Skip to main content

Interferometry of Correlated Particles

  • Chapter
More Than One Mystery
  • 145 Accesses

Abstract

In a 1935 paper [1] that has since become a classic in the literature regarding conceptual implications of quantum mechanics, Einstein and his colleagues Boris Podolsky and Nathan Rosen (to be designated EPR) raised in one of its starkest forms the issue of nonlocality—that is, the occurrence of interactions instantaneously at a distance in violation of physicists’ intuitive sense of cause and effect as embodied in the principles of special relativity. Actually, Einstein’s principal focus of concern was the completeness of quantum mechanics as a self-consistent theory of individual particles (as opposed to a purely statistical theory of ensembles of particles), but the Gedankenexperiment proposed by EPR illustrated what many physicists throughout the ensuing years have considered to be one of the strangest features of quantum mechanics.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 34.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 44.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Reference

  1. A. Einstein, B. Podolsky, and N. Rosen, Can Quantum Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev., 47, 777–780 (1935).

    Article  ADS  MATH  Google Scholar 

  2. N. Bohr, Can Quantum Mechanical Description of Physical Reality Be Considered Complete?, Phys. Rev., 48, 696–702 (1935).

    Article  ADS  MATH  Google Scholar 

  3. M. Jammer, The Philosophy of Quantum Mechanics (Wiley, New York, 1974), p. 187.

    Google Scholar 

  4. See, for example, the comprehensive technical discussion by J.F. Clauser and A. Shimony, Bell’s Thorem: Experimental Tests and Implications, Rep. Progr. Phys. 41, 1881–1927 (1978).

    Article  ADS  Google Scholar 

  5. and the popular articles by B. d’Espagnat, The Quantum Theory and Reality, Scientific American, 247, 158–181 (November, 1979);

    Article  Google Scholar 

  6. T.A. Heppenheimer, Experimental Quantum Mechanics, Mosaic 17, 19–27 (1986)

    Google Scholar 

  7. A. Shimony, The Reality of the Quantum World, Scientific American, 256, 46–53 (January, 1988).

    Article  ADS  Google Scholar 

  8. R. Hanbury Brown and R.Q. Twiss, Correlation between Photons in Two Coherent Beams of Light, Nature, 177, 27–29 (1956).

    Article  ADS  Google Scholar 

  9. R. Hanbury Brown, The Intensity Interferometer (Taylor and Francis, New York, 1974), p. 7.

    Google Scholar 

  10. E.M. Purcell, The Question of Correlation between Photons in Coherent Light Rays, Nature, 178, 1449–1450 (1956).

    Article  ADS  Google Scholar 

  11. A. Einstein, Zum gegenwärtigen Stand des Strahlungsproblems (On the Current State of the Radiation Problem),Phys. Zeit., 10, 185–193 (1909)..

    Google Scholar 

  12. For a comprehensive description of the nature of chaotic light, which includes black-body radiation as a special case, see R. Loudon, The Quantum Theory of Light, 2nd edn. (Oxford, New York, 1983), pp. 157–160. A significant feature is that the density or statistical operator of a chaotic radiation field is diagonal in a basis of photon number states. For example, in the case of a single optical mode, it would have the form \(\hat \rho = \sum\limits_{\{ n\} } {\rho _{n,n} \left| n \right\rangle \left\langle n \right|.}\)

    Google Scholar 

  13. See, for example, the proceedings of the XXth Solvay Conference on Physics: Quantum Optics, edited by P. Mandel, Phys. Rep. 219 (North-Holland, Amsterdam, 1992).

    Google Scholar 

  14. M.P. Silverman, Applications of Photon Correlation Techniques to Fermions, OSA Proceedings on Photon Correlation Techniques and Applications, Vol. 1, edited by J. B. Abbiss and A. E. Smart (OSA, Washington, DC, 1988), pp. 26–34.

    Google Scholar 

  15. M.P. Silverman, Second-Order Temporal and Spatial Coherence of Thermal Electrons, Nuovo Cimento B, 99, 227 (1987).

    Article  ADS  Google Scholar 

  16. M.P. Silverman, Two-Solenoid Aharonov—Bohm Experiment with Correlated Particles, Phys. Lett. A, 148, 154 (1990).

    Article  ADS  Google Scholar 

  17. M.A. Horne, A. Shimony, and A. Zeilinger, Two-Particle Interferometry, Phys. Rev. Lett., 62, 2209 (1989).

    Article  ADS  Google Scholar 

  18. A. Zeilinger, General Properties of Lossless Beam Splitters in Interferometry, Amer. J. Phys., 49, 882 (1981).

    Article  ADS  Google Scholar 

  19. M.P. Silverman, More Than One Mystery: Quantum Interference with Correlated Charged Particles and Magnetic Fields, Amer. J. Phys., 61, 514 (1993).

    Article  ADS  Google Scholar 

  20. M. P. Silverman, New Quantum Effect of Confined Magnetic Flux on Electrons, Phys. Lett. A, 118, 155 (1986).

    Article  ADS  Google Scholar 

  21. M.P. Silverman, Quantum Interference Effects on Fermion Clustering in a Fermion Interferometer, Physica B, 151, 291 (1988).

    Article  Google Scholar 

  22. The coherent states \(\left| \alpha \right\rangle \) of a single-mode oscillator (from which model the optical states are derived) can be expressed in a basis of energy (or excitation number) states as follows: \(\left| \alpha \right\rangle = \exp ( - \left| \alpha \right|^2 /2)\sum\limits_{n = 0}^\infty {\frac{{\alpha ^n }} {{\sqrt {n!} }}} \left| n \right\rangle \)For the properties of coherent states and a detailed exposition of photon statistics, see R.J. Glauber, Optical Coherence and Photon Statistics, in Quantum Optics and Electronics, edited by C. De Witt et al. (Gordon & Breach, New York, 1965), pp. 65–185.

    Google Scholar 

  23. See [10], pp. 226–229.

    Google Scholar 

  24. M.P. Silverman, Fermion Ensembles That Show Statistical Bunching, Phys. Lett. A, 124, 27–31 (1987).

    Article  ADS  Google Scholar 

  25. An introduction to the application of second quantization to light is given by D.F. Walls, A Simple Field Theoretic Description of Photon Interference, Amer. J. Phys., 45, 952–956 (1977).

    Article  ADS  Google Scholar 

  26. M.P. Silverman, On the Feasibility of Observing Electron Antibunching in a Field-Emission Beam, Phys. Lett. A, 120, 442–446 (1987).

    Article  ADS  Google Scholar 

  27. M.P. Silverman, Gravitationally Induced Quantum Interference Effects on Fermion Antibunching, Phys. Lett. A, 122, 226–230 (1987).

    Article  ADS  Google Scholar 

  28. R. Colella, A.W. Overhauser, and S.A. Werner, Observation of Gravitationally Induced Quantum Interference, Phys. Rev. Lett., 34, 1472–1474.

    Google Scholar 

  29. B. Yurke, Input States for Enhancement of Fermion Interferometer Sensitivity, Phys. Rev. Lett., 56, (1986) 1515–1517.

    Article  ADS  Google Scholar 

  30. D.H. Boal, C-K. Gelbke, and B.K. Jennings, Intensity Interferometry in Subatomic Physics, Rev. Mod. Phys., 62, 553–602 (1990).

    Article  ADS  Google Scholar 

  31. P. Hawkes and E. Kasper, Electron Optics, Vol. 2 (Academic Press, New York, 1989), p. 271.

    Google Scholar 

  32. M.P. Silverman, Distinctive Quantum Features of Electron Intensity Correlation Interferometry, Nuovo Cimento B, 97, 200 (1987).

    Article  ADS  Google Scholar 

  33. J.C.H. Spence, W. Qian, and M.P. Silverman, Electron Source Brightness and Degeneracy from Fresnel Fringes in Field Emission Point Projection Microscopy, J. Vac. Sci. Technol. A, 12, 542–547 (1994).

    Article  ADS  Google Scholar 

  34. J.M. Pasachoff, Contemporary Astronomy (W.B. Saunders, Philadelphia, 1977), pp. 167–168.

    Google Scholar 

  35. The degeneracy of a quasi-monochromatic laser source of power P, frequency ν, and bandwidth Δν or pulse width τ is effectively the number of photons δ = Pt c /hv emitted in a coherence time t c ~ 1/Δν or τ. Thus, a continuous-wave HeNe beam of wavelength 633 nm and spectral width 0.2 nm can be shown to have a degeneracy of approximately 2.14 × 104. A ruby laser producing a train of 5 mW pulses each of 1 μs duration at 694 nm emits about 1.8 × 1016 photons per pulse. See, for example, B. Lengyel, Lasers (Wiley, New York, 1971), p. 138.

    Google Scholar 

  36. D. Gabor, Light and Information, in Progress in Optics, Vol. 1, edited by E. Wolf (North-Holland, Amsterdam, 1961), pp. 109–153 (quotation from p. 148).

    Google Scholar 

  37. H.W. Fink, Point Source for Ions and Electrons, Phys. Scripta, 38, 260–263 (1988).

    Article  MathSciNet  ADS  Google Scholar 

  38. P.A. Serena, L. Escapa, J.J. Saenz, N. Garcia, and H. Rohrer, Coherent Electron Emission from Point Sources, J. Microscopy, 152, 43–51 (1988).

    Article  Google Scholar 

  39. W. Qian, M.R. Scheinfein, and J.C.H. Spence, Brightness Measurements of Nanometer-sized Field-Emission-Electron Sources, J. Appl. Phys. 73, 7041 (1993).

    Article  ADS  Google Scholar 

  40. P.A.M. Dirac, The Principles of Quantum Mechanics, 4th edn. (Oxford, London, 1958), p. 9.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 1995 springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Silverman, M.P. (1995). Interferometry of Correlated Particles. In: More Than One Mystery. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2504-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-2504-1_3

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-94376-3

  • Online ISBN: 978-1-4612-2504-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics