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In this paper, effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Under strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated by using the quantum reduced entropy and the quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and mutiphoton (k>2) are revealed respectively. The preparation of entangled states is discussed. The Einstein-Podolsky-Rosen states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.
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Keywords:
- intensity-dependent coupling /
- quantum entanglement /
- quantum reduced entropy /
- quantum relative entropy
[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Schrdinger E 1935 Naturwissenschaften 23 807
[3] Bell J S 1964 Physics 1 195
[4] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
[5] Shor P W 1995 Phys. Rev. A 52 2493
[6] Deusch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1998 Phys. Rev. Lett. 80 2022
[7] Gover L K 1997 Phys. Rev. Lett. 79 325
[8] Liu T K, Wang J S, Liu X J, Zhan M S 2000 Acta Phys. Sin. 49 708 (in Chinese) [刘堂昆、王继锁、柳晓军、詹明生 2000 49 708 ]
[9] Wang C Z, Fang M F 2002 Acta Phys. Sin. 51 1989 (in Chinese) [王成志、方卯发2002 51 1989]
[10] Liu X J, Fang M F 2003 Chin. Phys. 12 971
[11] Tan X, Zhang C Q, Xia Y J 2006 Acta Phys. Sin. 55 2263 (in Chinese) [谭 霞、 张成强、夏云杰 2006 55 2263]
[12] Zhou P, Peng J S 1992 J. Mod. Opt. 39 49
[13] Fang M F 1995 Acta Opt. Sin. 15 296 (in Chinese) [方卯发 1995光学学报 15 296]
[14] Li C X, Fang M F 2003 Chin. Phys. 12 294
[15] Gao Y F, Feng J, Zhang G M 2006 J. At. Mol. Phys. 20 887 (in Chinese) [高云峰、冯 健、张桂明 2006 原子与分子 20 887]
[16] Gu Z Y, Ji P Y 2002 Acta Phys. Sin. 51 1022 (in Chinese) [顾震宇、季沛勇 2002 51 1022]
[17] Tang Z L, Liang R S, Chang H S 2000 Acta Phys. Sin. 49 1076 (in Chinese) [唐志列、梁瑞生、常鸿森 2000 49 1076]
[18] Liu T K 1994 J. Central China Normal Univ. (Nat. Sci.) 28 185 (in Chinese) [刘堂昆 1994 华中师范大学学报 (自然科学版) 28 185]
[19] Zhang D Y 2002 Acta Photon. Sin. 31 537 (in Chinese) [张登玉 2002 光子学报 31 537]
[20] Zhang C Q, Tan X, Xia Y J 2006 Chin. J. Quantum Electron. 23 825 (in Chinese) [张成强、谭 霞、夏云杰 2006 量子电子学报 23 825]
[21] Zhou Q P 1998 Acta Opt. Sin. 18 712 (in Chinese) [周清平 1998 光学学报 18 712]
[22] Napoli A, Messin A 1996 J. Mod. Opt. 43 649
[23] Phoenix S J D, Knight P L 1998 Ann. Phys. 186 381
[24] Schmidt E 1907 Math. Ann. 63 433
[25] Vedral V, Plenio M B 1998 Phys. Rev. A 57 1619
[26] Rains E 1999 Phys. Rev. A 60 179
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[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Schrdinger E 1935 Naturwissenschaften 23 807
[3] Bell J S 1964 Physics 1 195
[4] Bouwmeester D, Pan J W, Mattle K, Eibl M, Weinfurter H, Zeilinger A 1997 Nature 390 575
[5] Shor P W 1995 Phys. Rev. A 52 2493
[6] Deusch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1998 Phys. Rev. Lett. 80 2022
[7] Gover L K 1997 Phys. Rev. Lett. 79 325
[8] Liu T K, Wang J S, Liu X J, Zhan M S 2000 Acta Phys. Sin. 49 708 (in Chinese) [刘堂昆、王继锁、柳晓军、詹明生 2000 49 708 ]
[9] Wang C Z, Fang M F 2002 Acta Phys. Sin. 51 1989 (in Chinese) [王成志、方卯发2002 51 1989]
[10] Liu X J, Fang M F 2003 Chin. Phys. 12 971
[11] Tan X, Zhang C Q, Xia Y J 2006 Acta Phys. Sin. 55 2263 (in Chinese) [谭 霞、 张成强、夏云杰 2006 55 2263]
[12] Zhou P, Peng J S 1992 J. Mod. Opt. 39 49
[13] Fang M F 1995 Acta Opt. Sin. 15 296 (in Chinese) [方卯发 1995光学学报 15 296]
[14] Li C X, Fang M F 2003 Chin. Phys. 12 294
[15] Gao Y F, Feng J, Zhang G M 2006 J. At. Mol. Phys. 20 887 (in Chinese) [高云峰、冯 健、张桂明 2006 原子与分子 20 887]
[16] Gu Z Y, Ji P Y 2002 Acta Phys. Sin. 51 1022 (in Chinese) [顾震宇、季沛勇 2002 51 1022]
[17] Tang Z L, Liang R S, Chang H S 2000 Acta Phys. Sin. 49 1076 (in Chinese) [唐志列、梁瑞生、常鸿森 2000 49 1076]
[18] Liu T K 1994 J. Central China Normal Univ. (Nat. Sci.) 28 185 (in Chinese) [刘堂昆 1994 华中师范大学学报 (自然科学版) 28 185]
[19] Zhang D Y 2002 Acta Photon. Sin. 31 537 (in Chinese) [张登玉 2002 光子学报 31 537]
[20] Zhang C Q, Tan X, Xia Y J 2006 Chin. J. Quantum Electron. 23 825 (in Chinese) [张成强、谭 霞、夏云杰 2006 量子电子学报 23 825]
[21] Zhou Q P 1998 Acta Opt. Sin. 18 712 (in Chinese) [周清平 1998 光学学报 18 712]
[22] Napoli A, Messin A 1996 J. Mod. Opt. 43 649
[23] Phoenix S J D, Knight P L 1998 Ann. Phys. 186 381
[24] Schmidt E 1907 Math. Ann. 63 433
[25] Vedral V, Plenio M B 1998 Phys. Rev. A 57 1619
[26] Rains E 1999 Phys. Rev. A 60 179
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