Dynamics of entanglement between two trapped atoms

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 4, 2002, Pages 421131-421139

  Mack, Holger ^a   Freyberger, Matthias ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; ELECTROMAGNETIC WAVE SCATTERING; MATHEMATICAL MODELS;

HARMONIC TRAPS;

QUANTUM THEORY;

EID: 0036818609     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (52)

1. A. Einstein, B. Podolsky, and N. Rosen, Phys. Rev. 47, 777 (1935).
2. J.S. Bell, Physics (Long Istand City, N.Y.) 1, 195 (1964).
3. John S. Bell on The Foundations of Quantum Mechanics, edited by M. Bell, K. Gottfried, and M. Veltmann (World Scientific, Singapore, 2001).
4. E. Schrödinger, Naturwissenschaften 48, 807 (1935); 49, 823 (1935); 50, 844 (1935).
5. E. Schrödinger, Naturwissenschaften 48, 807 (1935); 49, 823 (1935); 50, 844 (1935).
6. E. Schrödinger, Naturwissenschaften 48, 807 (1935); 49, 823 (1935); 50, 844 (1935).
7. For reviews on Bell inequalities, see J.F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978); N.D. Mermin, Rev. Mod. Phys. 65, 803 (1993).
8. For reviews on Bell inequalities, see J.F. Clauser and A. Shimony, Rep. Prog. Phys. 41, 1881 (1978); N.D. Mermin, Rev. Mod. Phys. 65, 803 (1993).
9. For a systematic overview of Belt inequalities see R.F. Werner and M.M. Wolf, Quantum Information and Computation 1, 1 (2001).
10. N. Gisin, Phys. Lett. A 154, 201 (1991); S. Popescu and D. Rohrlich, ibid. 166, 293 (1992).
11. N. Gisin, Phys. Lett. A 154, 201 (1991); S. Popescu and D. Rohrlich, ibid. 166, 293 (1992).
12. R.F. Werner, Phys. Rev. A 40, 4277 (1989).
13. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 78, 574 (1997).
14. S. Popescu, Phys. Rev. Lett. 74, 2619 (1995); C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, and W.K. Wootters, ibid. 76, 72 (1996).
15. S. Popescu, Phys. Rev. Lett. 74, 2619 (1995); C.H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J.A. Smolin, and W.K. Wootters, ibid. 76, 72 (1996).
16. M. Horodecki, P. Horodecki, and R. Horodecki, Phys. Rev. Lett. 80, 5239 (1998).
17. For a characterization of entanglement using positive maps, see M. Horodecki, P. Horodecki, and R. Horodecki in Quantum Information, edited by G. Alber et al., Springer Tracts in Modern Physics, Vol. 173 (Springer, New York, 2001), p. 151.
18. L. Vaidman, Phys. Rev. A 49, 1473 (1994); S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998); P. van Loock, S.L. Braunstein, and H.J. Kimble, Phys. Rev. A 62, 022309 (2000); P. van Loock and S.L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000).
19. L. Vaidman, Phys. Rev. A 49, 1473 (1994); S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998); P. van Loock, S.L. Braunstein, and H.J. Kimble, Phys. Rev. A 62, 022309 (2000); P. van Loock and S.L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000).
20. L. Vaidman, Phys. Rev. A 49, 1473 (1994); S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998); P. van Loock, S.L. Braunstein, and H.J. Kimble, Phys. Rev. A 62, 022309 (2000); P. van Loock and S.L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000).
21. L. Vaidman, Phys. Rev. A 49, 1473 (1994); S.L. Braunstein and H.J. Kimble, Phys. Rev. Lett. 80, 869 (1998); P. van Loock, S.L. Braunstein, and H.J. Kimble, Phys. Rev. A 62, 022309 (2000); P. van Loock and S.L. Braunstein, Phys. Rev. Lett. 84, 3482 (2000).
22. P. van Loock and S.L. Braunstein, Phys. Rev. Lett. 87, 247901 (2001).
23. S.L. Braunstein, Nature (London) 394, 47 (1998).
24. A. Furusawa, J.L. Sørensen, S.L. Braunstein, C.A. Fuchs, H.J. Kimble and E.S. Polzik, Science 282, 706 (1998).
25. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, ibid. 84, 2726 (2000); G. Giedke, B. Kraus, and M. Lewenstein, ibid. 87, 167904 (2001); G. Giedke, B. Kraus, and M. Lewenstein, Phys. Rev. A 64, 052303 (2001).
26. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, ibid. 84, 2726 (2000); G. Giedke, B. Kraus, and M. Lewenstein, ibid. 87, 167904 (2001); G. Giedke, B. Kraus, and M. Lewenstein, Phys. Rev. A 64, 052303 (2001).
27. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, ibid. 84, 2726 (2000); G. Giedke, B. Kraus, and M. Lewenstein, ibid. 87, 167904 (2001); G. Giedke, B. Kraus, and M. Lewenstein, Phys. Rev. A 64, 052303 (2001).
28. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 2722 (2000); R. Simon, ibid. 84, 2726 (2000); G. Giedke, B. Kraus, and M. Lewenstein, ibid. 87, 167904 (2001); G. Giedke, B. Kraus, and M. Lewenstein, Phys. Rev. A 64, 052303 (2001).
29. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 4002 (2000); T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000); W.P. Bowen, P.K. Lam, and T.C. Ralph, e-print quant-ph/0104108.
30. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 4002 (2000); T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000); W.P. Bowen, P.K. Lam, and T.C. Ralph, e-print quant-ph/0104108.
31. L.-M. Duan, G. Giedke, J.I. Cirac, and P. Zoller, Phys. Rev. Lett. 84, 4002 (2000); T. Opatrny, G. Kurizki, and D.-G. Welsch, Phys. Rev. A 61, 032302 (2000); W.P. Bowen, P.K. Lam, and T.C. Ralph, e-print quant-ph/0104108.
32. S. Parker, S. Bose, and M.B. Plenio, Phys. Rev. A 61, 032305 (2000).
33. K. Banaszek and K. Wódkiewicz, Phys. Rev. A 58, 4345 (1998).
34. A. Gilchrist, P. Deuar, and M.D. Reid, Phys. Rev. Lett. 80, 3169 (1998); M.D. Reid, ibid. 84, 2765 (2000); M.D. Reid, Phys. Rev. A 62, 022110 (2000).
35. A. Gilchrist, P. Deuar, and M.D. Reid, Phys. Rev. Lett. 80, 3169 (1998); M.D. Reid, ibid. 84, 2765 (2000); M.D. Reid, Phys. Rev. A 62, 022110 (2000).
36. A. Gilchrist, P. Deuar, and M.D. Reid, Phys. Rev. Lett. 80, 3169 (1998); M.D. Reid, ibid. 84, 2765 (2000); M.D. Reid, Phys. Rev. A 62, 022110 (2000).
37. Z.-B. Chen, J.-W. Pan, G. Hou, and Y.-D. Zhang, Phys. Rev. Lett. 88, 040406 (2002).
38. K. Wódkiewicz, New J. Phys. 2, 21 (2000).
39. M.D. Reid and P. Drummond, Phys. Rev. Lett. 60, 2731 (1988); M.D. Reid and P. Drummond, Phys. Rev. A 41, 3930 (1990); M.D. Reid, ibid. 40, 913 (1989).
40. M.D. Reid and P. Drummond, Phys. Rev. Lett. 60, 2731 (1988); M.D. Reid and P. Drummond, Phys. Rev. A 41, 3930 (1990); M.D. Reid, ibid. 40, 913 (1989).
41. M.D. Reid and P. Drummond, Phys. Rev. Lett. 60, 2731 (1988); M.D. Reid and P. Drummond, Phys. Rev. A 41, 3930 (1990); M.D. Reid, ibid. 40, 913 (1989).
42. S. Mancini and S. Bose, Phys. Rev. A 64, 032308 (2001); A.S. Parkins, J. Opt. B: Quantum Semiclassical Opt. 3, S18 (2001); A.S. Parkins and H.J. Kimble, Phys. Rev. A 61, 052104 (2000).
43. S. Mancini and S. Bose, Phys. Rev. A 64, 032308 (2001); A.S. Parkins, J. Opt. B: Quantum Semiclassical Opt. 3, S18 (2001); A.S. Parkins and H.J. Kimble, Phys. Rev. A 61, 052104 (2000).
44. S. Mancini and S. Bose, Phys. Rev. A 64, 032308 (2001); A.S. Parkins, J. Opt. B: Quantum Semiclassical Opt. 3, S18 (2001); A.S. Parkins and H.J. Kimble, Phys. Rev. A 61, 052104 (2000).
45. M.A. Cirone, K. Góral, K. Rza̧żewski, and M. Wilkens, J. Phys. B 34, 4571 (2001).
46. T. Busch, B.-G. Englert, K. Rza̧żewski, and M. Wilkens, Found. Phys. 28, 549 (1998).
47. Ch. Silberhorn, P.K. Lam, O. Weiß, F. König, N. Korolkova, and G. Leuchs, Phys. Rev. Lett. 86, 4267 (2001).
48. Z.Y. Ou, S.F. Pereira, H.J. Kimble, and K.C. Peng, Phys. Rev. Lett. 68, 3663 (1992).
49. J.F. Clauser, M.A. Home, A. Shimony, and R.A. Holt, Phys. Rev. Lett. 23, 880 (1969).
50. A. Royer, Phys. Rev. A 15, 449 (1977).
51. This has been described, for example, in the context of trapped ions, see D. Leibfried, D.M. Meekhof, B.E. King, C. Monroe, W.M. Itano, and D.J. Wineland, Phys. Rev. Lett. 77, 4281 (1996).
52. Handbook of Mathematical Functions edited by M. Abramowitz and I.A. Stegun (Dover, New York, 1972).