Non-classical behavior in multimode and disordered transverse structures in OPO. Use of the Q-representation

European Physical Journal D

Volumn 22, Issue 3, 2003, Pages 461-471

  Zambrini, R ^a   Barnett, S M ^b   Colet, P ^a   San Miguel, M ^a  

^a UNIVERSITAT DE LES ILLES BALEARS   (Spain)

^b UNIVERSITY OF STRATHCLYDE   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

CLASSICAL BEHAVIOR; CLASSICAL CORRELATION; DEGENERATE OPTICAL PARAMETRIC OSCILLATORS; DISORDERED STRUCTURES; MULTIMODES; STRIPE PATTERN;

OPTICAL PARAMETRIC OSCILLATORS;

EID: 0037357231     PISSN: 14346060     EISSN: None     Source Type: Journal    
DOI: 10.1140/epjd/e2003-00019-7     Document Type: Article

References (62)

1. L.A. Lugiato, M. Brambilla, A. Gatti, in Advances in Atomic Molecular and Optical Physics, edited by B. Bederson, H. Walther (Academic Press, New York, 1998), Vol. 40, p. 229
2. M.I. Kolobov, Rev. Mod. Phys. 71, 1539 (1999)
3. Quantum Structures in nonlinear Optics and Atomic Physics, Focus Issue, Opt. Expr. 3(2) (1998)
4. A. Gatti, E. Brambilla, L.A. Lugiato, M. Kolobov, J. Opt. B: Quant. Semiclass. Opt. 2, 196 (2000)
5. G.-L. Oppo, M. Brambilla, L.A. Lugiato, Phys. Rev. A 49, 2028 (1994); G.-L. Oppo, M. Brambilla, D. Camesasca, A. Gatti, L.A. Lugiato, J. Mod. Opt. 41, 1151 (1994)
6. G.-L. Oppo, M. Brambilla, L.A. Lugiato, Phys. Rev. A 49, 2028 (1994); G.-L. Oppo, M. Brambilla, D. Camesasca, A. Gatti, L.A. Lugiato, J. Mod. Opt. 41, 1151 (1994)
7. M. Vaupel, A. Maître, C. Fabre, Phys. Rev. Lett. 83, 5278 (1999); S. Ducci, N. Treps, A. Matre, C. Fabre, Phys. Rev. A 64, 023803 (2001)
8. M. Vaupel, A. Maître, C. Fabre, Phys. Rev. Lett. 83, 5278 (1999); S. Ducci, N. Treps, A. Matre, C. Fabre, Phys. Rev. A 64, 023803 (2001)
9. R. Graham, Phys. Rev. Lett. 52, 117 (1984)
10. A. Heidmann, R.J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, G. Camy, Phys. Rev. Lett. 59, 2555 (1987); A. Porzio, F. Sciarrino, A. Chiummo, M. Fiorentino, S. Solimeno, Opt. Commun. 194, 373 (2001)
11. A. Heidmann, R.J. Horowicz, S. Reynaud, E. Giacobino, C. Fabre, G. Camy, Phys. Rev. Lett. 59, 2555 (1987); A. Porzio, F. Sciarrino, A. Chiummo, M. Fiorentino, S. Solimeno, Opt. Commun. 194, 373 (2001)
12. K. Wiesenfeld, J. Stat. Phys. 38, 1071 (1985)
13. L.A. Luglato, A. Gatti, H. Ritsch, I. Marzoli, G.L. Oppo, J. Mod. Opt. 44, 1899 (1997)
14. I. Marzoli, A. Gatti, L.A. Lugiato, Phys. Rev. Lett. 78, 2092 (1997)
15. Note that even far below threshold, where the critical mode does not play an important role, any two opposite modes k and -k are entangled
16. A. Gatti, H. Wiedemann, L.A. Lugiato, I. Marzoli, G.L. Oppo, S.M. Barnett, Phys. Rev. A 56, 877 (1997)
