Analysis of the loss of coherence in interferometry with macromolecules

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 6, 2003, Pages 063610/1-063610/18

  Viale, A ^a   Vicari, M ^a   Zanghii N ^a  

^a INFN SEZIONE DI GENOVA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1142280207     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.68.063610     Document Type: Article

References (58)

1. M. Arndt, O. Nairz, J. Vos-Andræ, C. Keller, G. van der Zouw, and A. Zeilinger, Nature (London) 401, 680 (1999).
2. O. Nairz, M. Arndt, and A. Zeilinger, J. Mod. Opt. 47, 2811 (2000).
3. J.M. Combes, R.G. Newton, and R. Shtokhamer, Phys. Rev. D 11, 366 (1975).
4. M. Daumer, D. Dürr, S. Goldstein, and N. Zanghì, Lett. Math. Phys. 38, 103 (1996).
5. D. Dürr, S. Goldstein, S. Teufel, and N. Zanghì, Physica A 279, 416 (2000).
6. D. Dürr, K. Münch-Berndl, and S. Teufel, J. Math. Phys. 40, 1901 (1999).
7. M. Daumer, D. Dürr, S. Goldstein, and N. Zanghì, J. Stat. Phys. 88, 967 (1997).
8. E. Joos and H.D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
9. S. Goldstein, in Stanford Encyclopedia of Philosophy, edited by E.N. Zalta (Stanford University, Stanford, 2002), URL: http://plato.stanford.edu/archives/win2002/entries/qm-bohm/
10. C.R. Leavens, Phys. Lett. A 178, 27 (1993).
11. W.R. McKinnon and C.R. Leavens, Phys. Rev. A 51, 2748 (1995).
12. C.R. Leavens, Phys. Rev. A 58, 840 (1998).
13. G. Grübl and K. Rheinberger, J. Phys. A 35, 2907 (2002).
14. M. Born and E. Wolf, Principles of Optics (Cambridge University Press, Cambridge, 1999).
15. V. Allori, D. Dürr, S. Goldstein, and N. Zanghì, J. Opt. B: Quantum Semiclassical Opt. 4, 482 (2002).
16. D. Dürr, S. Goldstein, and N. Zanghì, J. Stat. Phys. 67, 843 (1992).
17. Here we just observe that the derivation of Eq. (1) given in Ref. [7] can formally be extended to quantum states described by the reduced density matrix ρ(r,r′) by noting that (1) the analysis in Ref. [7] extends to "conditional wave functions;" (2) the reduced density matrix ρ(r,r′) is indeed the projector onto the pure state defined by the conditional wave function averaged with respect to the "quantum equilibrium distribution." The notions of conditional wave function and quantum equilibrium distribution have been introduced in Ref. [16] and are crucial for a proper understanding of the empirical import of Bohmian mechanics. The only delicate point is current positivity. In order to ensure that the statistics of escape time and position is J, current positivity should hold for all the conditional wave functions whose average leads to ρ(r,r′).
18. M.R. Gallis and G.N. Fleming, Phys. Rev. A 42, 38 (1990).
19. D. Giulini, E. Joos, C. Kiefer, J. Kupsch, I.O. Stamatescu, and H.D. Zeh, Decoherence and the Appearance of a Classical World in Quantum Theory (Springer, Berlin, 1996).
20. D. Dürr, R. Figari, and A. Teta, J. Math. Phys. (to be published), e-print quant-ph/0210199.
21. A. Viale, degree thesis, Università degli Studi di Genova, 2002 (unpublished).
22. B. Vacchini, Phys. Rev. E 63, 066115 (2001).
23. B. Vacchini, J. Math. Phys. 42, 4291 (2001).
24. R. Alicki, Phys. Rev. A 65, 034104 (2002).
25. C. Brukner and A. Zeilinger, Philos. Trans. R. Soc. London, Ser. A 360, 1061 (2002).
26. M.R. Pederson and A.A. Quong, Phys. Rev. B 46, 13 584 (1992).
