Luis Aina, AlfredoSánchez Soto, Luis Lorenzo2023-06-202023-06-201997-07[1] L. Allen and J. H. Eberly, Optical Resonance and Two-Level Atoms (Dover, New York, 1987). [2] P. Meystre and M. Sargent III, Elements of Quantum Optics (Springer-Verlag, Berlin, 1991). [3] J. Bergou and B. G. Englert, Ann. Phys. (NY) 209, 479 (1991). [4] Phys. Scr. T48, 1 (1993), special issue on quantum phase. [5] A. Lukš, and V. Peřinová, Quantum Opt. 6, 125 (1994). [6] R. Lynch, Phys. Rep. 256, 367 (1995). [7] T. Tanaś, A. Miranowicz, and T. Gantsog, Prog. Opt. 36, 161 (1996). [8] A. Luis and L. L. Sánchez-Soto, Phys. Rev. A 48, 4702 (1993). [9] L. L. Sánchez-Soto and A. Luis, Opt. Commun. 105, 84 (1994). [10] A. Luis and L. L. Sánchez-Soto, Opt. Commun. 133, 159 (1997). [11] P. A. M. Dirac, Proc. R. Soc. London, Ser. A 114, 243 (1927). [12] P. Carruthers and M. M. Nieto, Rev. Mod. Phys. 40, 441 (1968). [13] L. Susskind and J. Glogower, Physics (Long Island City, NY) 1, 49 (1964). [14] U. Leonhardt, J. A. Vaccaro, B. Böhmer, and H. Paul, Phys. Rev. A 51, 84 (1995). [15] B.-G. Englert and K. Wódkiewicz, Phys. Rev. A 51, R2661 (1995); B.-G. Englert, K. Wódkiewicz, and P. Riegler, ibid. 52, 1704 (1995). [16] S. M. Barnett and D. T. Pegg, J. Mod. Opt. 36, 7 (1989). [17] J. H. Shapiro, S. R. Shepard, and N. C. Wong, Phys. Rev. Lett. 62, 2377 (1989); J. H. Shapiro and S. R. Shepard, Phys. Rev. A 43, 3795 (1991). [18] M. J. W. Hall, Quantum Opt. 3, 7 (1991). [19] U. Leonhardt and H. Paul, Phys. Rev. A 45, R2460 (1993). [20] M. Freyberger, K. Vogel, and W. Schleich, Phys. Lett. A 176, 41 (1993). [21] Y. Lai and H. A. Haus, Quantum Opt. 1, 99 (1989). [22] U. Leonhardt and H. Paul, Phys. Rev. A 48, 4598 (1993). [23] A. Ortowski, and A. Wünsche, Phys. Rev. A 48, 4697 (1993). [24] A. Luis and L. L. Sánchez-Soto, Phys. Rev. A 53, 495 (1996). [25] J. W. Noh, A. Fougères, and L. Mandel, Phys. Rev. Lett. 67, 1426 (1991); Phys. Rev. A 45, 424 (1992); 46, 2840 (1992). [26] U. Leonhardt, Phys. Rev. A 48, 3265 (1991). [27] J. M. Lévy-Leblond, Rev. Mex. Fis. 22, 15 (1973). [28] D. Ellinas, J. Math. Phys. (N.Y.) 32, 135 (1990). [29] A. Vourdas, Phys. Rev. A 41, 1653 (1990). [30] A. Bandilla, H. Paul, and H. H. Ritze, Quantum Opt. 3, 267 (1991). [31] A. Perelomov, Generalized Coherent States and their Applications (Springer-Verlag, Berlin, 1986). [32] J. R. Torgerson and L. Mandel, Phys. Rev. Lett. 76, 3939 (1996). [33] B. W. Shore and P. L. Knight, J. Mod. Opt. 40, 1195 (1993). [34] K. Zaheer and M. S. Zubairy, Phys. Rev. A 39, 2000 (1989). [35] J. I. Cirac and L. L. Sánchez-Soto, Phys. Rev. A 42, 2851 (1990). [36] C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Photons and Atoms: Introduction to Quantum Electrodynamics (John Wiley, New York, 1989). [37] T. Opatrný, J. Phys. A 27, 7201 (1994). [38] J. I. Cirac and L. L. Sánchez-Soto, Phys. Rev. A 40, 3743 (1989). [39] M. Fleischhauer and W. Schleich, Phys. Rev. A 45, 4258 (1993). [40] H. T. Dung, R. Tanaś, and A. S. Shumovsky, Opt. Commun. 79, 462 (1990); J. Mod. Opt. 38, 2069 (1991). [41] B. M. Garraway and P. L. Knight, Phys. Rev. A 46, 5346 (1992). [42] N. B. Narozhny, J. J. Sánchez-Mondragon, and J. H. Eberly, Phys. Rev. A 23, 236 (1981).1050-294710.1103/PhysRevA.56.994https://hdl.handle.net/20.500.14352/59709© 1997 The American Physical Society. We would like to thank Professor J. Peřina, Professor V. Peřinová, and Dr. A. Lukš for discussions. It is a pleasure to acknowledge S. Sweeney for a careful reading of the manuscript.Several quantum descriptions of the relative phase between an atomic dipole and a one-mode electromagnetic field are examined. Positive-operator measures for this variable are derived from dipole and field-phase formalisms. They are analyzed and compared with an operator defined by a polar decomposition. Some examples of time evolution are discussed.engRelative phase for a quantum field interacting with a two-level systemjournal articlehttp://dx.doi.org/10.1103/PhysRevA.56.994http://journals.aps.org/open access535Jaynes-Cummings modelOptical-phaseDifference operatorDistributionsUncertaintyStatesLightAtomÓptica (Física)2209.19 Óptica Física