Experimental aspects of transition phenomena in quantum optics

  • F. T. Arecchi
Systems far away from Equilibrium
Part of the Lecture Notes in Physics book series (LNP, volume 104)


Phase transitions in equilibrium systems are the result of a competition between the interparticle energy J and the thermal energy kBT which introduces disorder. In quantum optics, even when interparticle interactions are negligible as in a very dilute gas, there may be particle correlations due to the common radiation field. The transition from disorder to order consists in a passage from a regime where the atoms emit independently from one another, to a regime where the atoms emit in a strongly correlated way. It depends on a “cooperation number” C which is proportional to the atomic density. In a “pumped” system, as the density of active atoms is increased, the laser threshold is reached for C=1 and the coherent e.m. intensity is proportional to C-1.

The laser threshold and the optical bistability are discussed as examples, respectively, of 2nd and 1st order phase transitions in quantum optics. By photon statistics methods the statistical features of these phenomena can be measured with high accuracy.

Furthermore, in nonequilibrium optical systems it has been possible to study for the first time the transient build-up of an ordered state by a rapid passage through an instability. These transients are characterized by large fluctuations which display a scaling behaviour.


Order Phase Transition Photon Number Laser Field Saturable Absorber Laser Threshold 
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  1. 1)-.
    R.J.Glauber in Quantum Optics and Electronics (Proc.of 1964 Les Houches School), McGraw-Hill 1965, 65–185.Google Scholar
  2. 2)-.
    F.T.Arecchi in Quantum Optics (Proc.of 1967 Varenna School), Academic Press 1969, 57–110.Google Scholar
  3. 3)-.
    Since the first works on the subject (W.E.Lamb,Oral communication at the Third International Conference on Quantum Electronics,Paris Feb.11–15,1963,and Phys.Rev. 134,A 1429 (1964)Google Scholar
  4. 3a)-.
    H.Haken and H.Sauermann, Z.Phys.,173,47 (1963)), a large body of papers has appeared on the subjects dealing with the quantum and statistical aspects of the laser oscillator.Complete reviews can now be found in two books,namelyGoogle Scholar
  5. 3b)-.
    H.Haken,Laser Theory, Handbuch der S.Flügge,vol.XXV/2c, Springer 1970; andGoogle Scholar
  6. 3c)-.
    M.Sargent III, M.O.Scully, W.E.Lamb,Laser Physics,Addison-Wesley 1974. The laser around threshold was the first system in which to exploit the photon statistical methods introduced after the theory of Glauber (Ref. 1).A review is given in Ref.2. For interpreting the experiments it has been sufficient to use the phenomenological approaches introduced in the next Refs.4,5 and reviewed in Ref.6. Those phenomenological approaches exploit the statistical treatment of a nonlinear oscillator as given, for example, in Ref.7.Google Scholar
