Ensemble versus individual system in quantum optics

Fortschritte der Physik

Volumn 46, Issue 6-8, 1998, Pages 595-604

  Hegerfeldt, Gerhard C ^a  

^a NONE

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EID: 0032325914     PISSN: 00158208     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1521-3978(199811)46:6/8<595::AID-PROP595>3.0.CO;2-M     Document Type: Article

References (44)

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12. R. J. COOK and H. J. KIMBLE, Phys. Rev. Lett. 54, 1023 (1985); C. COHEN-TANNOUDJI and J. DALIBARD, Europhysics Lett. 1, 441 (1986); A. SCHENZLE, R. G. DEVOE, and R. G. BREWER, Phys. Rev. A 33, 2127 (1986); J. JAVANAINEN, Phys. Rev. A 33, 2121 (1986); D. T. PEGG, R. LOUDON, and P. L. KNIGHT, Phys. Rev. A 33, 4085 (1986), G. NIENHUIS, Phys. Rev. A 35, 4639 (1987); P. ZOLLER, M. MARTE, and D. J. WALLS, Phys. Rev. A 35, 198 (1987); S. REYNAUD, J. DALIBARD, and C. COHEN-TANNOUDJI, IEEE Journal of Quantum Electronics 24, 1395 (1988); M. PORRATI and S. PUTTERMAN, Phys. Rev. A 36, 925 (1987) and A 39, 3010 (1989); M. S. KIM and P. L. KNIGHT, Phys. Rev. A 40, 215 (1989) (1975).
13. R. J. COOK and H. J. KIMBLE, Phys. Rev. Lett. 54, 1023 (1985); C. COHEN-TANNOUDJI and J. DALIBARD, Europhysics Lett. 1, 441 (1986); A. SCHENZLE, R. G. DEVOE, and R. G. BREWER, Phys. Rev. A 33, 2127 (1986); J. JAVANAINEN, Phys. Rev. A 33, 2121 (1986); D. T. PEGG, R. LOUDON, and P. L. KNIGHT, Phys. Rev. A 33, 4085 (1986), G. NIENHUIS, Phys. Rev. A 35, 4639 (1987); P. ZOLLER, M. MARTE, and D. J. WALLS, Phys. Rev. A 35, 198 (1987); S. REYNAUD, J. DALIBARD, and C. COHEN-TANNOUDJI, IEEE Journal of Quantum Electronics 24, 1395 (1988); M. PORRATI and S. PUTTERMAN, Phys. Rev. A 36, 925 (1987) and A 39, 3010 (1989); M. S. KIM and P. L. KNIGHT, Phys. Rev. A 40, 215 (1989) (1975).
14. R. J. COOK and H. J. KIMBLE, Phys. Rev. Lett. 54, 1023 (1985); C. COHEN-TANNOUDJI and J. DALIBARD, Europhysics Lett. 1, 441 (1986); A. SCHENZLE, R. G. DEVOE, and R. G. BREWER, Phys. Rev. A 33, 2127 (1986); J. JAVANAINEN, Phys. Rev. A 33, 2121 (1986); D. T. PEGG, R. LOUDON, and P. L. KNIGHT, Phys. Rev. A 33, 4085 (1986), G. NIENHUIS, Phys. Rev. A 35, 4639 (1987); P. ZOLLER, M. MARTE, and D. J. WALLS, Phys. Rev. A 35, 198 (1987); S. REYNAUD, J. DALIBARD, and C. COHEN-TANNOUDJI, IEEE Journal of Quantum Electronics 24, 1395 (1988); M. PORRATI and S. PUTTERMAN, Phys. Rev. A 36, 925 (1987) and A 39, 3010 (1989); M. S. KIM and P. L. KNIGHT, Phys. Rev. A 40, 215 (1989) (1975).
15. R. J. COOK and H. J. KIMBLE, Phys. Rev. Lett. 54, 1023 (1985); C. COHEN-TANNOUDJI and J. DALIBARD, Europhysics Lett. 1, 441 (1986); A. SCHENZLE, R. G. DEVOE, and R. G. BREWER, Phys. Rev. A 33, 2127 (1986); J. JAVANAINEN, Phys. Rev. A 33, 2121 (1986); D. T. PEGG, R. LOUDON, and P. L. KNIGHT, Phys. Rev. A 33, 4085 (1986), G. NIENHUIS, Phys. Rev. A 35, 4639 (1987); P. ZOLLER, M. MARTE, and D. J. WALLS, Phys. Rev. A 35, 198 (1987); S. REYNAUD, J. DALIBARD, and C. COHEN-TANNOUDJI, IEEE Journal of Quantum Electronics 24, 1395 (1988); M. PORRATI and S. PUTTERMAN, Phys. Rev. A 36, 925 (1987) and A 39, 3010 (1989); M. S. KIM and P. L. KNIGHT, Phys. Rev. A 40, 215 (1989) (1975).
16. R. J. COOK and H. J. KIMBLE, Phys. Rev. Lett. 54, 1023 (1985); C. COHEN-TANNOUDJI and J. DALIBARD, Europhysics Lett. 1, 441 (1986); A. SCHENZLE, R. G. DEVOE, and R. G. BREWER, Phys. Rev. A 33, 2127 (1986); J. JAVANAINEN, Phys. Rev. A 33, 2121 (1986); D. T. PEGG, R. LOUDON, and P. L. KNIGHT, Phys. Rev. A 33, 4085 (1986), G. NIENHUIS, Phys. Rev. A 35, 4639 (1987); P. ZOLLER, M. MARTE, and D. J. WALLS, Phys. Rev. A 35, 198 (1987); S. REYNAUD, J. DALIBARD, and C. COHEN-TANNOUDJI, IEEE Journal of Quantum Electronics 24, 1395 (1988); M. PORRATI and S. PUTTERMAN, Phys. Rev. A 36, 925 (1987) and A 39, 3010 (1989); M. S. KIM and P. L. KNIGHT, Phys. Rev. A 40, 215 (1989) (1975).
