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.

  • Article
  • Published:

Hanbury Brown and Twiss interferometry with interacting photons

Abstract

Five decades ago, Hanbury Brown and Twiss (HBT) demonstrated that the angular size of stars can be measured by correlating the intensity fluctuations measured by two detectors at two different locations. Since then, non-local correlation measurements have become ubiquitous in many areas of physics and have also been applied, beyond photons, to electrons, matter waves and subatomic particles. An important assumption in HBT interferometry is that the particles do not interact on their way from the source to the detectors. However, this assumption is not always valid. Here, we study the effects of interactions on HBT interferometry by considering the propagation of light fields in a nonlinear medium that induces interactions between the photons. We show that interactions affect multipath interference, limiting the ability to extract information on the source. Nevertheless, we find that proper analysis of the intensity fluctuations can recover the size of the source, even in the presence of interactions.

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: Speckle interpretation of the HBT effect.
Figure 2: Experimental measurements of the effect of nonlinear interactions on Hanbury Brown–Twiss correlations.
Figure 3: Numerical investigation of the interacting Hanbury Brown–Twiss effect in a 1 + 1 geometry.

Similar content being viewed by others

References

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  3. Hanbury Brown, R. The Intensity Interferometer: Its Application to Astronomy (Taylor & Francis, 1974).

  4. Glauber, R. G. Photon correlations. Phys. Rev. Lett. 10, 84–86 (1963).

    Article  ADS  MathSciNet  Google Scholar 

  5. 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 

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

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  8. Polkovnikov, A., Altman, E. & Demler, E. Interference between independent fluctuating condensates. Proc. Natl Acad. Sci. USA 103, 6125–6129 (2006).

    Article  ADS  Google Scholar 

  9. Schellekens, M. et al. Hanbury Brown Twiss effect for ultracold quantum gases. Science 310, 648–651 (2005).

    Article  ADS  Google Scholar 

  10. Fölling, S. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481–484 (2005).

    Article  ADS  Google Scholar 

  11. Büttiker, M. Scattering theory of thermal and excess noise in open conductors. Phys. Rev. Lett. 65, 2901–2904 (1990).

    Article  ADS  Google Scholar 

  12. Martin, T. & Landauer, R. Wave-packet approach to noise in multichannel mesoscopic systems. Phys. Rev. B 45, 1742–1755 (1992).

    Article  ADS  Google Scholar 

  13. Samuelsson, P., Sukhorukov, E. V. & Büttiker, M. Two-particle Aharonov–Bohm effect and entanglement in the electronic Hanbury Brown–Twiss setup. Phys. Rev. Lett. 92, 026805 (2004).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Neder, I. et al. Interference between two indistinguishable electrons from independent sources. Nature 448, 333–337 (2007).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. 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  Google Scholar 

  19. Jeltes, T. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402–405 (2007).

    Article  ADS  Google Scholar 

  20. Lobo, C. & Gensemer, S. D. Techniques for measuring correlation functions in interacting gases. Phys. Rev. A 78, 023618 (2008).

    Article  ADS  Google Scholar 

  21. Goodman, J. W. Speckle Phenomena in Optics (Roberts & Co., 2007)

  22. Boitier, F., Godard, A., Rosencher, E. & Fabre, C. Measuring photon bunching at ultrashort timescale by two-photon absorption in semiconductors. Nature Phys. 5, 267–270 (2009).

    Article  ADS  Google Scholar 

  23. Pethick, C. J. & Smith, H. Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002).

  24. Mitchell, M. & Segev, M. Self-trapping of incoherent white light. Nature 387, 880–883 (1997).

    Article  ADS  Google Scholar 

  25. Rotschild, C., Schwartz, T., Cohen, O. & Segev, M. Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photon. 2, 371–376 (2008).

    Article  ADS  Google Scholar 

  26. Levi, L., Schwartz, T., Manela, O., Segev, M. & Buljan, H. Spontaneous pattern formation upon incoherent waves: from modulation-instability to steady-state. Opt. Express 16, 7818–7831 (2008).

    Article  ADS  Google Scholar 

  27. Picozzi, A. Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Opt. Express 15, 9063–9083 (2007).

    Article  ADS  Google Scholar 

  28. Aitchison, J. S. et al. Spatial optical solitons in planar glass waveguides. J. Opt. Soc. Am. B 8, 1290–1297 (1991).

    Article  ADS  Google Scholar 

  29. Martienssen, W. & Spiller, E. Coherence and fluctuations in light beams. Am. J. Phys. 32, 919–926 (1964).

    Article  ADS  Google Scholar 

  30. Rieckhoff, K. E. Self-induced divergence of CW laser beams in liquids—a new nonlinear effect in the propagation of light. Appl. Phys. Lett. 9, 87–88 (1966).

