RT Journal Article T1 Phase-difference operator A1 Luis Aina, Alfredo A1 Sánchez Soto, Luis Lorenzo AB We introduce a unitary operator representing the exponential of the phase difference between two modes of the electromagnetic field. The eigenvalue spectrum has a discrete character that is fully analyzed. We relate this operator with a suitable polar decomposition of the Stokes parameters of the field, obtaining a natural classical limit. The cases of weakly and highly excited states are considered, discussing to what extent it is possible to talk about the phase for a single-mode field. This operator is applied to some interesting two-mode fields. PB American Physical Society SN 1050-2947 YR 1993 FD 1993-12 LK https://hdl.handle.net/20.500.14352/59792 UL https://hdl.handle.net/20.500.14352/59792 LA eng NO [1] P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 441 (1968).[2] S. M. Barnett and D. T. Pegg, J. Phys. A 19, 3849 (1986).[3] D. T. Pegg and S. M. Barnett, Europhys. Lett. 6, 483 (1988); 3. Mod. Opt. 36, 7 (1989).[4] J. Bergou and B. G. Englert, Ann. Phys. (N.Y.) 209, 479 (1991).[5] H. Gerhardt, U. Buchler, and G. Lit6n, Phys. Lett. 49A, 119 (1974).[6] D. R. Matthys and E. T. Jaynes, J. Opt. Soc. Am. 70, 263 (1980).[7] N. G. Walker and J. E. Carrol, Opt. Quantum Electron. 18, 355 (1986).[8] R. Lynch, Phys. Rev. A 41, 2841 (1990).[9] C. C. Gerry and K. E. Urbansky, Phys. Rev. A 42, 662 (1990).[10] A. Bandilla, Opt. Commun. 80, 267 (1991).[11] J. W. Noh, A. Fougeres, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991).[12] L. Susskind and J. Glogower, Physics 1, 49 (1964).[13] E. C. Lerner, Nuovo Cimento B 56, 183 (1968).[14] M. Ban, 3. Math. Phys. 32, 3077 (1991);Opt. Commun. 94, 231 (1992) and references therein.[15] Z. Hradil, Quantum Opt. 4, 93 (1992); Phys. Rev. A 47, 2376 (1993).[16] Quantum Theory of Angular Momentum, edited by L. C. Biedenharn and H. van Dan (Academic, New York, 1965).[17] A. Vourdas, Phys. Rev. A 41, 1653 (1990).[18] D. Ellinas, J. Math. Phys. 32, 135 (1991).[19] A. Luis and L. L. Sanchez-Soto, Phys. Rev. A 47, 1492 (1993).[20] J. M. Levy-Leblond, Rev. Mex. Fis. 22, 15 (1973); Ann. Phys. (N.Y.) 101, 319 (1976).[21] S. M. Barnett and D. T. Pegg, Phys. Rev. A 42, 6713 (1990).[22] J. C. Garrison and J. Wong, J. Math. Phys. 11, 2242 (1970); A. Galindo, Lett. Math. Phys. 8, 495 (1984); 9, 263 (1985).[23] M. Born and E. Wolf, Principles of Optics (Pergamon, Oxford, 1980).[24] J. M. Jauch and F. Rohrlich, The Theory of Photons and Electrons (Addison-Wesley, Reading, MA, 1959).[25] R. Tanas and Ts. Gantsog, Opt. Commun. 87, 369 (1992).[26] A. I. Akhiezer and V. B. Berestetskii, Quantum Electro dynamics (Interscience, New York, 1965).[27] H. P. Yuen and 3. H. Shapiro, IEEE Trans. Inf. Theory IT-26, 78 (1980).[28] B. L. Schumaker, Opt. Lett. 9, 189 (1984).[29] B. Yurke, S. L. McCall, and J. R. Klauder, Phys. Rev. A 33, 4033 (1986).[30] S. Prasad, M. O. Scully, and W. Martienssen, Opt. Commun. 62, 139 (1987).[31] R. J. Glauber, Phys. Rev. 131, 2766 (1963).[32] C. M. Caves and B.L. Schumaker, Phys. Rev. A 31, 3068 (1985); B. L. Schumaker and C. M. Caves, ibid. 31, 3093 (1985).[33] Ts. Gantsog and R. Tanas, Phys. Lett. A 152, 251 (1991). NO © 1993 The American Physical Society.The authors would like to thank Professor A. Galindo and Professor R. Tanas for a critical reading of the manuscript and useful comments. They are grateful as well to Professor J.F. Carinena for helpful and enlightening discussions of some rather technical points. Finally, they benefited from the continuous interest and advice of Professor E. Bernabeu. DS Docta Complutense RD 1 sept 2024