17. F. Castelli, L.A. Lugiato, J. Mod. Opt. 44, 765 (1997)
18. K.J. McNeil, C.W. Gardiner, Phys. Rev. A 28, 1560 (1983); P. Kinsler, P.D. Drummond, Phys. Rev. A 52, 783 (1995); P.D. Drummond, K. Dechoum, S. Chaturvedi, Phys. Rev. A 65, 033806 (2002)
19. K.J. McNeil, C.W. Gardiner, Phys. Rev. A 28, 1560 (1983); P. Kinsler, P.D. Drummond, Phys. Rev. A 52, 783 (1995); P.D. Drummond, K. Dechoum, S. Chaturvedi, Phys. Rev. A 65, 033806 (2002)
20. K.J. McNeil, C.W. Gardiner, Phys. Rev. A 28, 1560 (1983); P. Kinsler, P.D. Drummond, Phys. Rev. A 52, 783 (1995); P.D. Drummond, K. Dechoum, S. Chaturvedi, Phys. Rev. A 65, 033806 (2002)
21. R. Zambrini, M. Hoyuelos, A. Gatti, P. Colet, L. Lugiato, M. San Miguel, Phys. Rev. A 62, 63801 (2000)
22. A. Gatti, S. Mancini, Phys. Rev. A 65, 013816 (2002)
23. D. Gomila, P. Colet, Phys. Rev. E 66, 046223 (2002)
24. M. Santagiustina, P. Colet, M. San Miguel, D. Walgraef, Phys. Rev. E 58, 3843 (1998)
25. R. Zambrini, S.M. Barnett, P. Colet, M. San Miguel, Phys. Rev. A 65, 023813 (2002)
26. R. Zambrini, M. San Miguel, Phys. Rev. A 66, 023807 (2002)
27. H. Carmichael, An Open Systems Approach to Quantum Optics, Lecture Notes in Physics (Springer, Berlin, 1993), Vol. m18
28. S.M. Barnett, P.M. Radmore, Methods in Theoretical Quantum Optics (Oxford Science Publications, Oxford 1997)
29. i
30. W.P. Schleich, Quantum Optics in Phase Space (Wiley-VCH, Berlin, Germany, 2001)
31. C.W. Gardiner, P. Zoller, Quantum Noise, 2nd edn. (Springer-Verlag, Berlin, 2000)
32. C.W. Gardiner, Stochastic Methods (Springer, Berlin, 1985)
33. T.W. Marshall, Proc. R. Soc. A 276, 475 (1963)
34. P.D. Drummond, P. Kinsler, Quant. Semiclass. Opt. 7, 727 (1995); P. Kinsler, Phys. Rev. A 53, 2000 (1996); S. Chaturvedi, P.D. Drummond, Phys. Rev. A 55, 912 (1997); D.T. Pope, P.D. Drummond, W.J. Munro, Phys. Rev. A 62, 042108 (2000)
35. P.D. Drummond, P. Kinsler, Quant. Semiclass. Opt. 7, 727 (1995); P. Kinsler, Phys. Rev. A 53, 2000 (1996); S. Chaturvedi, P.D. Drummond, Phys. Rev. A 55, 912 (1997); D.T. Pope, P.D. Drummond, W.J. Munro, Phys. Rev. A 62, 042108 (2000)
36. P.D. Drummond, P. Kinsler, Quant. Semiclass. Opt. 7, 727 (1995); P. Kinsler, Phys. Rev. A 53, 2000 (1996); S. Chaturvedi, P.D. Drummond, Phys. Rev. A 55, 912 (1997); D.T. Pope, P.D. Drummond, W.J. Munro, Phys. Rev. A 62, 042108 (2000)
37. P.D. Drummond, P. Kinsler, Quant. Semiclass. Opt. 7, 727 (1995); P. Kinsler, Phys. Rev. A 53, 2000 (1996); S. Chaturvedi, P.D. Drummond, Phys. Rev. A 55, 912 (1997); D.T. Pope, P.D. Drummond, W.J. Munro, Phys. Rev. A 62, 042108 (2000)
38. P.D. Drummond, C.W. Gardiner, J. Phys. A: Math. Gen. 13, 2353 (1980)
