Measuring the quantum mechanical wave function

Contemporary Physics

Volumn 38, Issue 5, 1997, Pages 343-355

  Raymer, M G ^a  

^a UNIVERSITY OF OREGON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031501967     PISSN: 00107514     EISSN: None     Source Type: Journal    
DOI: 10.1080/001075197182315     Document Type: Article

References (40)

1. For a mathematical discussion of the need for a complex wave function, see Bohm D., 1951, Quantum Theory., (Englewood Cliffs, New Jersey: Prentice-Hall), section 4.5.
2. Dehmelt H., 1990, Rev. Mod. Phys., 62, 525.
3. Pauli posed the question in 1933 whether the wave function can be determined uniquely from given distributions of position and momentum. See Pauli, W., 1980, General Principles of Quantum Mechanics, (Berlin: Springer-Verlag). The answer to this more restricted question is, 'No-such data is not tomographically complete'.
4. Ballentine, L. E., 1990, Quantum Mechanics, (Englewood Cliffs: Prentice Hall). This book is out of print and is available from the author.
5. This definition of state is consistent with the 'Statistical Interpretation' of quantum mechanics as discussed by Ballentine, L. E., 1970, Rev. Mod. Phys., 42, 358; Newton, R. G., 1980, Amer. J. Phys., 48, 1029. This interpretation, in its strongest form, assumes that quantum mechanics is a theory only of the behaviour of macroscopic objects (eg. measuring devices) and nothing more. My use of the assumptions 1-3 does not imply that I take this strong interpretation literally.
6. This definition of state is consistent with the 'Statistical Interpretation' of quantum mechanics as discussed by Ballentine, L. E., 1970, Rev. Mod. Phys., 42, 358; Newton, R. G., 1980, Amer. J. Phys., 48, 1029. This interpretation, in its strongest form, assumes that quantum mechanics is a theory only of the behaviour of macroscopic objects (eg. measuring devices) and nothing more. My use of the assumptions 1-3 does not imply that I take this strong interpretation literally.
7. For discussion of complementarity see [1], section 8.15.
8. From Quantum Physics and Philosophy (1958), reprinted in Kalckar J. (editor) 1996, Niels Bohr Collected Works, Foundations of Quantum Physics II, Vol. 7 (Amsterdam: Elsevier).
9. From Quantum Physics and Philosophy (1958), reprinted in Kalckar J. (editor) 1996, Niels Bohr Collected Works, Foundations of Quantum Physics II, Vol. 7 (Amsterdam: Elsevier).
10. Guy, C. N., 1996, Contemp. Phys., 37, 15.
11. Thomas, J. E., 1994, Contemp. Phys., 35, 257.
12. Wigner, E., 1932, Phys. Rev., 40, 749.
13. See, for example, Cohen-Tannoudji, C., Diu, B., and Laloe, F., 1977, Quantum Mechanics, (New York: Wiley) p. 1467.
14. Bertrand, J. and Bertrand P., 1987, Found. Phys., 17, 397.
15. Zurek, W. H., 1991, Phys. Today, October, 36.
16. Brune, M., Hagley, E., Dreyer, J., Maitre, X., Maali, A., Wunderlich, C., Raimond, J. M. and Haroche, S., 1996, Phys. Rev. Lett., 77, 4887. This experiment involved Rydberg atoms interacting one at a time with a few-photon coherent field trapped in a microwave cavity. The mesoscopic superposition created was the equivalent of an 'atom + measuring apparatus' system in which the 'meter' was pointing simultaneously towards two different directions, that is, a 'Schrödinger cat'. The decoherence phenomenon transforming this superposition into a statistical mixture was observed while it unfolded, providing a direct insight into a process at the heart of quantum measurement.
17. For a discussion of the density matrix see [5] and [11].
18. For an advanced treatment of the Wigner function and dynamics see Hillery, M., O'Connell, R. F., Scully, M. O. and Wigner E. P., 1984, Phys. Rep., 106, 121.
19. Ashburn, J. R., Cline, R. A., van der Burgt, P. J. M., Westerveld, W. B. and Risley, J. S., 1990, Phys. Rev. A, 41, 2407.
20. Dunn, T. J., Walmsley, I. A. and Mukamel, S., 1995, Phys. Rev. Lett., 74, 884.
21. In the context of optical measurements the tomographic method was first pointed out by Vogel, K. and Risken, H., 1989, Phys. Rev. A, 40, 2847; the first experiments were reported in Smithey, D. T., Beck, M., Raymer, M. G. and Faridani A., 1993, Phys. Rev. Lett., 70, 1244.
22. In the context of optical measurements the tomographic method was first pointed out by Vogel, K. and Risken, H., 1989, Phys. Rev. A, 40, 2847; the first experiments were reported in Smithey, D. T., Beck, M., Raymer, M. G. and Faridani A., 1993, Phys. Rev. Lett., 70, 1244.
23. Smithey, D. T., Beck, M., Cooper J. and Raymer, M. G., 1993, Phys. Rev. A. 48, 3159.
24. For example, see [11], chap. V.
25. For a discussion see Leonhardt, U., Munroe, M., Kiss, T., Richter, Th. and Raymer, M. G., 1996, Opt. Commun., 127, 144.
26. Schiller, S., Breitenbach, G., Pereira, S. F., Muller, T. and Mlynek, J., 1996, Phys. Rev. Lett., 77, 2933.
27. Itano, W. M., Bergquist, J. C. and Wineland, D. J., 1987, Science, 237, 612.
28. Leibfried, D., Meekhof, D. M., King, B. E., Monroe, C., Itano, W. M. and Wineland, D. J., 1996, Phys. Rev. Lett., 77, 4281.
29. Raymer, M. G., Beck, M. and McAlister, D. F., 1994, Phys. Rev. Lett., 72, 1137; Janicke, U. and Wilkens, M., 1995, J. Mod. Opt., 42, 2183.
30. Raymer, M. G., Beck, M. and McAlister, D. F., 1994, Phys. Rev. Lett., 72, 1137; Janicke, U. and Wilkens, M., 1995, J. Mod. Opt., 42, 2183.
31. For review see Adams, C. S., 1994, Contemp. Phys., 35, 1.
32. Raymer, M. G., 1997, J. Mod. Opt. 44, to appear.
33. Kurtsiefer, Ch., Pfau, T. and Mlynek, 1997, Nature, 386, 150.
34. Andrews, M. R., Townsend, C. G., Miesner, H.-J., Durfee, D. S., Kurn, D. M. and Ketterle, W., 1997, Science, 275, 637.
35. Anderson, M. H., Ensher, J. R., Matthews, M. R., Wieman, C. E., Cornell, E. A., 1995. Science, 269, 198.
36. Burnett, K., 1996, Contemp. Phys., 37, 1.
37. Leonhardt, U. and Raymer, M. G., 1996, Phys. Rev. Lett., 76, 1985.
38. Bell, J., 1990, Phys. World, 3, 33.
39. D'Ariano, G. M. and Yuen, H. P., 1996, Phys. Rev. Lett., 76, 2832; Alter, O. and Yamamoto Y., 1995, Phys. Rev. Lett., 74, 4106.
40. D'Ariano, G. M. and Yuen, H. P., 1996, Phys. Rev. Lett., 76, 2832; Alter, O. and Yamamoto Y., 1995, Phys. Rev. Lett., 74, 4106.