Skip to main content

Thank you for visiting 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.

A complementarity experiment with an interferometer at the quantum–classical boundary


To illustrate the quantum mechanical principle of complementarity, Bohr1 described an interferometer with a microscopic slit that records the particle's path. Recoil of the quantum slit causes it to become entangled with the particle, resulting in a kind of Einstein–Podolsky–Rosen pair2. As the motion of the slit can be observed, the ambiguity of the particle's trajectory is lifted, suppressing interference effects. In contrast, the state of a sufficiently massive slit does not depend on the particle's path; hence, interference fringes are visible. Although many experiments illustrating various aspects of complementarity have been proposed3,4,5,6,7,8,9 and realized10,11,12,13,14,15,16,17,18, none has addressed the quantum–classical limit in the design of the interferometer. Here we report an experimental investigation of complementarity using an interferometer in which the properties of one of the beam-splitting elements can be tuned continuously from being effectively microscopic to macroscopic. Following a recent proposal19, we use an atomic double-pulse Ramsey interferometer20, in which microwave pulses act as beam-splitters for the quantum states of the atoms. One of the pulses is a coherent field stored in a cavity, comprising a small, adjustable mean photon number. The visibility of the interference fringes in the final atomic state probability increases with this photon number, illustrating the quantum to classical transition.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Figure 1: Sketch of an interferometer with a recoiling slit, adapted from Bohr1.
Figure 2: Mach–Zehnder and Ramsey versions of Bohr's experiment.
Figure 3: From quantum to classical interferometer.
Figure 4: The unconditional quantum-eraser experiment.


  1. Bohr, N. in Albert Einstein: Philosopher Scientist (ed. Schilpp, P. A.) 200–241 (Library of Living Philosophers, Evanston, 1949); reprinted in Quantum Theory and Measurement (eds Wheeler, J. A. & Zurek, W. H.) 9–49 (Princeton Univ. Press, Princeton, 1983).

    Google Scholar 

  2. Einstein, A., Podolsky, B. & Rosen, N. Can quantum mechanical description of physical reality be considered complete? Phys. Rev. 47, 777–780 (1935).

    ADS  CAS  Article  Google Scholar 

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

    Book  Google Scholar 

  4. Scully, M. O., Englert, B. G. & Walther, H. Quantum optical tests of complementarity. Nature 351, 111–116 (1991).

    ADS  Article  Google Scholar 

  5. Haroche, S., Brune, M. & Raimond, J. M. Manipulations of optical fields by atomic interferometry: quantum variations on a theme by Young. Appl. Phys. B 54, 355–365 (1992).

    ADS  Article  Google Scholar 

  6. Englert, B. G. Fringe visibility and which-way information: an inequality. Phys. Rev. Lett. 77, 2154–2157 (1996).

    ADS  CAS  Article  Google Scholar 

  7. Englert, B. G., Scully, M. O. & Walther, H. Complementarity and uncertainty. Nature 375, 367 (1995).

    ADS  CAS  Article  Google Scholar 

  8. Storey, P., Tan, S., Collet, M. & Walls, D. Complementarity and uncertainty. Nature 375, 368 (1995).

    ADS  CAS  Article  Google Scholar 

  9. Wiseman, H. et al. Non local momentum transfer in welcher Weg measurements. Phys. Rev. A 56, 55–75 (1997).

    ADS  CAS  Article  Google Scholar 

  10. Badurek, G., Rausch, H. & Tuppinger, D. Neutron interferometric double resonance experiments. Phys. Rev. A 34, 2600–2608 (1985).

    ADS  Article  Google Scholar 

  11. Grangier, P., Roger, G. & Aspect, A. Experimental evidence for photon anticorrelation effect on a beam splitter: a new light on single-photon interference. Europhys. Lett. 1, 173–179 (1986).

    ADS  CAS  Article  Google Scholar 

  12. Pfau, T. et al. Loss of spatial coherence by a single spontaneous emission. Phys. Rev. Lett. 73, 1223–1227 (1994).

    ADS  CAS  Article  Google Scholar 

  13. Chapman, M. S. et al. Photon scattering from atoms in an atom interferometer: coherence lost and regained. Phys. Rev. Lett. 75, 3783–3787 (1995).

