Semiclassical theory of coherence and decoherence

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 2, 2003, Pages 10-

  Fiete, Gregory A ^a,b   Heller, Eric J ^a,c  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85037188380     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.68.022112     Document Type: Article

References (42)

1. Y. Ji, Y. Chung, D. Spinzak, M. Heiblum, D. Mahalu, and H. Shtrikman, Nature (London) 422, 415 (2003).
2. Mesoscopic Electron Transport, edited by L. L. Sohn, L. P. Kouwenhoven, and G. Schön (Kluwer, Dordrecht, 1997).
3. Y. Imry, Introduction to Mesoscopic Physics (Oxford University Press, New York, 1997).
4. See Bose-Einstein Condensation in Atomic Gases, Proceedings of the International School of Physics, “Enrico Fermi,” Course CXL, edited by M. Inguscio, S. Stringari, and C. Wieman (International Organisations Services, Amsterdam, 1999).
5. J.R. Anglin and W. Ketterle, Nature (London) 416, 211 (2002).
6. D.P. DiVincenzo, Science 270, 255 (1995).
7. M. A. Nielson and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, UK, 2000).
8. O. Nairz, M. Arndt, and A. Zeilinger, Am. J. Phys. 71, 319 (2003).
9. R. P. Feynman, R. B. Leighton, and M. Sands, The Feynman Lectures on Physics (Addison-Weslay, Massachusetts, 1965), Vol. III.
10. R.P. Feynman and F.L. Vernon, Ann. Phys. (N.Y.) 24, 118 (1963).
11. A.O. Caldeira and A.J. Leggett, Ann. Phys. (N.Y.) 149, 374 (1983).
12. A. Stern, Y. Aharonov, and Y. Imry, Phys. Rev. A 41, 3436 (1990).
13. N. Makri and K. Thompson, Chem. Phys. Lett. 291, 101 (1998).
14. K. Thompson and N. Makri, J. Chem. Phys. 110, 1343 (1999).
15. E.J. Heller and S. Tomsovic, Phys. Today 46, 38 (1993).
16. A. Stern, Y. Aharonov, and Y. Imry, in Quantum Coherence in Mesoscopic Systems, edited by B. Kramer (Plenum Press, New York, 1991).
17. A. Yacoby, M. Heiblum, D. Mahalu, and H. Shtrikman, Phys. Rev. Lett. 74, 4047 (1995).
18. W.T. Strunz, L. Diósi, and N. Gisin, Phys. Rev. Lett. 66, 4931 (1999).
19. N. van Kampen, Phys. Norv. 5, 279 (1971).
20. J.L. Skinner and D. Hsu, J. Phys. Chem. 90, 4931 (1986).
21. S. Chakravarty and A. Schmid, Phys. Rep. 140, 193 (1986).
22. B.L. Altshuler, A.G. Aronov, and D.E. Khemlnitsky, J. Phys. C 15, 7367 (1982).
23. D.S. Golubev and A. Zaikin, Phys. Rev. B 59, 9195 (1999).
24. D. Cohen and Y. Imry, Phys. Rev. B 59, 11 143 (1999).
25. P. Bertet, S. Osnaghi, A. Rauschenbeutel, G. Nogues, A. Auffeves, M. Brune, J. Raimond, and S. Haroche, Nature (London) 411, 166 (2001).
26. E.J. Heller, J. Chem. Phys. 62, 1544 (1975).
27. E.J. Heller, J. Chem. Phys. 65, 4979 (1976).
28. E.J. Heller, J. Chem. Phys. 67, 3339 (1977).
29. E.J. Heller, J. Chem. Phys. 62, 1544 (1975).
30. E. J. Heller, in 1989 NATO Les Houches Summer School on Chaos and Quantum Physics, edited by M-J. Giannoni, A. Voros, and J. Zinn-Justin (Elsevier, Amsterdam, 1991).
31. P.W. O’Connor, S. Tomsovic, and E.J. Heller, Physica D 55, 340 (1992).
32. P.W. O’Connor, S. Tomsovic, and E.J. Heller, J. Stat. Phys. 68, 131 (1992).
33. E.J. Heller, S. Tomsovic, and M.A. Sepulveda, Chaos 2, 105 (1992).
34. M.A. Sepulveda, S. Tomsovic, and E.J. Heller, Phys. Rev. Lett. 69, 402 (1992).
35. Y. Weissman, J. Phys. A 16, 2693 (1983).
36. Y. Weissman, J. Chem. Phys. 76, 4067 (1982).
37. D. Huber, E.J. Heller, and R.G. Littlejohn, J. Chem. Phys. 89, 2003 (1988).
38. This innocent looking final wave function actually neglects entangling on the right arm between the particle and the bath by writing the term (Formula presented) as a direct product which is not correct in general.
39. One must also be careful when interpreting the extrema of the interference term of Eq. (B3) (as a function of magnetic field in the Ahronov-Bohm experiment, for example) as a measure of the coherence. The difference of the maximum and minimum of the interference term must be normalized by the direct terms to divide out Debye-Waller factors which reduce both the direct terms above and the interference cross terms 42. In general one must normalize the interference term by a flux dependent term to prevent “flux blocking” effects from being interpreted as decoherence.
40. As SAI point out, what matters is the relative phase of the two arms of the Aharonov-Bohm ring. We are taking (Formula presented) in the left arm.
41. D. Loss and K. Mullen, Phys. Rev. B 43, 13 252 (1991).
42. Y. Imry, e-print cond-mat/0202044.