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Five Lectures on Dissipative Master Equations

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Book cover Coherent Evolution in Noisy Environments

Part of the book series: Lecture Notes in Physics ((LNP,volume 611))

Abstract

The damped harmonic oscillator is arguably the simplest open quantum system worth studying. It is also of great practical importance because it is an essential ingredient in the theoretical description of many quantum-optical experiments. One can assume rather safely that the quantum master equation of the simple harmonic oscillator would not be studied so extensively if it did not play such a central role in the quantum theory of lasers and the masers. Not surprisingly, then, all major textbook accounts of theoretical quantum optics [1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15] contain a fair amount of detail about damped harmonic oscillators. Fock state representations or phase space functions of some sort are invariably employed in these treatments.

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References

  1. J. R. Klauder, E. C. G. Sudarshan: Fundamentals of Quantum Optics (W. A. Benjamin, New York 1970)

    Google Scholar 

  2. R. Loudon: The Quantum Theory of Light (Oxford University Press, New York 1973)

    Google Scholar 

  3. W. H. Louisell: Quantum Statistical Properties of Radiation (John Wiley, New York 1973)

    Google Scholar 

  4. H. M. Nussenzveig: Introduction to Quantum Optics (Gordon and Breach, New York 1974)

    Google Scholar 

  5. M. Sargent III, M. O. Scully, W. E. Lamb Jr.: Laser Physics (Addison-Wesley, Reading 1974)

    Google Scholar 

  6. L. Allen, J. H. Eberly: Optical Resonance and Two-Level Atoms (John Wiley, New York 1975)

    Google Scholar 

  7. H. Haken: Light, Vols. I and II (North-Holland, Amsterdam 1981)

    Google Scholar 

  8. P. L. Knight, L. Allen: Concepts of Quantum Optics (Pergamon Press, Oxford 1983)

    Google Scholar 

  9. P. Meystre, M. Sargent III: Elements of Quantum Optics (Springer, Berlin 1990)

    Google Scholar 

  10. H. Carmichael: An Open System Approach to Quantum Optics (Springer, Heidelberg 1991)

    Google Scholar 

  11. W. Vogel, D.-G. Welsch: Lectures on Quantum Optics (Akademie Verlag, Berlin 1994)

    Google Scholar 

  12. D. F. Walls, G. J. Milburn: Quantum Optics (Springer, Heidelberg 1994)

    MATH  Google Scholar 

  13. M. O. Scully, M. S. Zubairy: Quantum Optics (Cambridge University Press, Cambridge 1997)

    Google Scholar 

  14. C.W. Gardiner, P. Zoller: Quantum Noise (Springer, Heidelberg 2000)

    MATH  Google Scholar 

  15. W. P. Schleich: Quantum Optics in Phase Space (Wiley-VCH, Berlin 2001)

    Book  MATH  Google Scholar 

  16. A. S. Holevo: Rep. Math. Phys. 33, 95 (1993)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  17. A. S. Holevo: J. Funct. Anal. 131, 255 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  18. B. Vacchini: Quantum optical versus quantum Brownian motion master-equation in terms of covariance and equilibrium properties, Preprint arXiv:quant-ph/0204071 (2002)

    Google Scholar 

  19. B.-G. Englert: Elements of Micromaser Physics, Preprint arXiv:quant-ph/0203052 (2002)

    Google Scholar 

  20. H.-J. Briegel, B.-G. Englert: Phys. Rev. A 47, 3311 (1993); errata in [37]

    Article  ADS  Google Scholar 

  21. B.-G. Englert, M. Naraschewski, A. Schenzle: Phys. Rev. A 50, 2667 (1994); the argument of the Laguerre polynomial has the wrong sign in (2.17)

    Article  ADS  Google Scholar 

  22. B.-G. Englert: J. Phys. A 22, 625 (1989)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. A. Royer: Phys. Rev. A 15, 449 (1977)

    Article  ADS  MathSciNet  Google Scholar 

  24. A. Grossmann: Commun. Math. Phys. 48, 191 (1976)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. S. M. Barnett, S. Stenholm: J. Mod. Opt. 47, 2869 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  26. H. Risken: The Fokker-Planck Equation, 2nd edn. (Springer, Heidelberg 1989)

