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.
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References
Hanbury Brown, R. &. Twiss, R. Q. A test of a new type of stellar interferometer on Sirius. Nature 178, 1046–1048 (1956).
Hanbury Brown, R. &. Twiss, R. Q. Correlations between photons in two coherent beams of light. Nature 177, 27–29 (1956).
Hanbury Brown, R. The Intensity Interferometer: Its Application to Astronomy (Taylor & Francis, 1974).
Glauber, R. G. Photon correlations. Phys. Rev. Lett. 10, 84–86 (1963).
Fano, U. Quantum theory of interference effects in the mixing of light from phase independent sources. Am. J. Phys. 29, 539–545 (1961).
Baym, G. The physics of Hanbury Brown–Twiss intensity interferometry: from stars to nuclear collisions. Acta. Phys. Pol. B 29, 1839–1884 (1998).
Altman, E., Demler, E. & Lukin, M. D. Probing many body correlations of ultra-cold atoms via noise correlations. Phys. Rev. A 70, 013603 (2004).
Polkovnikov, A., Altman, E. & Demler, E. Interference between independent fluctuating condensates. Proc. Natl Acad. Sci. USA 103, 6125–6129 (2006).
Schellekens, M. et al. Hanbury Brown Twiss effect for ultracold quantum gases. Science 310, 648–651 (2005).
Fölling, S. et al. Spatial quantum noise interferometry in expanding ultracold atom clouds. Nature 434, 481–484 (2005).
Büttiker, M. Scattering theory of thermal and excess noise in open conductors. Phys. Rev. Lett. 65, 2901–2904 (1990).
Martin, T. & Landauer, R. Wave-packet approach to noise in multichannel mesoscopic systems. Phys. Rev. B 45, 1742–1755 (1992).
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).
Oliver, W. D., Kim, J., Liu J. & Yamamoto, Y. Hanbury Brown and Twiss-type experiment with electrons. Science 284, 299–301 (1999).
Henny, M. et al. The fermionic Hanbury Brown and Twiss experiment. Science 284, 296–298 (1999).
Neder, I. et al. Interference between two indistinguishable electrons from independent sources. Nature 448, 333–337 (2007).
Kiesel, H., Renz, A. & Hasselbach, F. Observation of Hanbury Brown–Twiss anticorrelations for free electrons. Nature 418, 392–394 (2002).
Rom, T. et al. Free fermion antibunching in a degenerate atomic Fermi gas released from an optical lattice. Nature 444, 733–736 (2006).
Jeltes, T. et al. Comparison of the Hanbury Brown–Twiss effect for bosons and fermions. Nature 445, 402–405 (2007).
Lobo, C. & Gensemer, S. D. Techniques for measuring correlation functions in interacting gases. Phys. Rev. A 78, 023618 (2008).
Goodman, J. W. Speckle Phenomena in Optics (Roberts & Co., 2007)
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).
Pethick, C. J. & Smith, H. Bose–Einstein Condensation in Dilute Gases (Cambridge Univ. Press, 2002).
Mitchell, M. & Segev, M. Self-trapping of incoherent white light. Nature 387, 880–883 (1997).
Rotschild, C., Schwartz, T., Cohen, O. & Segev, M. Incoherent spatial solitons in effectively instantaneous nonlinear media. Nature Photon. 2, 371–376 (2008).
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).
Picozzi, A. Towards a nonequilibrium thermodynamic description of incoherent nonlinear optics. Opt. Express 15, 9063–9083 (2007).
Aitchison, J. S. et al. Spatial optical solitons in planar glass waveguides. J. Opt. Soc. Am. B 8, 1290–1297 (1991).
Martienssen, W. & Spiller, E. Coherence and fluctuations in light beams. Am. J. Phys. 32, 919–926 (1964).
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).
Trillo, S. & Torruellas, W. E. Spatial Solitons (Springer-Verlag, 2001).
Stegeman, G. I. & Segev, M. Optical spatial solitons and their interactions: universality and diversity. Science 286, 1518–1523 (1999).
Weiner, A. M. et al. Experimental observation of the fundamental dark soliton in optical fibers. Phys. Rev. Lett. 61, 2445–2448 (1988).
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).
Kivshar, Y. S. & Luther-Davies, B. Dark optical solitons: physics and applications. Phys. Rep. 298, 81–197 (1998).
Silberberg, Y. Collapse of optical pulses. Opt. Lett. 15, 1282–1284 (1990).
Franson, J. D. Bell inequality for position and time. Phys. Rev. Lett. 62, 2205–2208 (1989).
Yurke, B. & Stoler, D. Bell's-inequality experiments using independent-particle sources. Phys. Rev. A 46, 2229–2234 (1992).
Samuelsson, P., Neder, I. & Büttiker, M. Reduced and projected two-particle entanglement at finite temperatures. Phys. Rev. Lett. 102, 106804 (2009).
Neder, I., Heiblum, M., Levinson, Y., Mahalu, D. & Umansky, V. Unexpected behaviour in a two-path electron interferometer. Phys. Rev. Lett. 96, 016804 (2006).
Kimble, H. J., Dagenais, M. & Mandel, L. Photon antibunching in resonance fluorescence. Phys. Rev. Lett. 39, 691–695 (1977).
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).
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).
Mielke, S. L., Foster, G. T. & Orozco, L. A. Nonclassical intensity correlations in cavity QED. Phys. Rev. Lett. 80, 3948–3951 (1998).
Birnbaum, K. M. et al. Photon blockade in an optical cavity with one trapped atom. Nature 436, 87–90 (2005).
Kwiat, P. G. et al. New high-intensity source of polarization-entangled photon pairs. Phys. Rev. Lett. 75, 4337–4341 (1995).
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.
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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.
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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
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DOI: https://doi.org/10.1038/nphoton.2010.195
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