Skip to main content
SpringerLink
Log in

What Is a Quantized Mode of a Leaky Cavity?

  • Conference paper
  • First Online:
Modern Challenges in Quantum Optics

Part of the book series: Lecture Notes in Physics ((LNP,volume 575))

Abstract

Quantum optics conventionally represents the electromagnetic radiation in a leaky cavity by a normal-modes expansion, as if the cavity were closed and perfect, with the leakage being described by coupling these modes to a reservoir. This phenomenological approach is only a good approximation for stable resonators with very large quality factors. Here we show how the quantized field can be described by the actual natural cavity modes rather than these fictitious normal modes. Our approach leads to a radically different model for quantum dissipation, where reservoir and dissipative system operators no longer commute.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. G. Fox and T. Li: Proc. IRE 48, 1904 (1960) A. G. Fox and T. Li: Bell Sys. Tech. J. 40, 453 (1961)

    Google Scholar 

  2. A. E. Siegman: Appl. Phys. Lett. 36, 412 (1980)

    Article  ADS  Google Scholar 

  3. E. Fermi: Rev. Mod. Phys. 4, 87 (1932)

    Article  MATH  ADS  Google Scholar 

  4. I. R. Senitzky: Phys. Rev. 115, 227 (1959) I. R. Senitzky: Phys. Rev. 119, 670 (1960)

    Article  ADS  MathSciNet  Google Scholar 

  5. H. B. Callen and T. A. Welton: Phys. Rev. 83, 34 (1951)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. J. Weber: Phys. Rev. 90, 977 (1953)

    Article  MATH  ADS  Google Scholar 

  7. M. J. Collett and C. W. Gardiner: Phys. Rev. A 30, 1386 (1984) C. W. Gardiner and M. J. Collett: Phys. Rev. A 31, 3761 (1985) C. W. Gardiner: Quantum Noise (Springer-Verlag, Berlin 1991)

    Google Scholar 

  8. S. M. Dutra and G. Nienhuis: Phys. Rev. A 62, 063805 (2000)

    Article  ADS  Google Scholar 

  9. K. Petermann: IEEE J. Quantum Electron. 15, 566 (1979)

    Article  ADS  MathSciNet  Google Scholar 

  10. A. E. Siegman: Phys. Rev. A 39, 1253 (1989) A. E. Siegman: Phys. Rev. A 39, 1264 (1989)

    Article  ADS  Google Scholar 

  11. H. Helmholtz: J. f. d. reine u. Math. 100, 137 (1887) P. Havas: Sup. Nuovo Cimento 5, 363 (1957) C. Lanczos: The Variational Principles of Mechanics (University of Toronto Press, Toronto 1952)

    Google Scholar 

  12. H. Bateman: Phys. Rev. 38, 815 (1931) P. M. Morse and H. Feshbach: Methods of Theoretical Physics (McGraw-Hill, New York 1953) H. Feshbach and Y. Tikochinsky: Trans. N. Y. Acad. Sci. 38, 44 (1977) F. Riewe: Phys. Rev. E 53, 1890 (1996)

    Google Scholar 

  13. E. Kanai: Progr. Theoret. Phys. (Kyoto) 3, 440 (1948) W. E. Brittin: Phys. Rev. 77, 396 (1950) E. H. Kerner: Can. J. Phys. 36, 371 (1958) W. K. H. Stevens: Proc. Phys. Soc. (London) 72, 1027 (1958) V. W. Myers: Am. J. Phys. 27, 507 (1959)

    Article  ADS  Google Scholar 

  14. J. R. Ray: Am. J. Phys. 47, 626 (1979)

    Article  ADS  Google Scholar 

  15. H. Dekker: Phys. Rep. 80, 1 (1981)

    Article  ADS  MathSciNet  Google Scholar 

  16. W. H. Zurek: Phys. Today 44, 36 (1991) W. H. Zurek: Phys. Rev. D 24, 1516 (1981) W. H. Zurek: Phys. Rev. D 26, 1862 (1982) W. H. Zurek, S. Habib, and J. P. Paz: Phys. Rev. Lett. 70, 1187 (1993)

    Article  Google Scholar 

  17. W. Heisenberg: Physics and Philosophy (Harper & Row, New York 1962) pp. 177–178 R. Omnès: Rev. Mod. Phys. 64, 339 (1992) R. Omnès: The Interpretation of Quantum Mechanics (Princeton University Press, Princeton 1994) E. Wigner: Am. J. Phys. 31, 6 (1963) K. Gottfried: Quantum Mechanics I (W. A. Benjamin inc., New York 1966) pp. 165-232

    Google Scholar 

  18. B. M. Garraway and P. L. Knight: Phys. Rev. A 49, 1266 (1994) B. M. Garraway and P. L. Knight: Phys. Rev. A 50, 2548 (1994) L. Gilles, B. M. Garraway, and P. L. Knight: Phys. Rev. A 49, 2785 (1994) C. Gerry and E. E. Hach III: Phys. Lett. A 174, 185 (1993)