    Article  ADS  Google Scholar 

  31. Trillo, S. & Torruellas, W. E. Spatial Solitons (Springer-Verlag, 2001).

  32. Stegeman, G. I. & Segev, M. Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999).

    Article  Google Scholar 

  33. Weiner, A. M. et al. Experimental observation of the fundamental dark soliton in optical fibers. Phys. Rev. Lett. 61, 2445–2448 (1988).

    Article  ADS  Google Scholar 

  34. Swartzlander, G. A. Jr, Andersen, D. R., Regan, J. J., Yin, H. & Kaplan, A. E. Spatial dark-soliton stripes and grids in self-defocusing materials. Phys. Rev. Lett. 66, 1583–1586 (1991).

    Article  ADS  Google Scholar 

  35. Kivshar, Y. S. & Luther-Davies, B. Dark optical solitons: physics and applications. Phys. Rep. 298, 81–197 (1998).

    Article  ADS  Google Scholar 

  36. Silberberg, Y. Collapse of optical pulses. Opt. Lett. 15, 1282–1284 (1990).

    Article  ADS  Google Scholar 

  37. Franson, J. D. Bell inequality for position and time. Phys. Rev. Lett. 62, 2205–2208 (1989).

    Article  ADS  Google Scholar 

  38. Yurke, B. & Stoler, D. Bell's-inequality experiments using independent-particle sources. Phys. Rev. A 46, 2229–2234 (1992).

    Article  ADS  MathSciNet  Google Scholar 

  39. Samuelsson, P., Neder, I. & Büttiker, M. Reduced and projected two-particle entanglement at finite temperatures. Phys. Rev. Lett. 102, 106804 (2009).

    Article  ADS  Google Scholar 

  40. Neder, I., Heiblum, M., Levinson, Y., Mahalu, D. & Umansky, V. Unexpected behaviour in a two-path electron interferometer. Phys. Rev. Lett. 96, 016804 (2006).

    Article  ADS  Google Scholar 

  41. Kimble, H. J., Dagenais, M. & Mandel, L. Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1977).

    Article  ADS  Google Scholar 

  42. Tian, L. & Carmichael, H. J. Quantum trajectory simulations of two-state behaviour in an optical cavity containing one atom. Phys. Rev. A 46, R6801–R6804 (1992).

    Article  ADS  Google Scholar 

  43. Rempe, G., Thompson, R. J., Brecha, R. J., Lee, W. D. & Kimble, H. J. Optical bistability and photon statistics in cavity quantum electrodynamics. Phys. Rev. Lett. 67, 1727–1730 (1991).

    Article  ADS  Google Scholar 

  44. Mielke, S. L., Foster, G. T. & Orozco, L. A. Nonclassical intensity correlations in cavity QED. Phys. Rev. Lett. 80, 3948–3951 (1998).

    Article  ADS  Google Scholar 

  45. Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).

    Article  ADS  Google Scholar 

  46. Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

The authors would like to thank A. Natan, O. Katz and M. Covo for invaluable help. Financial support by the Crown Centre of Photonics is gratefully acknowledged. Y.L. is supported by the Adams fellowship of the Israeli Academy of Science and Humanities.

Author information

Authors and Affiliations

Authors

Contributions

Y.B. and Y.L. designed and performed the experiment, analysed the data and prepared the manuscript. E.S. performed the experiment and analysed the data. Y.S. designed the experiment, analysed the data and prepared the manuscript.

Corresponding author

Correspondence to Y. Silberberg.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information Figures and lengends (PDF 560 kb)

Supplementary information

Supplementary Movie (MOV 218 kb)

Supplementary information

Supplementary Movie (MOV 203 kb)

Supplementary information

Supplementary Movie (MOV 413 kb)

Supplementary information

Supplementary Movie (MOV 149 kb)

Supplementary information

Supplementary Movie (MOV 326 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bromberg, Y., Lahini, Y., Small, E. et al. Hanbury Brown and Twiss interferometry with interacting photons. Nature Photon 4, 721–726 (2010). https://doi.org/10.1038/nphoton.2010.195

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphoton.2010.195

This article is cited by

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