RT Journal Article T1 Probability distributions for the phase difference A1 Luis Aina, Alfredo A1 Sánchez Soto, Luis Lorenzo AB In this work we analyze the quantum phase properties of pairs of electromagnetic field modes. Since phases differing by 2π are physically indistinguishable, we propose a general procedure to obtain the correct mod(2π) probability distributions for the phase difference. This allows us to investigate the properties of a number of phase approaches. This procedure provides deeper insight into the quantum nature of the phase difference. We relate this problem to the representation of nonbijective canonical transformations in quantum mechanics. PB American Physical Society SN 1050-2947 YR 1996 FD 1996-01 LK https://hdl.handle.net/20.500.14352/59732 UL https://hdl.handle.net/20.500.14352/59732 LA eng NO [1] P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 441 (1968).[2] Phys. Scr. T48, 1 (1993), special issue on quantum phase.[3] A. Lukš and V. Peřinová, Quantum Opt. 6, 125 (1994).[4] J. Bergou and B. G. Englert, Ann. Phys. (N.Y.) 209, 479 (1991).[5] A. Luis and L. L. Sánchez-Soto, Phys. Rev. A 48, 4702 (1993).[6] A. Luis and L. L. Sánchez-Soto, Opt. Commun. 105, 84 (1994).[7] A. Luis, L. L. Sánchez-Soto, and R. Tanaś, Phys. Rev. A 51, 1634 (1995).[8] D. Ellinas, J. Mod. Opt. 38, 2393 (1991).[9] S. M. Barnett and D. T. Pegg, Phys. Rev. A 42, 6713 (1990).[10] S. M. Barnett and D. T. Pegg, Phys. Rev. A 41, 3427 (1990).[11] D. Judge and J. T. Lewis, Phys. Lett. 5, 190 (1963).[12] L. Susskind and J. Glogower, Physics 1, 49 (1964).[13] J. M. Lévy-Leblond, Rev. Mex. Fis. 22, 15 (1973); Ann. Phys. (N.Y.) 101, 319 (1976).[14] D. T. Pegg and S. M. Barnett, Europhys. Lett. 6, 483 (1988); J. Mod. Opt. 36, 7 (1989).[15] R. G. Newton, Ann. Phys. (N.Y.) 124, 327 (1980).[16] S. M. Barnett and D. T. Pegg, J. Phys. A 19, 3849 (1986).[17] J. C. Garrison and J. Wong, J. Math. Phys. 11, 2242 (1970); A. Galindo, Lett. Math. Phys. 8, 495 (1984); 9, 263 (1985).[18] A. Luis and L. L. Sánchez-Soto, Phys. Rev. A 51, 859 (1995).[19] H. Paul, Fortschr. Phys. 22, 657 (1974).[20] J. H. Shapiro and S. S. Wagner, IEEE J. Quantum Electron. QE-20, 803 (1984).[21] J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992); 46, 2840 (1992).[22] U. Leonhardt and H. Paul, Phys. Rev. A 47, R2460 (1993); 48, 4598 (1993).[23] D. Burak and K. Wódkiewicz, Phys. Rev. A 46, 2744 (1992).[24] K. Wódkiewicz, Phys. Lett. A 115, 304 (1986).[25] F. T. Arecchi, E. Courtens, R. Gilmore, and H. Thomas, Phys. Rev. A 6, 2211 (1972).[26] J. Schwinger, in Quantum Theory of Angular Momentum, edited by L. C. Bidenharn and H. van Dan (Academic Press, New York, 1965).[27] U. Leonhardt, J. A. Vaccaro, B. Böhmer, and H. Paul, Phys. Rev. A 51, 84 (1995).[28] P. Busch, M. Grabowski, and P. J. Lahti, Ann. Phys. (N.Y.) 237, 1 (1995).[29] W. Schleich, R. J. Horowicz, and S. Varro, Phys. Rev. A 40, 7405 (1989).[30] D. T. Smithey, M. Beck, A. Faridani, and M. G. Raymer, Phys. Rev. Lett. 70, 1244 (1993).[31] P. A. M. Dirac, Quantum Mechanics (Clarendon, Oxford, 1958).[32] P. A. Mello and M. Moshinsky, J. Math. Phys. 16, 2017 (1975); M. Moshinsky and T. H. Seligman, Ann. Phys. (N.Y.) 114, 243 (1978); 120, 402 (1979); J. Math. Phys. 22, 1338 (1981); P. Kramer, M. Moshinsky, and T. H. Seligman, ibid. 19, 683 (1978).[33] A. Luis and L. L. Sánchez-Soto, J. Phys. A 24, 2083 (1991). NO © 1996 The American Physical Society DS Docta Complutense RD 2 may 2024