Exact master equation and quantum decoherence of two coupled harmonic oscillators in a general environment

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 77, Issue 1, 2008, Pages

  Chou, Chung Hsien ^a,b   Yu, Ting ^c   Hu, B L ^b  

^a INSTITUTE OF PHYSICS   (Taiwan)

^b UNIVERSITY OF MARYLAND   (United States)

^c UNIVERSITY OF ROCHESTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; PROBABILITY DENSITY FUNCTION; QUANTUM THEORY; SPECTRAL DENSITY; TEMPERATURE MEASUREMENT;

HARMONIC OSCILLATORS; MESOSCOPIC OBJECTS; QUANTUM DECOHERENCE; SPECTRAL DENSITY FUNCTIONS;

OSCILLATORS (ELECTRONIC);

EID: 38349134516     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.77.011112     Document Type: Article

References (66)

1. M. Arndt, Nature (London) NATUAS 0028-0836 10.1038/44348 401, 680 (1999).
2. S. Bose, K. Jacobs, and P. L. Knight, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.59.3204 59, 3204 (1999).
3. J. Friedman, Nature (London) NATUAS 0028-0836 10.1038/35017505 406, 43 (2000)
4. C. H. van der Wal, Science SCIEAS 0036-8075 10.1126/science.290.5492.773 290, 773 (2000).
5. A. D. Armour, M. P. Blencowe, and K. C. Schwab, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.148301 88, 148301 (2002).
6. J. Eisert, M. B. Plenio, S. Bose, and J. Hartley, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.190402 93, 190402 (2004).
7. S. Mancini, V. Giovannetti, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.88.120401 88, 120401 (2002).
8. S. Mancini, D. Vitali, and P. Tombesi, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.90.137901 90, 137901 (2003).
9. W. Marshall, C. Simon, R. Penrose, and D. Bouwmeester, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.91.130401 91, 130401 (2003).
10. A. Bassi, E. Ippoliti, and S. L. Adler, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.030401 94, 030401 (2005).
11. M. Pinard, Europhys. Lett. EULEEJ 0295-5075 10.1209/epl/i2005-10317-6 72, 747 (2005).
12. T. J. Kippenberg, H. Rokhsari, T. Carmon, A. Scherer, and K. J. Vahala, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.033901 95, 033901 (2005).
13. A. Ferreira, A. Guerreiro, and V. Vedral, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.060407 96, 060407 (2006).
14. S. Bose, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.96.060402 96, 060402 (2006).
15. E. Buks and M. P. Blencowe, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.74.174504 74, 174504 (2006).
16. D. W. Hallwood, K. Burnett, and J. Dunningham, e-print arXiv:quant-ph/0609077
17. J. A. Dunningham, K. Burnett, R. Roth, and W. D. Phillips, e-print arXiv:quant-ph/0608242.
18. R. Feynman and F. L. Vernon, Ann. Phys. (N.Y.) APNYA6 0003-4916 10.1016/0003-4916(63)90068-X 24, 118 (1963).
19. A. O. Caldeira and A. J. Leggett, Physica A PHYADX 0378-4371 10.1016/0378-4371(83)90013-4 121, 587 (1983).
20. A sample of references is listed here: V. Hakim and V. Ambegaokar, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.423 32, 423 (1985)
21. F. Haake and R. Reibold, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.32.2462 32, 2462 (1985)
22. W. G. Unruh and W. H. Zurek, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.40.1071 40, 1071 (1989)
23. H. Grabert, P. Schramm, and G. L. Ingold, Phys. Rep. PRPLCM 0370-1573 10.1016/0370-1573(88)90023-3 168, 115 (1988)
24. J. J. Halliwell and A. Zoupas, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.52.7294 52, 7294 (1995).
25. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.45.2843 45, 2843 (1992)
26. B. L. Hu, J. P. Paz, and Y. Zhang, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.47.1576 47, 1576 (1993).
27. J. J. Halliwell and T. Yu, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.53.2012 53, 2012 (1996).
