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The physics of 2 ≠ 1 + 1

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Abstract

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost” interference and “ghost” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ≠ 1 + 1.

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References

  1. Einstein A., Podolsky B., and Rosen N., Phys. Rev., 1935, 35: 777

    Article  ADS  Google Scholar 

  2. Bohr N., Phys. Rev., 1935, 48: 696

    Article  MATH  ADS  Google Scholar 

  3. Quantum Theory and Measurement, Wheeler J. A., and Zurek W. H., eds., Princeton University Press, Princeton, 1983

    Google Scholar 

  4. Pais A., “Subtle is the lord ...” The Science and the Life of Albert Einstein, Oxford University Press, Oxford and New York, 1982

    Google Scholar 

  5. D’Angelo M., Kim Y. H., Kulik S. P., and Shih Y. H., Phys. Rev. Lett., 2004, 92: 233601

    Google Scholar 

  6. Bohm D., Phys. Rev., 1952, 85(166): 180

    Article  ADS  MathSciNet  Google Scholar 

  7. Bohm D., Causality and Chance in Modern Physics, Van D. Nostrand Co., Inc., Princeton, 1957

    Google Scholar 

  8. Bohm D. and Aharonov Y., Phys. Rev., 1957, 108: 1070

    Article  ADS  MathSciNet  Google Scholar 

  9. Bell J. S., Physics, 1964, 1: 195

    Google Scholar 

  10. Bell J. S., Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, New York, 1987

    Google Scholar 

  11. Clauser J. F. and Shimony A., Rep. Prog. Phys., 1978, 41: 1883

    Article  ADS  Google Scholar 

  12. Aspect A., et al., Phys. Rev. Lett., 1981, 47: 460

    Article  ADS  Google Scholar 

  13. Aspect A., et al., Phys. Rev. Lett., 1982, 49: 91

    Article  ADS  MathSciNet  Google Scholar 

  14. Aspect A., et al., Phys. Rev. Lett., 1982, 49: 1804

    Article  ADS  MathSciNet  Google Scholar 

  15. Shih Y. H. and Alley C. O., Phys. Rev. Lett., 1988, 61: 2921

    Article  ADS  Google Scholar 

  16. Ou Z. Y. and Mandel L., Phys. Rev. Lett., 1988, 62: 50

    Article  ADS  MathSciNet  Google Scholar 

  17. Kiess T. E., Shih Y. H., Sergienko A. V., and Alley C. O., Phys. Rev. Lett., 1993, 71: 3893

    Article  ADS  Google Scholar 

  18. Kwiat P. G. et al., Phys. Rev. Lett., 1995, 75: 4337

    Article  ADS  Google Scholar 

  19. Schrödinger E., Naturwissenschaften 1935, 23: 807, 823, 844. English translations appear in Ref. [3]

    Article  Google Scholar 

  20. Klyshko D. N., Photon and Nonlinear Optics, Gordon and Breach Science, New York, 1988

    Google Scholar 

  21. Shih Y. H., IEEE J. of Selected Topics in Quantum Electronics, 2003, 9: 1455

    Article  Google Scholar 

  22. Yariv A., Quantum Electronics, John Wiley and Sons, New York, 1989

    Google Scholar 

  23. Glauber R. J., Phys. Rev., 1963, 130: 2529

    Article  ADS  MathSciNet  Google Scholar 

  24. Glauber R. J., Phys. Rev., 1963, 131: 2766

    Article  ADS  MathSciNet  Google Scholar 

  25. Rubin M. H., Phys. Rev. A, 1996, 54: 5349

    Article  ADS  Google Scholar 

  26. Goodman J. W., Introduction to Fourier Optics, McGraw-Hill Publishing Company, New York, 1968

    Google Scholar 

  27. Shih Y. H., IEEE J. of Selected Topics in Quantum Electronics, 2007

  28. The effect was first proposed for lithography application, namely quantum lithography, by A.N. Boto et al., Phys. Rev. Lett., 2000, 85: 2733

    Article  ADS  Google Scholar 

  29. D’Angelo M., Chekhova M.V., and Shih Y. H., Phys. Rev. Lett., 2001, 87: 013603

    Google Scholar 

  30. D’Angelo M., Chekhova M. V., and Shih Y. H., Phys. Rev. Lett., 2001, 87: 013603 Note: Due to the lack of a two-photon absorber, the joint-detection measurement in this experiment was on the Fourier transform plane rather than on the image plane. It was implicit in Refs. [29, 30] that a second Fourier transform, by inserting a second lens in that experimental setup, would transfer the Fourier transform of the object onto its image plane, thus giving an image with doubled spatial resolution despite the Rayleigh diffraction limit. It might be helpful to point out that the observation of sub-wavelength interference in a Mach Zehnder type interferometer cannot lead to sub-diffraction-limited images, except a set of double modulated interference pattern. The Fourier transform argument works only for imaging setups as is in Refs. [29, 30].

  31. Pittman T. B., Shih Y. H., Strekalov D. V., and Sergienko A. V., Phys. Rev., A, 52: R3429

  32. Klyshko D. N., Usp. Fiz. Nauk, 1988, 154: 133

    Google Scholar 

  33. Klyshko D. N., Sov. Phys. Usp, 1988, 31: 74

    Article  Google Scholar 

  34. Klyshko D. N., Phys. Lett. A, 1988, 132: 299

    Article  ADS  Google Scholar 

  35. D’Angelo M., Valencia A., Rubin M. H., and Shih Y. H., Phys. Rev. A, 2005, 72: 013810

    Google Scholar 

  36. Strekalov D.V., Sergienko A.V., Klyshko D. N., and Shih Y. H., Phys. Rev. Lett., 1995, 74: 3600

    Article  ADS  Google Scholar 

  37. Popper K. R., in Open Questions in Quantum Physics, G. Tarozzi and A. van der Merwe, eds., D. Reidel Publishing Co., Dordrecht, 1985

    Google Scholar 

  38. Popper K. R., in Determinism in Physics, Bitsakis E.I. and Tambakis N., eds., Gutenberg Publishing Co., Athens, 1985

    Google Scholar 

  39. Popper K. R., Naturwissenschaften, 1934, 22: 807

    Article  Google Scholar 

  40. Popper K. R., Quantum Theory and the Schism in Physics, Hutchinson, London, 1982

    Google Scholar 

  41. For criticisms of Popper’s experiment, see for example, D. Bedford and F. Selleri, Lett. Nuovo Cimento, 1985, 42: 325

    Google Scholar 

  42. Collett M. J. and Loudon R., Nature, 1987, 326: 671

    Article  ADS  Google Scholar 

  43. Sudberg A., Philosophy of Science, 1985, 52: 470

    Article  MathSciNet  Google Scholar 

  44. Sudberg A., in Microphysical Reality, A. van der Merwe et al., eds., Kluwer Academic, Dordrecht, 1988

    Google Scholar 

  45. Horne M., Experimental Metaphysics, Cohen R.S., Horne M. and Stachel J., eds., Kluwer Academic, Dordrecht, 1997

    Google Scholar 

  46. Kim Y. H. and Shih Y. H., Foundations of Physics, 1999, 29: 1849

    Article  Google Scholar 

  47. Strekalov D.V., Kim Y. H., and Shih Y. H., Phys. Rev. A, 1999, 60: 2685

    Article  ADS  Google Scholar 

  48. Shannon C. E. and Weaver W., The Mathematical Theory of Communication, University of Illinois Press, Urbana, 1949

    MATH  Google Scholar 

  49. Cerf N. J. and Adami C., Phys. Rev. Lett., 1997, 79: 5194

    Article  MATH  ADS  MathSciNet  Google Scholar 

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Correspondence to Yanhua Shih.

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Shih, Y. The physics of 2 ≠ 1 + 1. Front. Phys. China 2, 125–152 (2007). https://doi.org/10.1007/s11467-007-0020-9

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  • DOI: https://doi.org/10.1007/s11467-007-0020-9

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