Hanbury Brown-Twiss intensity interferometry: From stars to nuclear collisions. Acta Phys. Pol. B 29, 1839–1884 (1998)

    ADS  CAS  Google Scholar 

  18. Boal, D. H., Gelbke, C.-K. & Jennings, B. K. Intensity interferometry in subatomic physics. Rev. Mod. Phys. 62, 553–602 (1990)

    Article  ADS  CAS  Google Scholar 

  19. Viana Gomes, J. et al. Theory for a Hanbury Brown Twiss experiment with a ballistically expanding cloud of cold atoms. Phys. Rev. A 74, 053607 (2006)

    Article  ADS  Google Scholar 

  20. Kimble, H. J., Dagenais, M. & Mandel, L. Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1978)

    Article  ADS  Google Scholar 

  21. Henny, M. et al. The fermionic Hanbury Brown and Twiss experiment. Science 284, 296–298 (1999)

    Article  ADS  CAS  Google Scholar 

  22. Oliver, W. D., Kim, J., Liu, R. C. & Yamamoto, Y. Hanbury Brown and Twiss-type experiment with electrons. Science 284, 299–301 (1999)

    Article  ADS  CAS  Google Scholar 

  23. Kiesel, H., Renz, A. & Hasselbach, F. Observation of Hanbury Brown-Twiss anticorrelations for free electrons. Nature 418, 392–394 (2002)

    Article  ADS  CAS  Google Scholar 

  24. Iannuzzi, M., Orecchini, A., Sacchetti, F., Facchi, P. & Pascazio, S. Direct experimental evidence of free-fermion antibunching. Phys. Rev. Lett. 96, 080402 (2006)

    Article  ADS  CAS  Google Scholar 

  25. Rom, T. et al. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 444, 733–736 (2006)

    Article  ADS  CAS  Google Scholar 

  26. Jagutzki, O. et al. A broad-application microchannel-plate detector system for advanced particle or photon detection tasks: Large area imaging, precise multi-hit timing information and high detection rate. Nucl. Instrum. Methods Phys. Res. A 477, 244–249 (2002)

    Article  ADS  CAS  Google Scholar 

  27. McNamara, J. M., Jeltes, T., Tychkov, A. S., Hogervorst, W. & Vassen, W. Degenerate Bose-Fermi mixture of metastable atoms. Phys. Rev. Lett. 97, 080404 (2006)

    Article  ADS  CAS  Google Scholar 

  28. Girardeau, M. Relationship between systems of impenetrable bosons and fermions in one dimension. J. Math. Phys. (NY) 1, 516–523 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  29. Olshanii, M. Atomic scattering in the presence of an external confinement and a gas of impenetrable bosons. Phys. Rev. Lett. 81, 938–941 (1998)

    Article  ADS  CAS  Google Scholar 

  30. Tychkov, A. S. et al. Metastable helium Bose-Einstein condensate with a large number of atoms. Phys. Rev. A 73, 031603(R) (2006)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the access programme of Laserlab Europe. The LCVU group in Amsterdam is supported by the ‘Cold Atoms’ programme of the Dutch Foundation for Fundamental Research on Matter (FOM) and by the Space Research Organization Netherlands (SRON). The Atom Optics group of LCFIO is a member of the IFRAF institute and of the Fédération LUMAT of the CNRS, and is supported by the French ANR and by the SCALA programme of the European Union.

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Authors and Affiliations

  1. Laser Centre Vrije Universiteit, De Boelelaan 1081, 1081 HV, Amsterdam, The Netherlands

    T. Jeltes, J. M. McNamara, W. Hogervorst & W. Vassen

  2. Laboratoire Charles Fabry de l’Institut d’Optique, CNRS, Univ. Paris-sud, Campus Polytechnique RD 128, 91127, Palaiseau Cedex, France

    V. Krachmalnicoff, M. Schellekens, A. Perrin, H. Chang, D. Boiron, A. Aspect & C. I. Westbrook

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Correspondence to W. Vassen or C. I. Westbrook.

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Supplementary information

Supplementary Information

This file contains Supplementary Figures 1-2 with legends and Supplementary Table 1 with Supplementary Data and commentary concerning the correlation length measurements. The Supplementary Figure 1 shows two examples of unnormalized histograms. The Supplementary Figure 2 and the Supplementary Table 1 show the detailed results our fits to a theoretical model. (PDF 530 kb)

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Jeltes, T., McNamara, J., Hogervorst, W. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402–405 (2007). https://doi.org/10.1038/nature05513

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