27. Equation (20) differs from the analog in Refs. [8,19] for numerical constants, which here have been corrected.
28. The values of pressure and cross section were kindly supplied by Dr. Olaf Nairz.
29. W. Krätschmer, L.D. Lamb, K. Fostiropoulos, and D.R. Huffman, Nature (London) 347, 354 (1990).
30. E. Kolodney, A. Budrevich, and B. Tsipinyuk, Phys. Rev. Lett. 74, 510 (1995).
31. B. Vacchini, A. Viale, M. Vicari, and N. Zanghì (unpublished).
32. R.E. Grisenti, W. Schöllkopf, J.P. Toennies, G.C. Hegerfeldt, and T. Köhler, Phys. Rev. Lett. 83, 1755 (1999).
33. K. Hornberger and J.E. Sipe, Phys. Rev. A 68, 012105 (2003).
34. A recent proposal could lead to localization factors smaller by a factor of 2 π [33]. In this case decoherence effects, which are already quite less relevant with respect the loss of coherence due to beam preparation, should be further negligible.
35. Equation (47) holds under the conditions (41), T≫τ with τ = MΔxℓ/ℏ, and (46), d/ℓ≪1. These conditions imply a large superposition of the wave packets on the screen. In fact, the ratio ℛ between the separation of the most distance slits (∼ Δx) and the size of the pattern I(x) (∼ λL/2πd = ℏT/Md) becomes ℛ≪d/ℓ.
36. 2]≈0.3 s.
37. L. Basano, P. Ottonello, G. Rottigni, and M. Vicari, Opt. Commun. 207, 77 (2002).
38. J.F. Clauser and S. Li, Phys. Rev. A 49, R2213 (1994).
39. M.S. Chapman, C.R. Ekstrom, T.D. Hammond, J. Schmiedmayer, B.E. Tannian, S. Wehinger, and D.E. Pritchard, Phys. Rev. A 51, R14 (1995).
40. S. Nowak, Ch. Kurtsiefer, C. David, and T. Pfau, Opt. Lett. 22, 1430 (1997).
41. O. Carnal, Q.A. Turchette, and H.J. Kimble, Phys. Rev. A 51, 3079 (1995).
42. B. Brezger, L. Hackermüller, S. Uttenthaler, J. Petschinka, M. Arndt, and A. Zeilinger, Phys. Rev. Lett. 88, 100404 (2002).
43. K. Hornberger, S. Uttenthaler, B. Brezger, L. Hackermüller, M. Arndt, and A. Zeilinger, Phys. Rev. Lett. 90, 160401 (2003).
44. H.F. Talbot, Philos. Mag. 9, 401 (1836).
45. J.T. Winthrop and C.R. Worthington, J. Opt. Soc. Am. 55, 373 (1965).
46. B. Brezger, M. Arndt, and A. Zeilinger, J. Opt. B: Quantum Semiclassical Opt. 5, S82 (2003).
47. H. Mack, M. Bienert, F. Haug, F.S. Straub, M. Freyberger, and W.P. Schleich, in Experimental Quantum Communication and Information, edited by F. De Martini and C. Monroe (Elsevier, Amsterdam, 2002).
48. S. Mancini and R. Bonifacio, J. Phys. B 34, 1909 (2001).
49. H. Scheckenhofer and A. Steyerl, Phys. Rev. Lett. 39, 1310 (1977).
50. R. Gähler and A. Zeilinger, Am. J. Phys. 59, 316 (1991).
51. A. Zeilinger, R. Gähler, C.G. Shull, W. Teimer, and W. Mampe, Rev. Mod. Phys. 60, 1067 (1988).
52. Atomic and Molecular Beam Methods, edited by G. Scoles (Oxford University Press, Oxford, 1988), Vol. 1.
53. s(x)'s in Eq. (31) to be characteristic functions with supports on the effective width of the slits. Numerical simulations show stability with respect to other equivalent choices for these functions.
54. E. Wolf, Opt. Lett. 8, 250 (1983).
55. E. Wolf and A. T. Friberg, Opt. Lett. 20, 623 (1994).
56. L. Basano, P. Ottonello, G. Rottigni, and M. Vicari, Appl. Opt. 42, 6239 (2003).
57. M. Arndt, O. Nairz, J. Petschinka, and A. Zeilinger, C. R. Acad. Sci., Ser IV: Phys., Astrophys., 2, 581 (2001).
58. O. Nairz, M. Arndt, and A. Zeilinger, Am. J. Phys. 71, 319 (2003).