    ADS  CAS  Article  Google Scholar 

  14. Eichman, U. et al. Young's interference experiment with light scattered from two atoms. Phys. Rev. Lett. 70, 2359–2362 (1993).

    ADS  Article  Google Scholar 

  15. Dürr, S., Nonn, T. & Rempe, G. Origin of quantum-mechanical complementarity probed by a “which way” experiment in an atom interferometer. Nature 395, 33–37 (1998).

    ADS  Article  Google Scholar 

  16. Dürr, S., Nonn, T. & Rempe, G. Fringe visibility and which-way information in an atom interferometer. Phys. Rev. Lett. 81, 5705–5709 (1998).

    ADS  Article  Google Scholar 

  17. Herzog, T. J., Kwiat, P. G., Weinfurter, H. & Zeilinger, A. Complementarity and the quantum eraser. Phys. Rev. Lett. 75, 3034–3037 (1995).

    ADS  CAS  Article  Google Scholar 

  18. Bucks, E., Schuster, R., Heiblum, M., Mahalu, D. & Umansky, V. Dephasing in electron interference by a “which-path” detector. Nature 391, 871–874 (1998).

    ADS  Article  Google Scholar 

  19. Zheng, S. B. A simplified scheme for testing complementarity and realising quantum eraser. Opt. Comm. 173, 265–267 (2000).

    ADS  CAS  Article  Google Scholar 

  20. Ramsey, N. Molecular Beams (Oxford Univ. Press, Oxford, UK, 1985).

    Google Scholar 

  21. Nogues, G. et al. Seeing a single photon without destroying it. Nature 400, 239–242 (1999).

    ADS  CAS  Article  Google Scholar 

  22. Rauschenbeutel, A. et al. Coherent operation of a tunable quantum phase gate. Phys. Rev. Lett. 83, 5166–5169 (1999).

    ADS  CAS  Article  Google Scholar 

  23. Brune, M. et al. From Lamb shift to light shifts: vacuum and sub-photon cavity fields measured by atomic interferometry. Phys. Rev. Lett. 72, 3339–3342 (1994).

    ADS  CAS  Article  Google Scholar 

  24. Brune, M. et al. Quantum Rabi oscillation: a direct test of field quantization in a cavity. Phys. Rev. Lett. 76, 1800–1803 (1996).

    ADS  CAS  Article  Google Scholar 

  25. Haroche, S. & Raimond, J. M. in Cavity Quantum Electrodynamics (ed. Berman, P.) 123–170 (Academic, New York, 1992).

    Google Scholar 

  26. Kim, J. I. et al. Classical behaviours with small quantum numbers: the physics of Ramsey interferometry of Rydberg atoms. Phys. Rev. Lett. 82, 4737–4740 (1999).

    ADS  CAS  Article  Google Scholar 

  27. Gerry, C. C. Complementarity and quantum erasure with dispersive atom-field interaction. Phys. Rev. A 53, 1179–1182 (1996).

    ADS  CAS  Article  Google Scholar 

  28. Brune, M. et al. Observing the progressive decoherence of the meter in a quantum measurement. Phys. Rev. Lett. 77, 4887–4890 (1996).

    ADS  CAS  Article  Google Scholar 

  29. Scully, M. O. & Srühl, K. Quantum eraser: a proposed photon correlation experiment concerning observation and “delayed choice” in quantum mechanics. Phys. Rev. A 25, 2208–2213 (1982).

    ADS  CAS  Article  Google Scholar 

  30. Kwiat, P. G., Steinberg, A. M. & Chiao, R. Y. Observation of a “quantum eraser”: a revival of coherence in a 2-photon interference experiment. Phys. Rev. A 45, 7729–7739 (1992).

    ADS  CAS  Article  Google Scholar 

Download references


Laboratoire Kastler Brossel is Unité Mixte de Recherches of Ecole Normale Supérieure, Université P. et M. Curie and Centre National de la Recherche Scientifique. This work was supported by the Commission of the European Community and by the Japan Science and Technology Corporation (International Cooperative Research Project, Quantum Entanglement Project).

Author information

Authors and Affiliations


Corresponding author

Correspondence to S. Haroche.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Bertet, P., Osnaghi, S., Rauschenbeutel, A. et al. A complementarity experiment with an interferometer at the quantum–classical boundary. Nature 411, 166–170 (2001).

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI:

Further reading


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.


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