Quantum feedback control and classical control theory

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 62, Issue 1, 2000, Pages 012105-012101

  Doherty, Andrew C ^a,c   Habib, Salman ^b   Jacobs, Kurt ^b   Mabuchi, Hideo ^c   Tan, Sze M ^a  

^a UNIVERSITY OF AUCKLAND   (New Zealand)

^b LOS ALAMOS NATIONAL LABORATORY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DIFFERENTIAL EQUATIONS; FEEDBACK CONTROL; PROBABILITY DISTRIBUTIONS; QUANTUM OPTICS;

BOSE-EINSTEIN CONDENSATION; CLASSICAL CONTROL THEORY; QUANTUM STATE VECTOR; QUANTUM STOCHASTIC DIFFERENTIAL EQUATIONS; STOCHASTIC MASTER EQUATION; STOCHASTIC SCHRODINGER EQUATION;

QUANTUM THEORY;

EID: 0034224703     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (56)

1. H. Mabuchi, J. Ye, and H.J. Kimble, Appl. Phys. B: Lasers Opt. 68, 1095 (1999); e-print quant-ph/9805076.
2. B.E. King, C.S. Wood, C.J. Myatt, Q.A. Turchette, D. Leibfried, W.M. Itano, C. Monroe, and D.J. Wineland, Phys. Rev. Lett. 81, 1525 (1998); e-print quant-ph/9803023.
3. MR. Andrews et al., Science 273, 84 (1996).
4. H.M. Wiseman and G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993); Phys. Rev. A 49, 2133 (1994); 49, 5159(E) (1994); 50, 4428(E) (1994).
5. H.M. Wiseman and G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993); Phys. Rev. A 49, 2133 (1994); 49, 5159(E) (1994); 50, 4428(E) (1994).
6. H.M. Wiseman and G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993); Phys. Rev. A 49, 2133 (1994); 49, 5159(E) (1994); 50, 4428(E) (1994).
7. H.M. Wiseman and G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993); Phys. Rev. A 49, 2133 (1994); 49, 5159(E) (1994); 50, 4428(E) (1994).
8. M.S. Taubman, H.M. Wiseman, D.E. McClelland, and H.-A. Bachor, J. Opt. Soc. Am. B 12, 1792 (1995); H.M. Wiseman, Phys. Rev. Lett. 81, 3840 (1998); e-print quant-ph/9805077.
9. M.S. Taubman, H.M. Wiseman, D.E. McClelland, and H.-A. Bachor, J. Opt. Soc. Am. B 12, 1792 (1995); H.M. Wiseman, Phys. Rev. Lett. 81, 3840 (1998); e-print quant-ph/9805077.
10. J.J. Slosser and G.J. Milburn, Phys. Rev. Lett. 75, 418 (1995); P. Tombesi and D. Vitali, Appl. Phys. B: Lasers Opt. 60, S69 (1995); Phys. Rev. A 51, 4913 (1995); P. Goetsch, P. Tombesi, and D. Vitali, ibid. 54, 4519 (1996); D.B. Horoshko and S.Ya. Kilin, Phys. Rev. Lett. 78, 840 (1997).
11. J.J. Slosser and G.J. Milburn, Phys. Rev. Lett. 75, 418 (1995); P. Tombesi and D. Vitali, Appl. Phys. B: Lasers Opt. 60, S69 (1995); Phys. Rev. A 51, 4913 (1995); P. Goetsch, P. Tombesi, and D. Vitali, ibid. 54, 4519 (1996); D.B. Horoshko and S.Ya. Kilin, Phys. Rev. Lett. 78, 840 (1997).
12. J.J. Slosser and G.J. Milburn, Phys. Rev. Lett. 75, 418 (1995); P. Tombesi and D. Vitali, Appl. Phys. B: Lasers Opt. 60, S69 (1995); Phys. Rev. A 51, 4913 (1995); P. Goetsch, P. Tombesi, and D. Vitali, ibid. 54, 4519 (1996); D.B. Horoshko and S.Ya. Kilin, Phys. Rev. Lett. 78, 840 (1997).
13. J.J. Slosser and G.J. Milburn, Phys. Rev. Lett. 75, 418 (1995); P. Tombesi and D. Vitali, Appl. Phys. B: Lasers Opt. 60, S69 (1995); Phys. Rev. A 51, 4913 (1995); P. Goetsch, P. Tombesi, and D. Vitali, ibid. 54, 4519 (1996); D.B. Horoshko and S.Ya. Kilin, Phys. Rev. Lett. 78, 840 (1997).
14. J.J. Slosser and G.J. Milburn, Phys. Rev. Lett. 75, 418 (1995); P. Tombesi and D. Vitali, Appl. Phys. B: Lasers Opt. 60, S69 (1995); Phys. Rev. A 51, 4913 (1995); P. Goetsch, P. Tombesi, and D. Vitali, ibid. 54, 4519 (1996); D.B. Horoshko and S.Ya. Kilin, Phys. Rev. Lett. 78, 840 (1997).
15. J.A. Dunningham, H.M. Wiseman, and D.F. Walls, Phys. Rev. A 55, 1398 (1997); S. Mancini and P. Tombesi, ibid. 56, 2466 (1997); S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 80, 688 (1998); e-print quant-ph/9802034.
16. J.A. Dunningham, H.M. Wiseman, and D.F. Walls, Phys. Rev. A 55, 1398 (1997); S. Mancini and P. Tombesi, ibid. 56, 2466 (1997); S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 80, 688 (1998); e-print quant-ph/9802034.
17. J.A. Dunningham, H.M. Wiseman, and D.F. Walls, Phys. Rev. A 55, 1398 (1997); S. Mancini and P. Tombesi, ibid. 56, 2466 (1997); S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. 80, 688 (1998); e-print quant-ph/9802034.
18. H.F. Hofman, G. Mahler, and O. Hess, Phys. Rev. A 57, 4877 (1998).
19. E. Knill, L. Viola, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999); L. Viola and S. Lloyd, Phys. Rev. A 58, 2733 (1998).
20. E. Knill, L. Viola, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999); L. Viola and S. Lloyd, Phys. Rev. A 58, 2733 (1998).
21. H. Rabitz, W.S. Warren, and M. Dahleh, Science 259, 1581 (1993).
22. V.P. Belavkin, Information Complexity and Control in Quantum Physics, edited by A. Blaquiere, S. Diner, and G. Lochak (Springer-Verlag. New York, 1987).
23. A.C. Doherty and K. Jacobs, Phys. Rev. A 60, 2700 (1999); e-print quant-ph/9812004.
24. P. Cohadon, A. Heidmann, and M. Pinard, Phys. Rev. Lett. 83, 3174 (1999); quant-ph/9903094.
25. O.L.R. Jacobs, Introduction to Control Theory (Oxford University Press, Oxford, 1993).
26. P.S. Maybeck, Stochastic Models, Estimation and Control (Academic Press, New York, 1982), Vols. II and III.
27. P. Whittle, Optimal Control (Wiley, Chichester, 1996).
28. A. Bensoussan, Stochastic Control of Partialy Observable Systems (Cambridge University Press, Cambridge, 1992).
29. B.D.O. Anderson and J.B. Moore, Optimal Control: Linear Quadratic Methods (Prentice-Hall, Englewood Cliffs, NJ, 1990).
30. K. Zhou, J.C. Doyle, and K. Glover, Robust and Optimal Control (Prentice-Hall, Englewood Cliffs, NJ, 1996).
31. H.J. Carmichael, S. Singh, R. Vyas, and P.R. Rice, Phys. Rev. A 39, 1200 (1989); G.C. Hegerfeldt and T.S. Wilser, in Proceedings of the 2nd International Wigner Symposium, Goslar, Germany, 1991, edited by H.D. Döbner, W. Scherer, and F. Schröck (World Scientific, Singapore, 1992); J. Dalibard, Y. Castin, and K. Molmer, Phys. Rev. Lett. 68, 580 (1992).
32. H.J. Carmichael, S. Singh, R. Vyas, and P.R. Rice, Phys. Rev. A 39, 1200 (1989); G.C. Hegerfeldt and T.S. Wilser, in Proceedings of the 2nd International Wigner Symposium, Goslar, Germany, 1991, edited by H.D. Döbner, W. Scherer, and F. Schröck (World Scientific, Singapore, 1992); J. Dalibard, Y. Castin, and K. Molmer, Phys. Rev. Lett. 68, 580 (1992).
33. H.J. Carmichael, S. Singh, R. Vyas, and P.R. Rice, Phys. Rev. A 39, 1200 (1989); G.C. Hegerfeldt and T.S. Wilser, in Proceedings of the 2nd International Wigner Symposium, Goslar, Germany, 1991, edited by H.D. Döbner, W. Scherer, and F. Schröck (World Scientific, Singapore, 1992); J. Dalibard, Y. Castin, and K. Molmer, Phys. Rev. Lett. 68, 580 (1992).
