Off-diagonal generalization of the mixed-state geometric phase

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 68, Issue 4 A, 2003, Pages

  Filipp, Stefan ^a   Sjöqvist, Erik ^b  

^a TU WIEN   (Austria)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

NEUTRONS; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; PHOTONS; POLARIZATION; TRANSPORT PROPERTIES; VECTORS;

HILBERT SPACE; MIXED STATE GEOMETRIC PHASE; QUANTUM PARALLEL TRANSPORT;

QUANTUM THEORY;

EID: 4444261270     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. S. Pancharatnam, Proc. Indian Acad. Sci., Sect. A 44, 247 (1956).
2. M.V. Berry, Proc. R. Soc. London, Ser. A 392, 45 (1984).
3. Y. Aharonov and J. Anandau, Phys. Rev. Lett. 58, 1593 (1987).
4. J. Samuel and R. Bhandari, Phys. Rev. Lett. 60, 2339 (1988).
5. A. Uhlmann, Rep. Math. Phys. 24, 229 (1986).
6. E. Sjöqvist, A.K. Pati, A. Ekert, J.S. Anandan, M. Ericsson, D.K.L. Oi, and V. Vedral, Phys. Rev. Lett. 85, 2845 (2000).
7. P.B. Slater, Lett. Math. Phys. 60, 123 (2002)
8. P.B. Slater, e-print math-ph/0112054
9. M. Ericsson, A.K. Pati, E. Sjöqvist, J. Brännlund, and D.K.L. Oi, Phys. Rev. Lett. 91, 090405 (2003).
10. M. Ericsson, E. Sjöqvist, J. Brännlund, D.K.L. Oi, and A.K. Pati, Phys. Rev. A 67, 020101(R) (2003).
11. K. Singh, D.M. Tong K. Basu, J.L. Chen, and J.F. Du, Phys. Rev. A 67, 032106 (2003).
12. J.F. Du, P. Zou, M. Shi, L.C. Kwek, J.-W. Pan, C.H. Oh, A. Ekert, D. K. L. Oi, and M. Ericsson, Phys. Rev. Lett. 91, 100403 (2003).
13. R. Bhandari, Phys. Lett. A 157, 221 (1991)
14. R. Bhandari, Phys. Lett. A 171, 262 (1992)
15. R. Bhandari, Phys. Lett. A 171; 267 (1992)
16. R. Bhandari, Phys. Lett. A 180, 15 (1993).
17. R. Bhandari, Phys. Rev. Lett. 89, 268901 (2002)
18. J.S. Anandan, E. Sjöqvist, A.K. Pati, A. Ekert, M. Ericsson, D.K.L. Oi, and V. Vedral, ibid. 89, 268902 (2002).
19. N. Manini and F. Pistolesi, Phys. Rev. Lett. 85, 3067 (2000).
20. N. Mukunda, Arvind S. Chaturvedi, and R. Simon, Phys. Rev. A 65, 012102 (2002).
21. Y. Hasegawa, R. Loidt, M. Baron, G. Badurek, and H. Rauch, Phys. Rev. Lett. 87, 070401 (2001).
22. Y. Hasegawa, R. Loidl, G. Badurek, M. Baron, N. Manini, F. Pistolesi, and H. Rauch, Phys. Rev. A 65, 052111 (2002).
23. S. Filipp and E. Sjöqvist, Phys. Rev. Lett. 90, 050403 (2003).
24. E. Sjöqvist and S. Filipp, in Foundations of Probability and Physics-2, edited by A. Khrennikov, Series Math. Modelling in Physics, Engineering and Cognitive Sciences Vol. 5 (Växjö University Press, Växjö, 2003), p. 545.
25. N-n the N-n torus, as structure group relevant to the geometric phase for such states, has been proposed in Ref. [9].
26. D. Bures, Trans. Am. Math. Soc. 135, 199 (1969)
27. A. Uhlmann, Rep. Math. Phys. 9, 273 (1976).
28. R. Jozsa, J. Mod. Opt. 41, 2315 (1994).
29. A.G. Wagh and V.C. Rakhecha, Phys. Lett. A 197, 107 (1995)
30. A.G. Wagh, V.C. Rakhecha, P. Fischer, and A.I. Ioffe, Phys. Rev. Lett. 81, 1992 (1998).
31. (1)(P)=0 for any projector P. Although considerations of such alternative definitions may have some mathematical interest, we believe the present choice is, from a physical point of view, the most natural, as it turns out to be rucible to the mixed-state phase of Ref. [6] for l = 1 [see Eq. (15)] and it can be realized experimentally, at least for l≤2 (see Sec. IV).
32. jk≥0.
33. J.D. Franson, Phys. Rev. Lett. 62, 2205 (1989).
34. P.G. Kwiat, E. Waks, A.G. White, I. Appelbaum, and P.H. Eberland, Phys. Rev. A 60, R773 (1999)
35. A.G. White, D. James, P. Eberhand, and P. Kwiat, Phys. Rev. Lett. 83, 3103 (1999).
36. B. Hessmo and E. Sjöqvist, Phys. Rev. A 62, 062301 (2000).