  7. 4)-.
    H.Risken, Z.Phys.,186,85 (1965) and 191, 302 (1966).CrossRefGoogle Scholar
  8. 5)-.
    R.D.Heampstead and M.Lax, Phys.Rev.161,350 (1967).CrossRefGoogle Scholar
  9. 6)-.
    H.Risken in Progress in Optics, E.Wolf 8,239–294 (1970).Google Scholar
  10. 7)-.
    R.L.Stratonovich, Topics in the theory of random noise, Gordon and Breach,vol. I (1963) and vol.II (1967).Google Scholar
  11. 8)-.
    L.Landau, Phys.Z.Sovietunion 11,26 (1937); 11,545 (1937).Google Scholar
  12. 9)-.
    H.E.Stanley, Introduction to phase transitions,Oxford Press 1971.Google Scholar
  13. 10)-.
    R.Landauer, J.Appl.Phys. 33, 2209 (1962).CrossRefGoogle Scholar
  14. 11)-.
    E.Pytte, H.Thomas, Phys.Rev.Letters 20,1167 (1968).CrossRefGoogle Scholar
  15. 12)-.
    R.Graham, H.Haken, Z.Physik 237,31 (1970).CrossRefGoogle Scholar
  16. 13)-.
    M.O.Scully, V.Degiorgio, Phys.Rev. A2,1170 (1970).Google Scholar
  17. 14)-.
    V.N.Lisitsyn, V.Chebotayev, JEPT Letters 7,1 (1968).Google Scholar
  18. 15)-.
    T.H.Lee, P.B.Schaefer, W.B.Barker,Appl.Phys.Letters 13,373 (1968).CrossRefGoogle Scholar
  19. 16)-.
    J.F.Scott, M.Sargent III, C.Cantrell,Opt.Comm. 15,13 (1975).CrossRefGoogle Scholar
  20. 17)-.
    L.A.Lugiato, P.Mandel, S.T.Dembinski, A.Kossakowski,Phys.Rev. A18,238 (1978).Google Scholar
  21. 18)-.
    H.M.Gibbs, S.L.McCall, T.Venkatesan, Phys.Rev.Letters 36,1135 (1976).CrossRefGoogle Scholar
  22. 19)-.
    R.Bonifacio, L.A.Lugiato, Optc.Comm. 19,172 (1976).CrossRefGoogle Scholar
  23. 20)-.
    R.Bonifacio, L.A.Lugiato, Lett.N.Cimento 21,517 (1978).Google Scholar
  24. 21)-.
    F.T.Arecchi, V.Degiorgio, B.Querzola, Phys.Rev.Letters 19,1168 (1967).CrossRefGoogle Scholar
  25. 22)-.
    F.T.Arecchi, V.Degiorgio, Phys.Rev. A3,1108 (1971).Google Scholar
  26. 23)-.
    R.Kubo in Synergetics, H.Haken, B.G.Teubner 1973.Google Scholar
  27. 24)-.
    M.Suzuki,Contribution to the XVII Solvay Conference on Physics,1978.Google Scholar
  28. 25)-.
    R.H.Dicke,Phys.Rev. 93,99 (1954).CrossRefGoogle Scholar
  29. 26)-.
    R.Bonifacio, P.Schwendimann, F.Haake, Phys.Rev. A4, 302 and 804 (1971).Google Scholar
  30. 27)-.
    R.Bonifacio, L.A.Lugiato,Phys.Rev. A11, 1507 and A12,587 (1975).Google Scholar
  31. 28)-.
    N.Sckribanowitz, I.Herman, J.MacGillivary, M.Feld,Phys.Rev.Lett. 30,30928)-(1973).CrossRefGoogle Scholar
  32. 29)-.
    M.Gross, C.Fabre, P.Pillet, S.Haroche,Phys.Rev.Letters 36, 1035 (1976).CrossRefGoogle Scholar
  33. 30)-.
    H.M.Gibbs,Q.Vrehen,H.Hikspoors,Phys.Rev.Letters 39,547 (1978).CrossRefGoogle Scholar
  34. 31)-.
    S.Grossmann, P.H.Richter,Z.Phys. 249,43 (1971) and 255,59 (1972).CrossRefGoogle Scholar
  35. 32)-.
    F.T.Arecchi, A.M. Ricca,Phys.Rev.A15,308 (1977).Google Scholar
  36. 33)-.
    M.M.Tehrani, L.Mandel,Phys.Rev.A17,694 (1978).Google Scholar
  37. 34)-.
