Abstract
In this paper, we consider a Hamiltonian model that includes interaction of two coupled two-level atoms with a single-mode quantized electromagnetic field in a cavity via the degenerate two-photon transition. The cavity is filled with a Kerr-like medium and is held at a temperature T. The free field Hamiltonian possesses the su(1,1) symmetry which realized by either even or odd photon-number states. The total number of excitation as a constant of motion, provides a decomposition of the Hilbert space of system into direct sums of invariant subspaces. As a results, the representation of the Hamiltonian becomes block-diagonal matrix with three blocks. After diagonalizing each block, we obtain thermal state of system in the whole Hilbert space and within its excitation subspaces. Finally, the effect of temperature, atom-atom and Kerr-type couplings on the degree of thermal entanglement between the atoms are investigated. Our results show that within the single-excitation subspace spanned with odd photon-number states, the entanglement between the atoms is thermally robust.
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Einstein, A., Podolsky, B., Rosen, N.: Phys. Rev. 47, 777 (1935)
Barenco, A., Deutsch, D., Ekert, A., Jozsa, R.: Phys. Rev. Lett. 74, 4083 (1995)
Bengtsson, I., Zyczkowski, K.: Geometry of quantum states: An introduction to quantum entanglement. Cambridge University Press, Cambridge (2006)
Bennett, C.H., Brassard, G., Crepeau, C., Jozsa, R., Peres, A., Wootters, W.K.: Phys. Rev. Lett 70, 1895 (1993)
Li, X., Pan, Q., Jing, J., Zhang, J., Xie, C., Peng, K.: Phys. Rev. Lett 88, 047904 (2002)
Bennett, C.H., Wiesner, S.J.: Phys. Rev. Lett. 69, 2881 (1992)
Ekert, A.K.: Phys. Rev. Lett. 67, 661 (1991)
Jaynes, E.T., Cummings, F.W.: Proc. IEEE 51, 89 (1963)
Eberly, J.H., Narozhny, N.B., Sanchez-Mondragan, J. J.: Phys. Rev. Lett 44, 1323 (1980)
Narozhny, N.B., Sanchez-Mondragan, J.J., Eberly, J.H.: Phys. Rev. A 23, 236 (1981)
Meystre, P., Zubairy, M.S.: Phys. Lett. A 89, 390 (1982)
Kuklinski, J.R., Madajczyk, J.L.: Phys. Rev. A 37, 3175 (1988)
Short, R.G., Mandel, L.: Phys. Rev. Lett 51, 384 (1983)
Diedrich, F., Walther, H.: Phys. Rev. Lett 58, 203 (1987)
Milonni, P.W., Ackerhalt, J.R., Galbraith, H.W.: Phys. Rev. Lett 50, 966 (1983)
Bertet, P., Osnaghi, S., Milman, P., Auffeves, A., Maioli, P., Brune, M., Raimond, J.M., Haroche, S.: Phys. Rev. Lett. 88, 143601 (2002)
Brune, M., Hagley, E., Dreyer, J., Maitre, X., Maali, A., Wunderlich, C., Raimond, J.M., Haroche, S.: Phys. Rev. Lett. 77, 4887 (1996)
Auffeves, A., Maioli, P., Meunier, T., Gleyzes, S., Nogues, G., Brune, M., Raimond, J.M., Haroche, S.: Phys. Rev. Lett. 91, 230405 (2003)
Zavatta, A., Viciani, S., Bellini, M.: Science 306, 660 (2004)
Walther, H., Varcoe, B.T.H., Englert, B.-G., Becker, T.: Rep. Prog. Phys. 69, 1325 (2006)
Yadollahi, F., Tavassoly, M.K.: Opt. Commun 284, 608 (2011)
Baghshahi, H.R., Tavassoly, M.K.: Eur. Phys. J. D 130, 37 (2015)
Tavassoly, M.K., Yadollahi, F.: Int. J. Mod. Phys. B 26, 1250027 (2012)
Obada, A.S.F., Ahmed, M.M.A., Khalil, E.M., Ali, S.I.: Opt. Comm, 287, 215 (2013)
Buzek, V.: J. Mod. Opt 39, 949 (1992)
Sivakumar, S.: Int. J. Theor. Phys 43, 2405 (2004)
Faghihi, M.J., Tavassoly, M.K.: J. Opt. Soc. Am. B 30, 2810 (2013)
Dehghani, A., Mojaveri, B., Shirin, S., Amiri Feseghandis, S.: Sci. Rep 6, 38069 (2016)
Prants, S.V., Yacoupova, L.S.: J. Mod. Opt. 39, 961 (1992)
Joshi, A., Lawande, S.V.: Phys. Rev. A 48, 2276 (1993)
Gruver, J.L., Aliaga, J., Cerdeira, H.A.: Phys. Rev. A 50, 5274 (1994)
Buzek, V.: Phys. Rev. A 39, 3196 (1989)
Fink, J.M., Göppl, M., Baur, M., Bianchetti, R., Leek, P.J., Blais, A., Wallraff, A.: Nature 454, 315 (2008)
Agarwal, G.S., Puri, R.R.: Phys. Rev. A 39, 2969 (1989)
Puri, R.R., Agarwal, G.S.: Phys. Rev. A 37, 3879 (1988). r. r. puri, Mathematical Methods of Quantum Optics Springer Series in Optical Sciences 79 (2001), Chapters 7, 8
Netto, P.A.M., Davidovich, L., Raimond, J.M.: Phys. Rev. A 43, 5073 (1991)
Buck, B., Sukumar, C.V.: Phys. Lett. A 81, 132 (1981)
Agarwal, G.S.: J. Opt. Soc. Am. B 2, 480 (1985)
Zhou, P., Peng, J.S.: Phys. Rev. A 44, 3331 (1991)
Gauthier, D.J., Wu, L.Q., Morrin, S.E., Mossberg, T.W.: Phys. Rev. Lett 68, 464 (1992)
Khalil, E.M.: Optik 124, 1820 (2013)
Khalil, E.M., Sebawe Abdalla, M., Obada, A.S.-F., Perina, J.: J. Opt. Soc. Am. B 37, 266 (2010)
Khalil, E.M., Sebawe Abdalla, M., Obada, A.S.-F.: Ann. Phys 321, 421 (2006)
Sebawe Abdalla, M., Obada, A.S.-F., Abdel-Aty, M.: Ann. Phys 318, 266 (2005)
Obada, A.S.-F., Ahmed, M. M. A., Khalil, E. M., Ali, S. I.: Opt. Comm 287, 215 (2013)
Plenio, M.B., Huelga, S.F., Beige, A., Knight, P.L.: Phys. Rev. A 59, 2468 (1999)
Yi, X.X., Yu, C.S., Zhou, L., Song, H.S.: Phys. Rev. A 68, 052304 (2003)
Kim, M.S., Lee, J., Ahn, D., Knight, P.L. : Phys. Rev. A 65, 040101 (2002)
Zhou, L., Song, H.S., Li, C.: J. Opt. B: Quantum Semiclass. Opt 4, 425 (2002)
Zhou, L., Yi, X.X., Song, H.S., Quo, Y.Q.: J. Opt. B: Quantum Semiclass. Opt 6, 378 (2004)
Zhang, B.: Opt. Comm 283, 4676 (2010)
Tahira, R., Ikram ands, M., Zubairy, S.: Opt. Commun. 284, 3643 (2011)
Zhang Li, W., Shen, L.T.: Eur. Phys. J. E 67, 111 (2013)
Wang, X.: Phys. Rev. A 64, 012313 (2001)
Wang, X.: Phys. Rev. A 66, 34302 (2002)
Wang, X.: Phys. Rev. A 66, 044305 (2002)
Arnesen, C.M., Bose, S., Vedral, V.: Phys. Rev. Lett 87, 017901 (2001)
Kamta, G.L., Starace, A.F.: Phys. Rev. Lett. 88, 107901 (2002)
Zhou, L., Song, H.S., Guo, Y.Q., Li, C.: Phys. Rev. A 68, 024301 (2003)
Kheirandish, F., Akhtarshenas, S.J., Mohammadi, H.: Phys. Rev. A 77 (4), 042309 (2008)
Guo-Hui, Y.: Int. J. Theor. Phys 55, 3191 (2016)
Wang, A.G., Yang, W.S., Fang Lv, S., Yue, X.F., Wu, S. L., Liu, J.: Int. J. Theor. Phys 56, 339 (2017)
Najarbashi, G., Balazadeh, L., Tavana, A.: Int. J. Theor. Phys 57, 95111 (2018)
Abbasi, M.R., Golshan, M.M.: Physica A 392, 6161 (2013)
Abbasi, M.R.: Physica. A 426, 1 (2015)
Abbasi, M.R.: Ann. Phys 365, 198 (2016)
Alizadeh, S.h., Safaiee, R., Golshan, M.M.: Physica A 428, 133 (2015)
Mojaveri, B., Dehghani, A., Fasihi, M.A., Mohammadpour, T.: submitted for publication in Int. J. Mod. Phys. B
Bargmann, V.: Ann. Math 48, 568 (1947)
Bishop, F.R., Vourdas, A.: J. Phys. A: Math. Gen 20, 3727 (1987)
Von Neumann, J.: Mathematical foundations of quantum mechanics. Princeton University Press, Princeton (1955)
Wootters, W.K.: Phys. Rev. Lett 80, 2245 (1998)
Uhlmann, A.: Phys. Rev. A 62, 032307 (2000)
Vidal, G., Werner, R.F.: Phys. Rev. A 65, 032314 (2002)
Zhang, Y.-Q., Tan, L.: Eur. Phys. J. D 64, 585 (2011)
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Mojaveri, B., Dehghani, A., Fasihi, M.A. et al. Thermal Entanglement Between Two Two-Level Atoms in a Two-Photon Jaynes-Cummings Model with an Added Kerr Medium. Int J Theor Phys 57, 3396–3409 (2018). https://doi.org/10.1007/s10773-018-3853-9
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DOI: https://doi.org/10.1007/s10773-018-3853-9