Photon quantum mechanics and beam splitters

American Journal of Physics

Volumn 70, Issue 3, 2002, Pages 260-265

  Holbrow, C H ^a   Galvez, E ^a   Parks, M E ^a  

^a Assistant Professor in the University Libraries   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23044530892     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1432972     Document Type: Article

References (21)

1. R. Y. Chiao, P. G. Kwiat, and A. M. Steinberg, "Optical tests of quantum mechanics, " in Advances in Atomic, Molecular, and Optical Physics (Academic, New York, 1994), Vol. 34, pp. 35-83.
2. Our Web site is at http://departments.coIgate.edu/physics/research/ Photon/ photon-quantum-mechanics.htm.
3. D. Griffiths, Quantum Mechanics (Prentice-Hall, Englewood Cliffs, NJ, 1995), pp. 154-176. Chapter 3 of this book supplies a nice summary of the concepts and terminology of linear algebra relevant to quantum mechanics (pp. 75-120). It may be too brief for our purposes.
4. J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge U.P., Cambridge, 1987). See particularly "On the Einstein-Podolsky- Rosen paradox, " pp. 14-21, and "Bertlmann's socks and the nature of reality, " pp. 139-158.
5. D. Mermin, "Is the moon there when nobody looks? Reality and quantum theory, " Phys. Today 38(4), 38-47 (1985).
6. An important long-range goal of our project is to achieve a design that exploits advances in technology to bring the cost of the apparatus within the budgets of colleges.
7. A significant part of this laboratory experiment will be devoted to introducing students to the statistics of counting.
8. A. P. French and Edwin F. Taylor, Introduction to Quantum Physics (Chapman and Hall, London, 1974), pp. 231-278.
9. H. J. Lipkin, "Polarized photons for pedestrians, " in Quantum Mechanics: New Approaches to Selected Topics (North-Holland, New York, 1973), pp. 2-29.
10. R. P. Feynman, R. B. Leighton, and M. L. Sands, The Feynman Lectures on Physics (Addison-Wesley, Reading, MA, 1963), Vol. 3, Chaps. 5 and 6. Feynman develops quantum mechanics largely in terms of two-state systems. We will make extensive use of his material.
11. R. P. Feynman, QED, the Strange Theory of Light and Matter (Princeton U.P., Princeton, 1985).
12. I2 D. F. Styer, The Strange World of Quantum Mechanics (Cambridge U.P., New York, 2000).
13. A. Zeilinger, "General properties of lossless beam splitters in interferom-etry, " Am. J. Phys. 49, 882-883 (1981). This article expresses the general 2X2 unitary matrix in terms of Pauli spin matrices. This approach would be particularly useful for further familiarizing students in a quantum mechanics course with these important mathematical tools.
14. The exit probabilities are independent of whether the transmitted beam leads or lags the reflected beam by π/2 rad. In other words, a matrix R in which t=-i is equivalent to one with t=i
15. I5 D. M. Greenberger, M. A. Horne, and A. Zeilinger, "Multiparticle inter-ferometry and the superposition principle, " Phys. Today 46(8), 22-29 (1993). This article is an excellent source of explanations of the kinds of quantum effects that our project is intended to display.
16. I6 R. Loudon, "Spatially-localized two-particle interference at a beam split-
17. ter, " in Coherence and Quantum Optics VI, edited by J. H. Eberly et al. (Plenum, New York, 1990), pp. 703-708.
18. C. K. Hong, Z. Y. Ou, and L. Mandel, "Measurement of subpicosecond time intervals between two photons by interference, " Phys. Rev. Lett. 59, 2044-2046 (1987).
19. I8 A. Einstein, N. Rosen, and B. Podolsky, "Can quantum-mechanical description of physical reality be considered complete?, " Phys. Rev. 47, 777-780 (1935).
20. 19 C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, "Teleporting an unknown quantum state via dual classic and Einstein-Podolsky-Rosen channels, " Phys. Rev. Leu. 70, 1895-1899 (1993).
21. D. Bouwmeester, J.-W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, "Experimental quantum teleportation, " Nature (London) 390, 575-579 (1997).