    Article  ADS  Google Scholar 

  19. S. M. Dutra: Eur. J. Phys. 18, 194 (1997)

    Article  Google Scholar 

  20. L. Knöll, W. Vogel, and D. G. Welsch, Phys. Rev. A 43, 543 (1991) L. Knöll and D.-G. Welsch: Prog. Quant. Electr. 16, 135 (1992) W. Vogel and D.-G. Welsch: Lectures on quantum optics (Akademie Verlag, Berlin 1994) Chap. 8

    Google Scholar 

  21. R. J. Glauber: Phys. Rev. 131, 2766 (1963) E. C. G. Sudarshan: Phys. Rev. Lett. 10, 277 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  22. J. R. Klauder, J. McKenna, and D. G. Currie: J. Math. Phys. 6, 734 (1965)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  23. H. M. Nussenzveig: Introduction to Quantum Optics (Gordon and Breach, London 1973), pp. 54–69

    Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. R. H. Dicke, Molecular amplification and generation systems and methods, U.S. Patent 2 851 652, 9 September 1958, reprinted in Lasers: A collection of reprints with commentary ed. J. Weber (Gordon and Breach, New York, 1968) p. 645

    Google Scholar 

  26. A. L. Schawlow and C. H. Townes: Phys. Rev. 29, 1940 (1958)

    Article  ADS  Google Scholar 

  27. A. M. Prokhorov: Sov. Phys. JETP 7, 1140 (1958)

    Google Scholar 

  28. S. R. Barone: J. Appl. Phys. 34, 831 (1963)

    Article  ADS  Google Scholar 

  29. A. E. Siegman: Opt. Commun. 31, 369 (1979)

    Article  ADS  Google Scholar 

  30. A. E. Siegman: Lasers (Oxford University Press, Oxford 1987)

    Google Scholar 

  31. M. A. Rippin and G. H. C. New: J. Mod. Opt. 43, 993 (1996)

    Article  ADS  Google Scholar 

  32. P. M. Morse and H. Feshbach: Methods of Theoretical Physics (McGraw-Hill, New York 1953)

    MATH  Google Scholar 

  33. W. E. Lamb Jr.: Phys. Rev. 134, A1429 (1964)

    Article  ADS  Google Scholar 

  34. P. Meystre and M. Sargent: Elements of quantum optics (Springer-Verlag, Berlin 1991)

    Google Scholar 

  35. J. J. Thomson: Proc. Lond. Math. Soc. 15, 197 (1884) J. J. Thomson: Notes on Recent Researches in Electricity and Magnetism: intended as a sequel to Professor Clerk-Maxwell’s treatise on Electricity and Magnetism (Clarendon Press, Oxford 1893) A. Sommerfeld: Partial Differential Equations in Physics (Academic Press, New York 1949), pp. 214-224 (this is Sommerfeld’s pedagogic account of the original problem of a lossy electromagnetic resonator solved by Thomson)

    Google Scholar 

  36. G. Beck and H. M. Nussenzveig: Nouvo Cimento 16, 416 (1960) H. M. Nussenzveig: Causality and Dispersion Relations (Academic Press, New York 1972) Chap. 4 R. Peierls: More Surprises in Theoretical Physics (Princeton University Press, Princeton 1991) pp. 76-82

    Google Scholar 

  37. L. A. Vaînshteîn: J. Tech. Phys. 34, 1541 (1964) L. A. Vaînshteîn: High-Power Electronics 4, 157 (1965) L. A. Weinstein: Open Resonators and Open Waveguides (The Golem Press, Boulder 1969)

    Google Scholar 

  38. L. Ronchi: ‘Optical Resonators’. In: Laser Handbook I. ed. by F. T. Arecchi and E. O. Schulz-DuBois (North-Holland, Amsterdam 1972) pp. 151–190

    Google Scholar 

  39. R. Lang, M. O. Scully, and W. E. Lamb Jr.: Phys. Rev. A 7, 1788 (1973)

    Article  ADS  Google Scholar 

  40. J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, and K. Wódkiewicz: Phys. Rev. A 41, 369 (1990) J. Gea-Banacloche, N. Lu, L. M. Pedrotti, S. Prasad, M. O. Scully, and K. Wódkiewicz: Phys. Rev. A 41, 381 (1990)

    Article  ADS  Google Scholar 

  41. R. W. F. van der Plank and L. G. Suttorp: Phys. Rev. A 53, 1791 (1996) R. W. F. van der Plank: Ph.D. thesis (University of Amsterdam, Amsterdam 1997)

    Article  ADS  Google Scholar 

  42. P. J. Bardro. and S. Stenholm: Phys. Rev. A 60, 2529 (1999) P. J. Bardro. and S. Stenholm: Phys. Rev. A 61, 023806 (2000)