    For a complete discussion including a microscopic approach, see R.Graham,contribution to the XVII Solvay Conference on Physics, 1978.Google Scholar
  38. 35)-.
    For a detailed treatment see H.Haken, Synergetics, Springer Verlag, 1977.Google Scholar
  39. 36)-.
    F.T.Arecchi, E.Courtens, Phys.Rev. A2,1730 (1970).Google Scholar
  40. 37)-.
    F.T.Arecchi, R.Bonifacio, IEEE J.Quantum E1.1,169 (1965).CrossRefGoogle Scholar
  41. 38)-.
    S.McCall, E.L.Hahn, Phys.Rev.Letters 18,908 (1967).CrossRefGoogle Scholar
  42. 39)-.
    F.T.Arecchi, V.Degiorgio, C.Someda,Phys. Letters A27,588 (1968).Google Scholar
  43. 40)-.
    W.Chow, M.Scully, E.van Stryland,Opt.Comm.15,6 (1975).Google Scholar
  44. 41)-.
    L.A.Lugiato, Lett.Nuovo Cimento (to be published).Google Scholar
  45. 42)-.
    R.Bonifacio, L.A.Lugiato,Phys.Rev.Letters 40,1023 (1978).Google Scholar
  46. 43)-.
    F.T.Arecchi, E.Courtens, R.Gilmore, H.Thomas in Proc.of Esfahan Symposium, 1971 and Phys.Rev. A6,2211 (1972).Google Scholar
  47. 44)-a).
    F.Haake, R.J.Glauber,Phys.Rev. A5,1457 (1972)Google Scholar
  48. 44)-b).
    L.M.Narducci, C.Coulter, C.Bowden,Phys.Rev. A9,829 (1974).Google Scholar
  49. 45)-.
    F.T.Arecchi, Phys.Rev.Letters 15,912 (1965).Google Scholar
  50. 46)-.
    F.T.Arecchi, A.Berné P.Burlamacchi,Phys.Rev.Letters 16,32 (1966).Google Scholar
  51. 47)-.
    F.T.Arecchi, A.Berné A.Sona,Phys.Rev.Letters 17,260 (1966).Google Scholar
  52. 48)-.
    F.T.Arecchi, V.Degiorgio in Laser Handbook, North Holland,1972, vol.I,pp.191–264.Google Scholar
  53. 49)-.
    F.T.Arecchi, V.Degiorgio,Phys.Letters 27A,429 (1968).Google Scholar
  54. 50)-.
    A.E.Siegman, R.Arrathoon,Phys.Rev.Letters 20,901 (1968)Google Scholar
  55. 50)-a.
    K.R.Manes, A.E.Siegman,Phys.Rev.A4,373 (1971).Google Scholar
  56. 51)-.
    H.Gerhardt, H.Welling, A.Gütner,Phys.Letters 40A,191 (1973).Google Scholar
  57. 52)-.
    F.T.Arecchi, G.Rodari, A.Sona,Phys.Letters 25A,59 (1967).Google Scholar
  58. 53)-.
    M.O.Scully, W.E.Lamb,Phys.Rev.159,208 (1967).Google Scholar
  59. 54)-.
    C.Freed, H.Haus,Phys.Rev.141,287 (1966).Google Scholar
  60. 55)-.
    F.T.Arecchi, M.Giglio, A.Sona,Phys.Letters 25A, 341 (1967).Google Scholar
  61. 56)-.
    J.A.Armstrong, A.W.Smith, Phys.Rev. 140,A 55 (1965).Google Scholar
  62. 57)-.
    M.Corti, V.Degiorgio, F.T.Arecchi,Opt.Comm.8,329 (1973).Google Scholar
  63. 58)-.
    A.Schawlow, C.H.Townes,Phys.Rev.112,1940 (1958).Google Scholar
  64. 59)-.
    M.Sargent, M.O.Scully, W.E.Lamb,Appl.Optics 9,2423 (1970).Google Scholar
  65. 60)-.
    E.Baklanov, S.Rautian, B.Troshin, V.Chebotayev, Sov.Phys.JEPT 29, 601 (1969).Google Scholar
  66. 61)-.
    D.Meltzer, L.Mandel, Phys.Rev.Letters 25, 1151 (1970).Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • F. T. Arecchi
    • 1
  1. 1.Università di Firenze and Istituto Nazionale di OtticaFirenze

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