17. G. C. HEGERFELDT and T. S. WILSER, in: Classical and Quantum Systems. Proceedings of the II. International Wigner Symposium, July 1991, edited by H. D. Doebner, W. Scherer, and F. Schroeck; World Scientific (Singapore 1992), p. 104.
18. T. S. WILSER, Doctoral Dissertation, University of Göttingen (1991).
19. G. C. HEGERFELDT, Phys. Rev. A 47, 449 (1993).
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21. H. CARMICHAEL, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics, Springer (Berlin 1993).
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23. G. C. Hegerfeldt and M. B. PLENIO, Phys. Rev. A 47, 2186 (1993).
24. G. C. Hegerfeldt and M. B. PLENIO, Quantum Optics 6, 15 (1994).
25. G. C. Hegerfeldt and D. G. SONDERMANN, Quantum Semiclass. Opt. 8, 121 (1996).
26. M. B. PLENIO and P. L. KNIGHT, preprint, quant-ph/9702007.
27. Alternatively one can use the Markov assumption. Cf., e.g., R. REIBOLD, J. Phys. A 26, 179 (1993). See also M. PORRATI and S. PUTTERMAN, Phys. Rev. A 39, 3010 (1989).
28. Alternatively one can use the Markov assumption. Cf., e.g., R. REIBOLD, J. Phys. A 26, 179 (1993). See also M. PORRATI and S. PUTTERMAN, Phys. Rev. A 39, 3010 (1989).
29. As will be pointed out further below, the calculation of the photon emission probabilities will automatically give zero for the present case when Δt → 0. This is a special manifestation of the quantum Zeno effect. Extensive references on this effect can befound in A. BEIGE and G. C. HEGERFELDT, Phys. Rev. A 53 (1996) and in A. BEIGE, G. C. HEGERFELDT, and D. G. SONDERMANN, Found. Physics (Dec. 1997, in press).
30. As will be pointed out further below, the calculation of the photon emission probabilities will automatically give zero for the present case when Δt → 0. This is a special manifestation of the quantum Zeno effect. Extensive references on this effect can befound in A. BEIGE and G. C. HEGERFELDT, Phys. Rev. A 53 (1996) and in A. BEIGE, G. C. HEGERFELDT, and D. G. SONDERMANN, Found. Physics (Dec. 1997, in press).
31. For a similar requirement cf. P. A. M. DIRAC, The Principles of Quantum Mechanics, 4th Ed., Clarendon Press (Oxford 1959), p. 181.
32. The projection postulate as commonly used nowadays is due to G. LÜDERS, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. VON NEUMANN, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool. Cf. also the remark in P. A. M. DIRAC, The Principles of Quantum Mechanics, 1st Ed., Clarendon Press (Oxford 1930), p. 49, about measurements causing minimal disturbance. In later editions this passage has been omitted.
33. The projection postulate as commonly used nowadays is due to G. LÜDERS, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. VON NEUMANN, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool. Cf. also the remark in P. A. M. DIRAC, The Principles of Quantum Mechanics, 1st Ed., Clarendon Press (Oxford 1930), p. 49, about measurements causing minimal disturbance. In later editions this passage has been omitted.
34. The projection postulate as commonly used nowadays is due to G. LÜDERS, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. VON NEUMANN, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool. Cf. also the remark in P. A. M. DIRAC, The Principles of Quantum Mechanics, 1st Ed., Clarendon Press (Oxford 1930), p. 49, about measurements causing minimal disturbance. In later editions this passage has been omitted.
