Restriction on relaxation times derived from the lindblad-type master equations for two-level systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 66, Issue 6, 2002, Pages 621131-621134

  Kimura, Gen ^a  

^a WASEDA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; MATRIX ALGEBRA; POLARIZATION; RELAXATION PROCESSES;

TWO-LEVEL SYSTEMS;

QUANTUM THEORY;

EID: 0036997246     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (42)

1. C.W. Gardiner and P. Zoller, Quantum Noise, 2nd ed. (Springer-Verlag, Heidelberg, 2000).
2. E.B. Davies, Quantum Theory of Open Systems (Academic Press, London, 1976).
3. R. Alicki and K. Lendi, Quantum Dynamical Semigroups and Application, Lecture Notes in Physics Vol. 286 (Springer-Verlag, Berlin, 1987).
4. n.
5. K. Kraus, Ann. Phys. (N.Y.) 64, 311 (1971); States, Effects, and Operations (Springer-Verlag, Heidelberg, 1983).
6. K. Kraus, Ann. Phys. (N.Y.) 64, 311 (1971); States, Effects, and Operations (Springer-Verlag, Heidelberg, 1983).
7. G. Lindblad, Commun. Math. Phys. 48, 119 (1976).
8. V. Gorini, A. Kossakowski, and E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976); V. Gorini, A. Frigerio, M. Verri, A. Kossakowski, and E.C.G. Sudarshan, Rep. Math. Phys. 13, 149 (1978).
9. V. Gorini, A. Kossakowski, and E.C.G. Sudarshan, J. Math. Phys. 17, 821 (1976); V. Gorini, A. Frigerio, M. Verri, A. Kossakowski, and E.C.G. Sudarshan, Rep. Math. Phys. 13, 149 (1978).
10. A. Kossakowski, Rep. Math. Phys. 3, 247 (1972); Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 21, 1021 (1972); R.S. Ingarden and A. Kossakowski, Ann. Phys. (N.Y.) 89, 451 (1975).
11. A. Kossakowski, Rep. Math. Phys. 3, 247 (1972); Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 21, 1021 (1972); R.S. Ingarden and A. Kossakowski, Ann. Phys. (N.Y.) 89, 451 (1975).
12. A. Kossakowski, Rep. Math. Phys. 3, 247 (1972); Bull. Acad. Pol. Sci., Ser. Sci., Math., Astron. Phys. 21, 1021 (1972); R.S. Ingarden and A. Kossakowski, Ann. Phys. (N.Y.) 89, 451 (1975).
13. Here we consider N-level systems. See Ref. [6] for the case of infinite-level systems.
14. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000); M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993).
15. M.A. Nielsen and I.L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge, England, 2000); M. Ohya and D. Petz, Quantum Entropy and Its Use (Springer-Verlag, Berlin, 1993).
16. I.C. Percival, Quantum State Diffusion (Cambridge University Press, New York, 1998).
17. D. Braun, Dissipative Quantum Chaos and Decoherence (Springer-Verlag, New York, 2000).
18. F. Benatti and R. Floreanini, Phys. Lett. B 389, 100 (1996); Nucl. Phys. B 488, 335 (1997).
19. F. Benatti and R. Floreanini, Phys. Lett. B 389, 100 (1996); Nucl. Phys. B 488, 335 (1997).
20. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, New York, 1961); C.P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1990).
21. A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, New York, 1961); C.P. Slichter, Principles of Magnetic Resonance (Springer-Verlag, Berlin, 1990).
22. F. Bloch, Phys. Rev. 70, 460 (1946).
23. Here, Ω is a renormalized frequency and b is a constant vector which determines the stationary state.
24. W.J. Munro and C.W. Gardiner, Phys. Rev. A 53, 2633 (1996); A.S. Parkins, C.W. Gardiner, and M.L. Steyn-Ross, Z. Phys. B: Condens. Matter 83, 413 (1991).
25. W.J. Munro and C.W. Gardiner, Phys. Rev. A 53, 2633 (1996); A.S. Parkins, C.W. Gardiner, and M.L. Steyn-Ross, Z. Phys. B: Condens. Matter 83, 413 (1991).
26. G. Kimura, K. Yuasa, and K. Imafuku, Phys. Rev. Lett. 89, 140403 (2002).
27. ij, as is used in Ref. [7].
28. ij] are purely imaginary, after transforming with some orthogonal matrix. Notice that this diagonalization has already been done in Eq. (6) without losing any generalities to the discussion. See also Eq. (A1) in the Appendix, in which this diagonalization has not been done.
29. A. Kossakowski, Bull. Acad. Poi. Sci., Ser. Sci., Math., Astron. Phys. 21, 649 (1973).
30. 2≥0 follows. Similarly, all γ's are shown to be positive.
31. i≥0(i = 1,2,3) follows from the above proposition.
32. R1.
33. F. Benatti and R. Floreanini, Phys. Lett. B 401, 337 (1997).
34. A. Royer, Phys. Rev. Lett. 77, 3272 (1996).
35. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994); 75, 3021 (1995); R. Alicki, ibid. 75, 3020 (1995).
36. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994); 75, 3021 (1995); R. Alicki, ibid. 75, 3020 (1995).
37. P. Pechukas, Phys. Rev. Lett. 73, 1060 (1994); 75, 3021 (1995); R. Alicki, ibid. 75, 3020 (1995).
38. P. Štelmachovič and V. Buzěk, Phys. Rev. A 64, 062106 (2001).
39. B. d'Espagnat, Conceptual Foundations of Quantum Mechanics, 2nd ed. (Benjamin, New York, 1971).
40. Quantum Theory and Measurement, edited by J.A. Wheeler and W.H. Zurek (Princeton University Press, Princeton, NJ, 1983); New Techniques and Ideas in Quantum Measurement Theory, edited by D.M. Greenberger, Annals of the New York Academy of Sciences Vol. 480 (The New York Academy of Sciences, New York, 1986).
41. Quantum Theory and Measurement, edited by J.A. Wheeler and W.H. Zurek (Princeton University Press, Princeton, NJ, 1983); New Techniques and Ideas in Quantum Measurement Theory, edited by D.M. Greenberger, Annals of the New York Academy of Sciences Vol. 480 (The New York Academy of Sciences, New York, 1986).
42. 2, and the right-hand side of this inequality is positive from Eqs. (8).