Continuous quantum measurement and the quantum to classical transition

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 67, Issue 4, 2003, Pages 421031-4210312

  Bhattacharya, Tanmoy ^a   Habib, Salman ^a   Jacobs, Kurt ^a  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; CHAOS THEORY; ELECTROMAGNETISM; STATISTICAL METHODS;

QUANTUM MEASUREMENT;

QUANTUM THEORY;

EID: 0038308838     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (45)

1. H.J. Korsch and M.V. Berry, Physica D 3, 627 (1981); T. Hogg and B.A. Huberman, Phys. Rev. Lett. 48, 711 (1982); R.L. Ingram, M.E. Goggin, and P. W. Milonni, in Coherence and Quantum Optics VI, edited by J.H. Eberly (Plenum, New York, 1990).
2. H.J. Korsch and M.V. Berry, Physica D 3, 627 (1981); T. Hogg and B.A. Huberman, Phys. Rev. Lett. 48, 711 (1982); R.L. Ingram, M.E. Goggin, and P. W. Milonni, in Coherence and Quantum Optics VI, edited by J.H. Eberly (Plenum, New York, 1990).
3. H.J. Korsch and M.V. Berry, Physica D 3, 627 (1981); T. Hogg and B.A. Huberman, Phys. Rev. Lett. 48, 711 (1982); R.L. Ingram, M.E. Goggin, and P. W. Milonni, in Coherence and Quantum Optics VI, edited by J.H. Eberly (Plenum, New York, 1990).
4. A.O. Caldeira and A.J. Leggett, Physica A 121, 587 (1983).
5. C.W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer, Berlin, 2000).
6. Early work includes A. Barchielli, L. Lanz, and G.M. Prosperi, Nuovo Cimento B 72B, 79 (1982); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. 114A, 451 (1986); for a review, see A. Barchielli, Int. J. Theor. Phys. 32, 2221 (1993).
7. Early work includes A. Barchielli, L. Lanz, and G.M. Prosperi, Nuovo Cimento B 72B, 79 (1982); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. 114A, 451 (1986); for a review, see A. Barchielli, Int. J. Theor. Phys. 32, 2221 (1993).
8. Early work includes A. Barchielli, L. Lanz, and G.M. Prosperi, Nuovo Cimento B 72B, 79 (1982); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. 114A, 451 (1986); for a review, see A. Barchielli, Int. J. Theor. Phys. 32, 2221 (1993).
9. Early work includes A. Barchielli, L. Lanz, and G.M. Prosperi, Nuovo Cimento B 72B, 79 (1982); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. 114A, 451 (1986); for a review, see A. Barchielli, Int. J. Theor. Phys. 32, 2221 (1993).
10. V.P. Belavkin and P. Staszewski, Phys. Lett. 40A, 359 (1989).
11. C.M. Caves and G.J. Milburn, Phys. Rev. A 36, 5543 (1987).
12. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993).
13. H.M. Wiseman and G.J. Milburn, Phys. Rev. A 47, 642 (1993).
14. K. Hepp, Helv. Phys. Acta 45, 237 (1972); W.H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982); E. Joos and H.D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
15. K. Hepp, Helv. Phys. Acta 45, 237 (1972); W.H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982); E. Joos and H.D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
16. K. Hepp, Helv. Phys. Acta 45, 237 (1972); W.H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982); E. Joos and H.D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
17. K. Hepp, Helv. Phys. Acta 45, 237 (1972); W.H. Zurek, Phys. Rev. D 24, 1516 (1981); 26, 1862 (1982); E. Joos and H.D. Zeh, Z. Phys. B: Condens. Matter 59, 223 (1985).
18. See, e.g., S. Habib, K. Shizume, and W.H. Zurek, Phys. Rev. Lett. 80, 4361 (1998).
19. T.P. Spiller and J.F. Ralph, Phys. Lett. A 194, 235 (1994).
20. M. Schlautmann and R. Graham, Phys. Rev. E 52, 340 (1995).
21. R. Schack, T.A. Brun, and I.C. Percival, J. Phys. A 28, 5401 (1995); T.A. Brun, I.C. Percival, and R. Schack, ibid. 29, 2077 (1996); I.C. Percival and W.T. Strunz, ibid. 31, 1815 (1998); 31, 1801 (1998).