    Article  ADS  Google Scholar 

  43. P. Grangier and J.-P. Poizat: Eur. Phys. J. D 1, 97 (1998) P. Grangier and J.-P. Poizat: Eur. Phys. J. D 7, 99 (1999)

    Article  ADS  Google Scholar 

  44. B. M. Garraway and P. L. Knight: Phys. Rev. A 54, 3592 (1996) B. M. Garraway: Phys. Rev. A 55, 2290 (1997) B. M. Garraway: Phys. Rev. A 55, 4636 (1997)

    Article  ADS  Google Scholar 

  45. B. J. Dalton, S. M. Barnett, and P. L. Knight: J. Mod. Opt. 46, 1315 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  46. K. Ujihara: Phys. Rev. A 12, 148 (1975)

    Article  ADS  Google Scholar 

  47. K. Ujihara: Phys. Rev. A 20, 1096 (1979) X.-P. Feng and K. Ujihara: IEEE J. Quantum Electron. 25, 2332 (1989) X.-P. Feng and K. Ujihara: Phys. Rev. A 41, 2668 (1990)

    Article  ADS  Google Scholar 

  48. P. T. Leung, S. S. Tong, and K. Young: J. Phys. A 30, 2139 (1997) P. T. Leung, S. S. Tong, and K. Young: J. Phys. A 30, 2153 (1997) P. T. Leung, W. M. Suen, C. P. Sun, and K. Young: Phys. Rev. E 57, 6101 (1998) E. S. C. Ching, P. T. Leung, A. M. V. D. Brink, W. M. Suen, S. S. Tong, and K. Young: Rev. Mod. Phys. 70, 1545 (1998)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  49. H. Ogura, Y. Yoshida, I. Iwamoto: J. Phys. Soc. Japan 22, 1421 (1967)

    Article  ADS  Google Scholar 

  50. C. Lamprecht and H. Ritsch: Phys. Rev. Lett. 82, 3787 (1999)

    Article  ADS  Google Scholar 

  51. W. A. Hamel and J. P. Woerdman: Phys. Rev. A 40, 2785 (1989) W. A. Hamel: Ph.D. thesis (Leiden University, Leiden, The Netherlands 1991)

    Article  ADS  Google Scholar 

  52. L. A. Lugiato and L. M. Narducci, Z. Phys. B 71, 129 (1988)

    Article  ADS  Google Scholar 

  53. D. J. Santos and R. Loudon: Phys. Rev. A 52, 1538 (1995)

    Article  ADS  Google Scholar 

  54. P. W. Milonni: Phys. Rev. A 25, 1315 (1982) E. A. Power and T. Thirunamachandran: Phys. Rev. A 25, 2473 (1982) S. M. Barnett, C. R. Gilson, B. Huttner, and N. Imoto: Phys. Rev. Lett. 77, 1739 (1996)

    Article  ADS  Google Scholar 

  55. S. M. Dutra and G. Nienhuis: J. Opt. B 2, 584 (2000) S. M. Dutra and G. Nienhuis: Acta Phys. Slov. 50, 275 (2000)

    MathSciNet  ADS  Google Scholar 

  56. P. Goldberg, P. W. Milonni, and B. Sundaram: J. Mod. Opt. 38, 1421 (1991) P. Goldberg, P. W. Milonni, and B. Sundaram: Phys. Rev. A 44, 1969 (1991) P. Goldberg, P. W. Milonni, and B. Sundaram: Phys. Rev. A 44, 4556 (1991) P. Grangier and J.-P. Poizat: Eur. Phys. J. D 1, 97 (1998) P. Grangier and J.-P. Poizat: Eur. Phys. J. D 7, 99 (1999)

    Article  ADS  Google Scholar 

  57. R. E. Prange: Phys. Rev. 131, 1083 (1963)

    Article  ADS  MathSciNet  Google Scholar 

  58. J. Fransson, O. Eriksson, B. Johansson, and I. Sandalov: Physica B 272, 28 (1999)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Huygens Laboratory, Leiden University, P.O. Box 9504, 2300, Leiden, RA, The Netherlands

    S.M. Dutra & G. Nienhuis

Authors
  1. S.M. Dutra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. G. Nienhuis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Dept. de Física, Pontificia Universidad Católica de Chile, 306, Santiago 22, Casilla, Chile

    Miguel Orszag

  2. Dept. de Física, Universidad de Santiago de Chile, Avda. Ecuador correo 2, 3493, Santiago, Chile

    Juan Carlos Retamal

Rights and permissions

Reprints and permissions

Copyright information

© 2001 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Dutra, S., Nienhuis, G. (2001). What Is a Quantized Mode of a Leaky Cavity?. In: Orszag, M., Retamal, J.C. (eds) Modern Challenges in Quantum Optics. Lecture Notes in Physics, vol 575. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45409-8_21

Download citation

  • DOI: https://doi.org/10.1007/3-540-45409-8_21

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41957-0

  • Online ISBN: 978-3-540-45409-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation