Two-mode generalization of the Jaynes-Cummings and anti-Jaynes-Cummings models. (English) Zbl 1377.81064
Summary: We introduce two generalizations of the Jaynes-Cummings (JC) model for two modes of oscillation. The first model is formed by two Jaynes-Cummings interactions, while the second model is written as a simultaneous Jaynes-Cummings and Anti-Jaynes-Cummings (AJC) interactions. We study some of its properties and obtain the energy spectrum and eigenfunctions of these models by using the tilting transformation and the Perelomov number coherent states of the two-dimensional harmonic oscillator. Moreover, as physical applications, we connect these new models with two important and novel problems: The relativistic non-degenerate parametric amplifier and the relativistic problem of two coupled oscillators.
MSC:
| 81R30 | Coherent states |
References:
| [1] | Ito, D.; Mori, K.; Carrieri, E., Nuovo Cimento A, 51, 1119 (1967) |
| [2] | Cook, P. A., Lett. Nuovo Cimento, 1, 419 (1971) |
| [3] | Moshinsky, M.; Szczepaniak, A., J. Phys. A, 22, L817 (1989) |
| [4] | Moreno, M.; Zentella, A., J. Phys. A: Math. Gen., 22, L821 (1989) |
| [5] | Quesne, C.; Moshinsky, M., J. Phys. A, 23, 2263 (1990) · Zbl 0725.35083 |
| [6] | Benítez, J.; Martínez y. Romero, R. P.; Núñez Yépez, H. N.; Salas-Brito, A. L., Phys. Rev. Lett., 64, 1643 (1990) |
| [7] | Martínez y. Romero, R. P.; Salas-Brito, A. L., J. Math. Phys., 33, 1831 (1992) |
| [8] | Villalba, V. M., Phys. Rev. A, 49, 586 (1994) |
| [9] | Boumali, A.; Hassanabadi, H., Eur. Phys. J. Plus., 128, 124 (2013) |
| [10] | C. Quimbay, P. Strange, Quantum phase transition in the chirality of the \(( 2 + 1 )\) arXiv:1312.5251; C. Quimbay, P. Strange, Quantum phase transition in the chirality of the \(( 2 + 1 )\) arXiv:1312.5251 |
| [11] | C. Quimbay, P. Strange, Graphene physics via the Dirac oscillator in \(( 2 + 1 )\) arXiv:1311.2021; C. Quimbay, P. Strange, Graphene physics via the Dirac oscillator in \(( 2 + 1 )\) arXiv:1311.2021 |
| [12] | Pacheco, M. H.; Maluf, R. V.; Almeida, C. A.S.; Landim, R. R., Europhys. Lett., 108, 10005 (2014) |
| [13] | Panella, O.; Roy, P., Phys. Rev. A, 90, 042111 (2014) |
| [14] | Menculini, L.; Panella, O.; Roy, P., Phys. Rev. D, 91, 045032 (2015) |
| [15] | Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D., Commun. Theor. Phys., 63, 271 (2015) · Zbl 1310.81089 |
| [16] | Boumali, A., Phys. Scr., 90, 109501 (2015) |
| [17] | Sadurni, E., AIP Conf. Proc., 1334, 249 (2010) |
| [18] | Nogami, Y.; Toyama, F. M., Can. J. Phys., 74, 114 (1996) |
| [19] | Toyama, F. M.; Nogami, Y.; Coutinho, F. A.B., J. Phys. A: Math. Gen., 30, 2585 (1997) · Zbl 0924.35120 |
| [20] | Szmytkowski, R.; Gruchowski, M., J. Phys. A: Math. Gen., 34, 4991 (2001) · Zbl 0983.81012 |
| [21] | Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D., J. Math. Phys., 57, 062104 (2016) · Zbl 1341.81053 |
| [22] | Bermudez, A.; Martin-Delgado, M. A.; Solano, E., Phys. Rev. A, 76, 041801 (2007) |
| [23] | Bermudez, A.; Martin-Delgado, M. A.; Luis, A., Phys Rev. A, 77, 063815 (2008) |
| [24] | Luo, Y.; Cui, Y.; Long, Z.; Jing, J., Int. J. Theor. Phys., 50, 2992 (2011) · Zbl 1252.81079 |