39. + implies a much larger computational effort in the simulation of the Langevin equations. This is a critical problem with spatial degrees of freedom and justifies the search for alternative representations and methods
40. A. Gilchrist, C.W. Gardiner, P.D. Drummond, Phys. Rev. A 55, 3014 (1997)
41. See U. Leonhardt, Measuring the Quantum State of Light (Cambridge University Press, Cambridge, UK, 1997), Chap. VI and references therein
42. R.F. Pawula, Phys. Rev. 162, 186 (1967)
43. See Appendix of: K. Vogel, H. Risken, Phys. Rev. A 38, 2409 (1988)
44. H.P. Yuen, P. Tombesi, Opt. Commun. 59, 155 (1986)
45. R. Zambrini, S.M. Barnett, Phys. Rev. A 65, 053810 (2002)
46. M. Bache, P. Scotto, R. Zambrini, M. San Miguel, M. Saffman, Phys. Rev. A 66, 013809 (2002)
47. When the condition for a positive diffusion (Eq. (14)) is fulfilled, the arguments of the square roots in equation (16) are all positive
48. S. Trillo, M. Haelterman, A. Sheppard, Opt. Lett. 22, 970 (1997); N.B. Pettiaux, R.D. Li, P. Mandel, Opt. Commun. 72, 256 (1989); P.D. Drummond, K.J. McNeil, D.F. Walls, Opt. Acta 27, 321 (1980)
49. S. Trillo, M. Haelterman, A. Sheppard, Opt. Lett. 22, 970 (1997); N.B. Pettiaux, R.D. Li, P. Mandel, Opt. Commun. 72, 256 (1989); P.D. Drummond, K.J. McNeil, D.F. Walls, Opt. Acta 27, 321 (1980)
50. S. Trillo, M. Haelterman, A. Sheppard, Opt. Lett. 22, 970 (1997); N.B. Pettiaux, R.D. Li, P. Mandel, Opt. Commun. 72, 256 (1989); P.D. Drummond, K.J. McNeil, D.F. Walls, Opt. Acta 27, 321 (1980)
51. C. Etrich, D. Michaelis, F. Lederer, J. Opt. Soc. Am. B 19, 792 (2002)
52. D. Gomila, P. Colet, M. San Miguel, A.J. Scroggie, G.-L. Oppo, Issue on Cavily Solitons, IEEE J. Quant. Elect. (to be published, 2003)
53. D. Gomila, P. Colet, M. San Miguel, G.-L. Oppo, Phys. Rev. Lett. 87, 194101 (2001)
54. P. Coullet, C. Elphick, D. Rappaux, Phys. Rev. Lett. 65, 1352 (1990)
55. x for the variance of the quadrature superpositions is associated to the commutator of creation and destruction operators. A detailed evaluation of this quantity can be found in reference [20]
56. M.D. Reid, P.D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); Phys. Rev. A 40, 4493 (1989)
57. M.D. Reid, P.D. Drummond, Phys. Rev. Lett. 60, 2731 (1988); Phys. Rev. A 40, 4493 (1989)
58. K.V. Kheruntsyan, K.G. Petrosyan, Phys. Rev. A 62, 015801 (2000)
59. - = 0
60. -2) leads to a disordered structure
61. c. With our choice of parameters Δk - 0.075
62. Even very rare events, however, can have a profound influence on physical systems, so our procedure cannot be entirely satisfactory. A good example is found in laser cooling: F. Bardou, J.-P. Bouchaud, A. Aspect, C. Cohen-Tannoudji, Lévy Statistics and Laser Cooling (Cambridge University Press, Cambridge, 2002)