28. W. T. Strunz and T. Yu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052115 69, 052115 (2004).
29. C. H. Fleming, A. Roura, and B. L. Hu, e-print arXiv:0705.2766.
30. M. S. Kim, J. Lee, D. Ahn, and P. L. Knight, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.040101 65, 040101 (R) (2002).
31. D. Braun, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.89.277901 89, 277901 (2002).
32. M. Paternostro, W. Son, and M. S. Kim, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.92.197901 92, 197901 (2004).
33. Z. Ficek and R. Tanas, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.74. 024304 74, 024304 (2006).
34. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer, Berlin, 1991).
35. C. W. Gardiner and P. Zoller, Quantum Noise (Springer, Berlin, 2002).
36. This equation was originally derived for the Markovian limit. We have added the name Markov to it since we want to call the equation 30 which covers the more general cases of the Fokker-Planck equation. This more general equation is sometimes called the Wigner equation.
37. C. Anastopoulos and B. L. Hu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.033821 62, 033821 (2000).
38. B. L. Hu and Y. Zhang, Int. J. Mod. Phys. A IMPAEF 0217-751X 10.1142/S0217751X95002102 10, 4537 (1995).
39. C. Hörhammer and H. Büttner, J. Phys. A JPHAC5 0305-4470 10.1088/0305-4470/38/33/008 38, 7325 (2005).
40. K. Shiokawa and B. L. Hu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.062106 70, 062106 (2004).
41. T. Yu and J. H. Eberly, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.140404 93, 140404 (2004)
42. T. Yu and J. H. Eberly, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.97.140403 97, 140403 (2006).
43. P. J. Dodd and J. J. Halliwell, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.052105 69, 052105 (2004).
44. J. P. Paz, S. Habib, and W. H. Zurek, Phys. Rev. D PRVDAQ 0556-2821 10.1103/PhysRevD.47.488 47, 488 (1993).
45. L. M. Duan, G. Giedke, J. I. Cirac, and P. Zoller, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2722 84, 2722 (2000).
46. R. Simon, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.2726 84, 2726 (2000).
47. C. Anastopoulos, S. Shresta, and B. L. Hu, e-print arXiv:quant-ph/ 0610007.
48. L. Diósi and C. Kiefer, J. Phys. A 35, 2675 (2002). 0022-3689
49. T. Yu and J. H. Eberly, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.66.193306 66, 193306 (2002).
50. S. Y. Lin, C. H. Chou, and B. L. Hu (unpublished).
51. R. Landauer, IBM J. Res. Dev. 5, 183 (1961).
52. C. H. Bennett, Stud. Hist. Philos. Mod. Phys. 34, 501 (2003).
53. C. M. Caves, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.47.4010 47, 4010 (1993).
54. J. Bub, Stud. Hist. Philos. Mod. Phys. 32, 569 (2001).
55. O. J. E. Maroney, e-print arXiv:quant-ph/0702094
56. O. J. E. Maroney, e-print arXiv:quant-ph/0701127
57. O. J. E. Maroney, e-print arXiv:quant-ph/0411172.
58. C. Hörhammer and H. Büttner, e-print arXiv:0710.1716.
59. C. H. Fleming, A. Roura, and B. L. Hu, e-print arXiv:0705.2766.
60. N. Cummings and B. L. Hu, e-print arXiv:0708.2257.
61. D. Vitali, S. Gigan, A. Ferreira, H. R. Bohm, P. Tombesi, A. Guerreiro, V. Vedral, A. Zeilinger, and M. Aspelmeyer, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.030405 98, 030405 (2007).
62. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, e-print arXiv:0705.1728.
63. H. Mueller-Ebhardt, H. Rehbein, R. Schnabel, K. Danzmann, and Y. Chen, e-print arXiv:quant-ph/0702258.
64. T. Yu, C. Fleming, and B. L. Hu (unpublished).
65. C. Galley, C. H. Chou, and B. L. Hu (unpublished).
66. C. H. Chou, B. L. Hu, and T. Yu, Physica A 387, 432 (2008). 0378-4371