    MATH  Google Scholar 

  27. G. Lindblad: Commun. Math. Phys. 48, 119 (1976)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  28. R. Alicki, K. Lendi: Quantum Dynamical Semigroups and Applications (Springer, Heidelberg 1987)

    Book  MATH  Google Scholar 

  29. A. S. Holevo: Statistical Structure of Quantum Theory (Springer, Berlin 2001)

    MATH  Google Scholar 

  30. G. Raithel, C. Wagner, H. Walther, L. M. Narducci, M. O. Scully: ‘The Micromaser: A Proving Ground for Quantum Physics’. In: Cavity Quantum Electrodynamics, ed. by P. R. Berman (Academic Press, New York 1994) pp. 57–121

    Google Scholar 

  31. S. Haroche, J.-M. Raimond: ‘Manipulation of Non-Classical Field States in a Cavity by Atomic Interferometry’. In: Cavity Quantum Electrodynamics, ed. by P. R. Berman (Academic Press, New York 1994) pp. 123–170

    Google Scholar 

  32. H. Walther: Opt. Spectrosc. 91, 327 (2001)

    Article  ADS  Google Scholar 

  33. J.-M. Raimond, M. Brune, S. Haroche: Rev. Mod. Phys. 73, 565 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  34. H. Walther, B. T. H. Varcoe, B.-G. Englert: Cavity Quantum Electrodynamics (in preparation for Rep. Prog. Phys., to be submitted shortly)

    Google Scholar 

  35. B. T. H. Varcoe, S. Brattke, M. Weidinger, H. Walther: Nature (London) 403, 743 (2000)

    Article  ADS  Google Scholar 

  36. S. Brattke, B.-G. Englert, B. T. H. Varcoe, H. Walther: J. Mod. Opt. 47, 2857 (2000)

    MATH  ADS  MathSciNet  Google Scholar 

  37. H.-J. Briegel, B.-G. Englert: Phys. Rev. A 52, 2361 (1995)

    Article  ADS  Google Scholar 

  38. B.-G. Englert, N. Sterpi, H. Walther: Opt. Commun. 100, 526 (1993)

    Article  ADS  Google Scholar 

  39. H.-J. Briegel, B.-G. Englert, N. Sterpi, H. Walther: Phys. Rev. A 49, 2962 (1994)

    Article  ADS  Google Scholar 

  40. B. Kümmerer, H. Maassen: An Ergodic Theorem for Quantum Counting Processes, LANL eprint quant-ph/0102134 (2001)

    Google Scholar 

  41. N. D. Mermin: ‘Whose Knowledge?’. In: Quantum (Un)speakables. From Bell to Quantum Information, ed. by R. A. Bertlmann, A. Zeilinger (Springer, Berlin 2002) pp. 171–180

    Google Scholar 

  42. T. A. Brun, J. Finkelstein, N. D. Mermin: Phys. Rev. A 65, 032315 (2002)

    Article  ADS  Google Scholar 

  43. C. M. Caves, C. A. Fuchs, R. Schack: Conditions for compatibility of quantum state assignments, LANL eprint quant-ph/0206110 (2002)

    Google Scholar 

  44. B.-G. Englert, M. Löffler, O. Benson, B. Varcoe, M. Weidinger, H. Walther: Fortschr. Phys. 46, 897 (1998)

    Article  Google Scholar 

  45. G. Rempe, F. Schmidt-Kaler, H. Walther: Phys. Rev. Lett. 64, 2783 (1990)

    Article  ADS  Google Scholar 

  46. G. Rempe, H. Walther: Phys. Rev. A 42, 1650 (1990)

    Article  ADS  Google Scholar 

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Englert, BG., Morigi, G. (2002). Five Lectures on Dissipative Master Equations. In: Buchleitner, A., Hornberger, K. (eds) Coherent Evolution in Noisy Environments. Lecture Notes in Physics, vol 611. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45855-7_2

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  • DOI: https://doi.org/10.1007/3-540-45855-7_2

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