| [25] | P. Majari, A. Luis, M.R. Setare, Mapping of the \(2 + 1\) arXiv:1702.03077; P. Majari, A. Luis, M.R. Setare, Mapping of the \(2 + 1\) arXiv:1702.03077 |
| [26] | Jaynes, E. T.; Cummings, F. W., Proc. IEEE, 51, 89 (1963) |
| [27] | Haroche, S.; Raimond, J. M., Exploring the Quantum: Atoms, Cavities and Photons (2007), Oxford University Press: Oxford University Press Oxford |
| [28] | Eberly, J. H.; Narozhny, N. B.; Sanchez-Mondragon, J. J., Phys. Rev. Lett., 44, 1323 (1980) · Zbl 1404.81338 |
| [29] | Kuklinski, J. R.; Madajczyk, J., Phys. Rev. A, 37, 3175 (1988) |
| [30] | Goy, P.; Raimond, J. M.; Gross, M.; Haroche, S., Phys. Rev. Lett., 50, 1903 (1983) |
| [31] | Brune, M.; Schmidt-Kaler, F.; Maali, A.; Dreyer, J.; Hagley, E.; Raimond, J. M.; Haroche, S., Phys. Rev. Lett., 76, 1800 (1996) · Zbl 1244.81072 |
| [32] | Guerlin, C.; Bernu, J.; Deleglise, S.; Sayrin, C.; Gleyzes, S.; Kuhr, S.; Brune, M.; Raimond, J. M.; Haroche, S., Nature, 448, 889 (2007) |
| [33] | Panahi, H.; Asghari Rad, S., Int. J. Theor. Phys., 52, 4068 (2013) · Zbl 1282.81211 |
| [34] | Larson, J., Phys. Scr., 76, 146 (2007) · Zbl 1138.81064 |
| [35] | Lamata, L.; León, J.; Schätz, T.; Solano, E., Phys. Rev. Lett., 98, 253005 (2007) |
| [36] | Gerritsma, R.; Kirchmair, G.; Zähringer, F.; Solano, E.; Blatt, R.; Roos, C. F., Nature (London), 463, 68 (2010) |
| [37] | Lamata, L.; Casanova, J.; Gerritsma, R.; Roos, C. F.; García-Ripoll, J. J.; Solano, E., New J. Phys., 13, 095003 (2011) |
| [38] | Johanning, M.; Varón, A. F.; Wunderlich, C., J. Phys. B: At. Mol. Opt. Phys., 42, 154009 (2009) |
| [39] | Romero, G.; Ballester, D.; Wang, Y. M.; Scarani, V.; Solano, E., Phys. Rev. Lett., 108, 120501 (2012) |
| [40] | Mirza, I. M.; van Enk, S. J., Opt. Commun., 343, 172 (2015) |
| [41] | Mirza, I. M., Phys. Lett. A, 379, 1643 (2015) |
| [42] | Mirza, I. M.; Schotland, J. C., Phys. Rev. A, 94, 012309 (2016) |
| [43] | Gerry, C. C., Phys. Rev. A, 39, 3204 (1989) |
| [44] | Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D., J. Math. Phys., 55, 042109 (2014) · Zbl 1292.81055 |
| [45] | Ojeda-Guillén, D.; Mota, R. D.; Granados, V. D., Commun. Theor. Phys., 64, 34 (2015) · Zbl 1319.81051 |
| [46] | Walls, D. F.; Milburn, G. J., Quantum Optics (1994), Springer-Verlag: Springer-Verlag Berlin · Zbl 1138.81586 |
| [47] | Louisell, W. H., Quantum Statistical Properties of Radiation (1973), Wiley: Wiley New York · Zbl 1049.81683 |
| [48] | Fan, H.; Li, C.; Jiang, Z., Phys. Lett. A, 327, 416 (2004) · Zbl 1138.81443 |
| [49] | Vourdas, A., Phys. Rev. A, 41, 1653 (1990) |
| [50] | Gerry, C. C., Phys. Rev. A, 31, 2721 (1985) |
| [51] | Perelomov, A. M., Generalized Coherent States and their Applications (1986), Springer: Springer Berlin · Zbl 0605.22013 |
| [52] | Ojeda-Guillén, D.; Salazar-Ramírez, M.; Mota, R. D.; Granados, V. D., J. Nonlinear Math. Phys., 23, 607 (2016) · Zbl 1421.81061 |
| [53] | Vourdas, A., J. Phys. A, 39, R65 (2006) · Zbl 1093.81038 |
| [54] | Arecchi, F. T.; Courtens, E.; Gilmore, R.; Thomas, H., Phys. Rev. A, 6, 2211 (1972) |
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