SpringerLink
Log in

A nonlocal wave–particle duality

  • Regular Paper
  • Published:
Quantum Studies: Mathematics and Foundations Aims and scope Submit manuscript

Abstract

We propose and analyse a modified ghost-interference experiment, and show that revealing the particle nature of a particle passing through a double-slit hides the wave nature of a spatially separated particle which it is entangled with. We derive a nonlocal duality relation, \({\mathcal D}_1^2 + {\mathcal V}_2^2 \le 1\), which connects the path distinguishability of one particle to the interference visibility of the other. It extends Bohr’s principle of complementarity to a nonlocal scenario. We also propose a ghost quantum eraser in which, erasing the which-path information of one particle brings back the interference fringes of the other.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Germany)

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Bohr, N.: The quantum postulate and the recent development of atomic theory. Nature (London) 121, 580–591 (1928)

    Article  MATH  Google Scholar 

  2. Greenberger, D.M., Yasin, A.: Simultaneous wave and particle knowledge in a neutron interferometer. Phys. Lett. A 128, 391 (1988)

    Article  Google Scholar 

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

    Article  Google Scholar 

  4. Strekalov, D.V., Sergienko, A.V., Klyshko, D.N., Shih, Y.H.: Observation of two-photon ghost interference and diffraction. Phys. Rev. Lett. 74, 3600 (1995)

    Article  Google Scholar 

  5. D’Angelo, M., Kim, Y.-H., Kulik, S.P., Shih, Y.: Identifying entanglement using quantum ghost interference and imaging. Phys. Rev. Lett. 92, 233601 (2004)

    Article  Google Scholar 

  6. Thanvanthri, S., Rubin, M.H.: Ghost interference with an optical parametric amplifier. Phys. Rev. A 70, 063811 (2004)

    Article  Google Scholar 

  7. Zhai, Y.-H., Chen, X.-H., Zhang, D., Wu, L.-A.: Two-photon interference with true thermal light. Phys. Rev. A 72, 043805 (2005)

    Article  Google Scholar 

  8. Jie, L., **g, C.: Lensless ghost diffraction with partially coherent sources: effects of the source size, transverse coherence, detector size and defocusing length. Chin. Phys. Lett. 28, 094203 (2011)

    Article  Google Scholar 

  9. Kofler, J., Singh, M., Ebner, M., Keller, M., Kotyrba, M.: Einstein-Podolsky-Rosen correlations from colliding Bose-Einstein condensates A. Zeiling er. Phys. Rev. A 86, 032115 (2012)

  10. Chingangbam, P., Qureshi, T.: Ghost interference and quantum erasure. Prog. Theor. Phys. 127, 383–392 (2012)

    Article  MATH  Google Scholar 

  11. Ding, D.-S., Zhou, Z.-Y., Shi, B.-S., Zou, X.-B., Guo, G.-C.: Two-color ghost interference. AIP Adv. 2, 032177 (2012)

    Article  Google Scholar 

  12. Shafaq, S., Qureshi, T.: Theoretical analysis of two-color ghost interference. Eur. Phys. J. D 68, 52 (2014)

    Article  Google Scholar 

  13. Qureshi, T., Chingangbam, P., Shafaq, S.: Understanding ghost interference. ar**v:1406.0633 [quant-ph]

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

    Article  MATH  Google Scholar 

  15. Klyshko, D.N.: A simple method of preparing pure states of an optical field, of implementing the EinsteinPodolsky Rosen experiment, and of demonstrating the complementarity principle. Sov. Phys. Usp. 31, 74 (1988)

    Article  Google Scholar 

  16. Walborn, S.P., Monken, C.H., Pádua, S., Souto Ribeiro, P.H.: Spatial correlations in parametric down-conversion. Phys. Rep. 495, 87–139 (2010)

    Article  Google Scholar 

  17. Vaccaro, J.A.: Particle-wave duality: a dichotomy between symmetry and asymmetry. Proc. R. Soc. A. 468, 1065–1084 (2012)

    Article  MathSciNet  Google Scholar 

  18. Qureshi, T.: Understanding Popper’s experiment. Am. J. Phys. 73, 541–544 (2005)

    Article  MathSciNet  Google Scholar 

  19. Born, M., Wolf, E.: Principles of Optics, 7th edn. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  20. Barbosa, G.A.: Quantum images in double-slit experiments with spontaneous down-conversion light. Phys. Rev. A 54, 4473 (1996)

    Article  Google Scholar 

  21. Wang, L.J., Zou, X.Y., Mandel, L.: Induced coherence without induced emission. Phys. Rev. A 44, 4614 (1991)

    Article  Google Scholar 

  22. Zou, X.Y., Wang, L.J., Mandel, L.: Induced coherence and indistinguishability in optical interference. Phys. Rev. Lett. 67, 318 (1991)

    Article  Google Scholar 

  23. Ou, Z.Y., Wang, L.J., Mandel, L.: Vacuum effects on interference in two-photon down conversion. Phys. Rev. A 40, 1428 (1989)

    Article  Google Scholar 

  24. Hong, C.K., Mandel, L.: Experimental realization of a localized one-photon state. Phys. Rev. Lett. 56, 58 (1986)

    Article  Google Scholar 

  25. Jaynes, E.: In: Barut, A.O. (ed.) Foundations of radiation theory and quantum electrodynamics, p. 37. Plenum, New York (1980)

  26. Scully, M.O., Englert, B.-G., Walther, H.: Quantum optical tests of complementarity. Nature (London) 351, 111 (1991)

    Article  Google Scholar 

  27. Walborn, S.P., Terra, M.O.: Cunha, S. Pádua, C.H. Monken.: Double-slit quantum eraser. Phys. Rev. A 65, 033818 (2002)

  28. Walborn, S.P., Terra Cunha, M.O., Pádua, S., Monken, C.H.: Quantum erasure. Am. Sci. 91, 336–343 (2003)

    Article  Google Scholar 

  29. Kim, Y.-H., Yu, R., Kulik, S.P., Shih, Y.: Delayed ‘choice’ quantum eraser. Phys. Rev. Lett. 84, 1 (2000)

    Article  Google Scholar 

  30. Scarcelli, G., Zhou, Y., Shih, Y.: Random delayed-choice quantum eraser via two-photon imaging. Eur. Phys. J. D 44, 167–173 (2007)

    Article  Google Scholar 

  31. Peng, T., Chen, H., Shih, Y.: Delayed-choice quantum eraser with thermal light. Phys. Rev. Lett. 112, 180401 (2014)

    Article  Google Scholar 

Download references

Acknowledgments

M. A. Siddiqui thanks the University Grants Commission, India, for financial support. Authors thank an anonymous referee for suggesting changes which improved the clarity of the discussion.

Author information

Authors and Affiliations

  1. Centre for Theoretical Physics, Jamia Millia Islamia, New Delhi, India

    Mohd Asad Siddiqui & Tabish Qureshi

Authors
  1. Mohd Asad Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tabish Qureshi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Tabish Qureshi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Siddiqui, M.A., Qureshi, T. A nonlocal wave–particle duality. Quantum Stud.: Math. Found. 3, 115–122 (2016). https://doi.org/10.1007/s40509-015-0064-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40509-015-0064-4

Keywords

Search

Navigation