Continuous quantum measurement and the emergence of classical chaos

Physical Review Letters

Volumn 85, Issue 23, 2000, Pages 4852-4855

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

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DEGREES OF FREEDOM (MECHANICS); EQUATIONS OF MOTION; MATHEMATICAL OPERATORS; MATRIX ALGEBRA; PHASE SPACE METHODS; RANDOM PROCESSES;

CONTINUOUS QUANTUM MEASUREMENT; LYAPUNOV EXPONENT; STOCHASTIC MASTER EQUATION;

QUANTUM THEORY;

EID: 0034427770     PISSN: 00319007     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevLett.85.4852     Document Type: Article

References (32)

1. H. J. Korsch and M. V. Berry, Physica (Amsterdam) 3D, 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 (Amsterdam) 3D, 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 (Amsterdam) 3D, 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. M.C. Gutzwiller, J. Math. Phys. (N.Y.) 12, 343 (1971); see also E. J. Heller and S. Tomsovic, Phys. Today 46, No. 7, 38 (1993).
5. M.C. Gutzwiller, J. Math. Phys. (N.Y.) 12, 343 (1971); see also E. J. Heller and S. Tomsovic, Phys. Today 46, No. 7, 38 (1993).
6. See, e.g., A. Peres, Phys. Rev. A 30, 1610 (1984); M. Toda and K. Ikeda, Phys. Lett. A 124, 165 (1987); Y. Gu, ibid. 149, 95 (1990); R. Schack and C. M. Caves, Phys. Rev. E 53, 3257 (1996).
7. See, e.g., A. Peres, Phys. Rev. A 30, 1610 (1984); M. Toda and K. Ikeda, Phys. Lett. A 124, 165 (1987); Y. Gu, ibid. 149, 95 (1990); R. Schack and C. M. Caves, Phys. Rev. E 53, 3257 (1996).
8. See, e.g., A. Peres, Phys. Rev. A 30, 1610 (1984); M. Toda and K. Ikeda, Phys. Lett. A 124, 165 (1987); Y. Gu, ibid. 149, 95 (1990); R. Schack and C. M. Caves, Phys. Rev. E 53, 3257 (1996).
9. See, e.g., A. Peres, Phys. Rev. A 30, 1610 (1984); M. Toda and K. Ikeda, Phys. Lett. A 124, 165 (1987); Y. Gu, ibid. 149, 95 (1990); R. Schack and C. M. Caves, Phys. Rev. E 53, 3257 (1996).
10. 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).
11. 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).
12. 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).
13. 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).
14. S. Habib, K. Shizume, and W. H. Zurek, Phys. Rev. Lett. 80, 4361 (1998).
15. See, e.g., T. P. Spiller and J. F. Ralph, Phys. Lett. A 194, 235 (1994); M. Schlautmann and R. Graham, Phys. Rev. E 52, 340 (1995); T. A. Brun, I. C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996).
16. See, e.g., T. P. Spiller and J. F. Ralph, Phys. Lett. A 194, 235 (1994); M. Schlautmann and R. Graham, Phys. Rev. E 52, 340 (1995); T. A. Brun, I. C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996).
17. See, e.g., T. P. Spiller and J. F. Ralph, Phys. Lett. A 194, 235 (1994); M. Schlautmann and R. Graham, Phys. Rev. E 52, 340 (1995); T. A. Brun, I. C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996).
18. W. H. Zurek and J. P. Paz, Phys. Rev. Lett. 72, 2508 (1994).
19. Early work includes A. Barchielli, L. Lanz, and G. M. Prosperi, Nuovo Cimento Soc. Ital. Fis. 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).
20. Early work includes A. Barchielli, L. Lanz, and G. M. Prosperi, Nuovo Cimento Soc. Ital. Fis. 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).
21. Early work includes A. Barchielli, L. Lanz, and G. M. Prosperi, Nuovo Cimento Soc. Ital. Fis. 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).
22. Early work includes A. Barchielli, L. Lanz, and G. M. Prosperi, Nuovo Cimento Soc. Ital. Fis. 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).
23. V. P. Belavkin and P. Staszewski, Phys. Lett. 40A, 359 (1989).
24. C. M. Caves and G. J. Milburn, Phys. Rev. A 36, 5543 (1987).
25. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993); H. M. Wiseman and G. J. Milburn, Phys. Rev. A 47, 642 (1993).
26. H. Carmichael, An Open Systems Approach to Quantum Optics (Springer-Verlag, Berlin, 1993); H. M. Wiseman and G. J. Milburn, Phys. Rev. A 47, 642 (1993).
27. A. C. Doherty and K. Jacobs, Phys. Rev. A 60, 2700 (1999).
28. J. K. Breslin and G. J. Milburn, Phys. Rev. A 55, 1430 (1997); J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995).
29. J. K. Breslin and G. J. Milburn, Phys. Rev. A 55, 1430 (1997); J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995).
30. xF. This does not change the argument in the body of the paper.
31. 2]|F/p| and E|p;/(4F)| evaluated at a typical point of the trajectory are comparable to the action of the system, and define this to be ℏs.
32. W. A. Lin and L. E. Ballentine. Phys. Rev. Lett. 65, 2927 (1990).