34. C.W. Gardiner, A.S. Parkins, and P. Zoller, Phys. Rev. A 46, 4363 (1992).
35. H.J. Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics (Springer-Verlag, Berlin, 1993), Vol. m18.
36. H.M. Wiseman and G.J. Milburn, Phys. Rev. A 47, 642 (1993).
37. M.D. Srinivas and E.B. Davies, Opt. Acta 28, 981 (1981); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. A 114, 451 (1986).
38. M.D. Srinivas and E.B. Davies, Opt. Acta 28, 981 (1981); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. A 114, 451 (1986).
39. M.D. Srinivas and E.B. Davies, Opt. Acta 28, 981 (1981); N. Gisin, Phys. Rev. Lett. 52, 1657 (1984); L. Diosi, Phys. Lett. A 114, 451 (1986).
40. H.M. Wiseman, Phys. Rev. A 75, 4587 (1995).
41. V.P. Belavkin, Autom. Remote Control (Engl. Transl.) 44, 178 (1983).
42. V.P. Belavkin, Rep. Math. Phys. 43, 405 (1999).
43. C.A. Fuchs and C.M. Caves, Phys. Rev. Lett. 73, 3047 (1994).
44. J. Botina and H. Rabitz, Phys. Rev. A 55, 1634 (1997).
45. T.A. Brun, I.C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996); M. Patriarca, C. Presilla, and R. Onofrio, ibid. 30, 7385 (1997); T. Bhattacharya, S. Habib, and K. Jacobs, e-print quant-ph/9906092.
46. T.A. Brun, I.C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996); M. Patriarca, C. Presilla, and R. Onofrio, ibid. 30, 7385 (1997); T. Bhattacharya, S. Habib, and K. Jacobs, e-print quant-ph/9906092.
47. T.A. Brun, I.C. Percival, and R. Schack, J. Phys. A 29, 2077 (1996); M. Patriarca, C. Presilla, and R. Onofrio, ibid. 30, 7385 (1997); T. Bhattacharya, S. Habib, and K. Jacobs, e-print quant-ph/9906092.
48. A.C. Doherty, S.M. Tan, A.S. Parkins, and D.F. Walls, Phys. Rev. A 60, 2380 (1999); e-print quant-ph/9903030.
49. K. Jacobs and P.L. Knight, Phys. Rev. A 57, 2301 (1998); e-print quant-ph/9801042.
50. G.M. Huang, T.J. Tarn, and J.W. Clark, J. Math. Phys. 24, 2608 (1983); V. Ramakrishna, M.V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Phys. Rev. A 51, 960 (1995).
51. G.M. Huang, T.J. Tarn, and J.W. Clark, J. Math. Phys. 24, 2608 (1983); V. Ramakrishna, M.V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Phys. Rev. A 51, 960 (1995).
52. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995); D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); S. Lloyd, e-print quant-ph/9703042; S. Lloyd and S.L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999); e-print quant-ph/9810082.
53. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995); D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); S. Lloyd, e-print quant-ph/9703042; S. Lloyd and S.L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999); e-print quant-ph/9810082.
54. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995); D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); S. Lloyd, e-print quant-ph/9703042; S. Lloyd and S.L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999); e-print quant-ph/9810082.
55. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995); D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995); S. Lloyd, e-print quant-ph/9703042; S. Lloyd and S.L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999); e-print quant-ph/9810082.
56. J.J. Halliwell and A. Zoupas, Phys. Rev. D 52, 7294 (1995).