35. The projection postulate as commonly used nowadays is due to G. LÜDERS, Ann. Phys. 8, 323 (1951). For observables with degenerate eigenvalues his formulation differs from that of J. VON NEUMANN, Mathematische Grundlagen der Quantenmechanik, Springer (Berlin 1932) (English translation: Mathematical Foundations of Quantum Mechanics, Princeton University Press, 1955), Chapter V.1. The projection postulate intends to describe the effects of an ideal measurement on the state of a system, and it has been widely regarded as a useful tool. Cf. also the remark in P. A. M. DIRAC, The Principles of Quantum Mechanics, 1st Ed., Clarendon Press (Oxford 1930), p. 49, about measurements causing minimal disturbance. In later editions this passage has been omitted.
36. It would indeed be very interesting if there were non-ergodic quantum trajectories. Then there could be different time averages for different trajectories.
37. M. D. SRINIVAS and E. B. DAVIES, Optica Acta 28, 981 (1981).
38. R. B. GRIFFITHS, this conference.
39. G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 52, 3333 (1995); G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 53, 1178 (1996); M. B. PLENIO, Doctoral Dissertation, University of Göttingen, 1994.
40. G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 52, 3333 (1995); G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 53, 1178 (1996); M. B. PLENIO, Doctoral Dissertation, University of Göttingen, 1994.
41. G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 52, 3333 (1995); G. C. HEGERFELDT and M. B. PLENIO, Phys. Rev. A 53, 1178 (1996); M. B. PLENIO, Doctoral Dissertation, University of Göttingen, 1994.
42. The quantum trajectories can therefore be used to obtain numerical solutions of the Bloch equations by simulations. This was stressed in Ref. [7]. For the simulation of the Bloch equations also other trajectories can be used which do not have the same physical meaning as in the above approach. Cf. e.g. N. GISIN, Phys. Rev. Lett. 52, 1657 (1984); N. GISIN and I. C. PERCIVAL, J. Phys. A: Math. Gen. 25, 5677 (1992) and the survey by D. G. SONDERMANN, in: Nonlinear, deformed and irreversible quantum systems, edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann, World Scientific 1995; p. 273.
43. The quantum trajectories can therefore be used to obtain numerical solutions of the Bloch equations by simulations. This was stressed in Ref. [7]. For the simulation of the Bloch equations also other trajectories can be used which do not have the same physical meaning as in the above approach. Cf. e.g. N. GISIN, Phys. Rev. Lett. 52, 1657 (1984); N. GISIN and I. C. PERCIVAL, J. Phys. A: Math. Gen. 25, 5677 (1992) and the survey by D. G. SONDERMANN, in: Nonlinear, deformed and irreversible quantum systems, edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann, World Scientific 1995; p. 273.
44. The quantum trajectories can therefore be used to obtain numerical solutions of the Bloch equations by simulations. This was stressed in Ref. [7]. For the simulation of the Bloch equations also other trajectories can be used which do not have the same physical meaning as in the above approach. Cf. e.g. N. GISIN, Phys. Rev. Lett. 52, 1657 (1984); N. GISIN and I. C. PERCIVAL, J. Phys. A: Math. Gen. 25, 5677 (1992) and the survey by D. G. SONDERMANN, in: Nonlinear, deformed and irreversible quantum systems, edited by H.-D. Doebner, V. K. Dobrev, and P. Nattermann, World Scientific 1995; p. 273.