Quantum-invariant processes in phase space

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 70, Issue 5 A, 2004, Pages

  Luis, Alfredo ^a  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATION THEORY; DEGREES OF FREEDOM (MECHANICS); FREQUENCY DOMAIN ANALYSIS; HAMILTONIANS; MAGNETOELECTRIC EFFECTS; MATRIX ALGEBRA;

HILBERT SPACE; LINEAR TRANSFORMATIONS; QUANTUM STATES; QUANTUM-INVARIANT PROCESSES;

QUANTUM THEORY;

EID: 45849154781     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.70.052118     Document Type: Article

References (92)

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21. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
22. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
23. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
24. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
25. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
26. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
27. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
28. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
29. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
30. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
31. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
32. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
33. D. M. Kaplan and G. C. Summerfield, Phys. Rev. 187, 639 (1969); F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972); N. Mukunda, Am. J. Phys. 47, 182 (1979); J. P. Bizarro, Phys. Rev. A 49, 3255 (1994); J. Vaccaro, ibid. 52, 3474 (1995); Opt. Commun. 113, 421 (1995); G. S. Agarwal, Phys. Rev. A 24, 2889 (1981); M. O. Scully, Phys. Rev. D 28, 2477 (1983); J. C. Várilly and J. M. Gracia-Bondía, Ann. Phys. (N.Y.) 190, 107 (1989); A. Luis and L. L. Sánchez-Soto, Quantum Opt. 5, 33 (1993); G. Ramachandran, A. R. Usha-Devi, P. Devi, and S. Sirsi, Found. Phys. 26, 401 (1996); V. V. Dodonov and V. I. Man'ko, Phys. Lett. A 229, 335 (1997); C. Brif and A. Mann, Phys. Rev. A 59, 971 (1999); S. M. Chumakov, A. Frank, and K. B. Wolf, ibid. 60, 1817 (1999); S. M. Chumakov, A. B. Klimov, and K. B. Wolf, ibid. 61, 034101 (2000); V. P. Karassiov and A. V. Masalov, J. Opt. B: Quantum Semiclassical Opt. 4, S366 (2002).
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