22. R. Schack, T.A. Brun, and I.C. Percival, J. Phys. A 28, 5401 (1995); T.A. Brun, I.C. Percival, and R. Schack, ibid. 29, 2077 (1996); I.C. Percival and W.T. Strunz, ibid. 31, 1815 (1998); 31, 1801 (1998).
23. R. Schack, T.A. Brun, and I.C. Percival, J. Phys. A 28, 5401 (1995); T.A. Brun, I.C. Percival, and R. Schack, ibid. 29, 2077 (1996); I.C. Percival and W.T. Strunz, ibid. 31, 1815 (1998); 31, 1801 (1998).
24. R. Schack, T.A. Brun, and I.C. Percival, J. Phys. A 28, 5401 (1995); T.A. Brun, I.C. Percival, and R. Schack, ibid. 29, 2077 (1996); I.C. Percival and W.T. Strunz, ibid. 31, 1815 (1998); 31, 1801 (1998).
25. T. Bhattacharya, S. Habib, and K. Jacobs, Phys. Rev. Lett. 85, 4852 (2000).
26. A.J. Scott and G.J. Milburn, Phys. Rev. A 63, 042101 (2001).
27. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996); C.J. Hood, M.S. Chapman, T.W. Lynn, and H.J. Kimble, ibid. 80, 4157 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, ibid. 80, 4111 (1998); B.G. Klappauf, W.H. Oskay, D.A. Steck, and M.G. Raizen, ibid. 81, 1203 (1998).
28. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996); C.J. Hood, M.S. Chapman, T.W. Lynn, and H.J. Kimble, ibid. 80, 4157 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, ibid. 80, 4111 (1998); B.G. Klappauf, W.H. Oskay, D.A. Steck, and M.G. Raizen, ibid. 81, 1203 (1998).
29. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996); C.J. Hood, M.S. Chapman, T.W. Lynn, and H.J. Kimble, ibid. 80, 4157 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, ibid. 80, 4111 (1998); B.G. Klappauf, W.H. Oskay, D.A. Steck, and M.G. Raizen, ibid. 81, 1203 (1998).
30. M. Brune, E. Hagley, J. Dreyer, X. Maitre, A. Maali, C. Wunderlich, J.M. Raimond, and S. Haroche, Phys. Rev. Lett. 77, 4887 (1996); C.J. Hood, M.S. Chapman, T.W. Lynn, and H.J. Kimble, ibid. 80, 4157 (1998); H. Ammann, R. Gray, I. Shvarchuck, and N. Christensen, ibid. 80, 4111 (1998); B.G. Klappauf, W.H. Oskay, D.A. Steck, and M.G. Raizen, ibid. 81, 1203 (1998).
31. C.W. Gardiner, Stochastic Methods (Springer-Verlag, Berlin, 1990).
32. G.J. Milburn, K. Jacobs, and D.F. Walls, Phys. Rev. A 50, 5256 (1994).
33. A.C. Doherty and K. Jacobs, Phys. Rev. A 60, 2700 (1999).
34. 2/dt averaged over the noise dW is positive definite.
35. This follows most simply by treating each observer as having access to a separate output channel, or environment, but it is clear from [22] that one could obtain the same result by dividing up the available light using a sequence of beam splitters. For an explicit treatment of multiple observers see Ref. [23]. A recent and less mathematical treatment is also given in Ref. [24].
36. H.M Wiseman, Ph.D. thesis, University of Queensland, Australia.
37. A. Barchielli, Int. J. Theor. Phys, 32, 2221 (1993).
38. J. Dziarmaga, D.A.R Dalvit, and W.H. Zurek, e-print quant-ph/0107033.
39. S. Habib (unpublished).
40. Positivity at this second cumulant level does not require the noise term: the covariance matrix stays positive even without the addition of this piece.
41. Since complex conjugation along with P → - P leaves the algebra [X,P] = iℏ unchanged, the momentum flip along with H → -H (i.e., m → -m and F → -F) and ρ → ρ* is an invariance of Eq. 3. Thus our results also apply to the negative mass case mutatis mutandis.
42. P.S. Maybeck, Stochastic Models, Estimation and Control (Academic Press, New York, 1982).
43. A.C. Doherty, S. Habib, K. Jacobs, H. Mabuchi, and S.M. Tan, Phys. Rev. A 62, 012105 (2000).
44. T. Bhattacharya, S. Habib, K. Jacobs, and K. Shizume, Phys. Rev. A 65, 032115 (2002).
45. S. Ghose, P.M. Alsing, I.H. Deutsch, T. Bhattacharya, S. Habib, and K. Jacobs, e-print quant-ph/0208064.