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By means of Von Neumann entropy and Schmidt number K, we study the time evolution properties of the entanglement between a two-level atom and spontaneous emission field in anisotropic photonic crystal. The evolution properties of the atom-field entanglement are directly related to the relative position of the upper level from the band edge. The atom-field entanglement can keep steady when the atomic upper level is within the band gap. The atom-field entanglement increases to the maximum value firstly and then decay to zero when the atomic upper level is within the transmitting band. The atom-field entanglement also depends on the initial state of the atom. We can control the time evolution properties of the atom-field entanglement by choosing special atomic initial state and the relative position of the upper level from the band edge.
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Keywords:
- entanglement /
- photonic crystal /
- atomic quantum entropy /
- Schmidt number K
[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Pereira S F , Ou Z Y ,Kimble H J 2000 Phys. Rev. A 62 042311
[3] Grover L K 1997 Phys. Rev. Lett. 79 325
[4] Bouwmeaster D, Pan J W, Mattle K, Elbl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Zhang Q , Li F L, Li H R 2006 Acta Phys. Sin. 55 2275 (in Chinese)[张 茜、李福利、李宏荣 2006 55 2275]
[5] Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1996 Phys. Rev. Lett. 77 2818 Ekert A K 1991 Phys. Rev. Lett. 67 661
[6] Fang M F, Zhu S Y 2006 Physica A 369 475 Cheng Q L, Xie S Y, Yang Y P 2008 Acta Phys. Sin. 57 6968 (in Chinese)[成秋丽、谢双媛、羊亚平 2008 57 6968] Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese)[郭 亮、梁先庭 2009 58 0050] Zhang L H, Li G X, Gan Z W 2003 Acta Phys. Sin. 52 1168 (in Chinese)[张立辉、李高翔、甘仲惟 2003 52 1168] Zhang Y J, Zhou Y,Xia Y J 2008 Acta Phys. Sin. 57 0021 (in Chinese)[张英杰、周 原、夏云杰 2008 57 0021] Huang C J, He H Y, Zhou M,Fang J Y,Huang Z H 2006 Acta Phys. Sin. 55 1764 (in Chinese)[黄春佳、贺慧勇、周 明、方家元、黄祖洪 2006 55 1764] Wang J X, Yang Z Y, An Y Y 2007 Acta Phys. Sin. 56 6420 (in Chinese)[王菊霞、杨志勇、安毓英 2007 56 6420]
[7] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[8] Bellomo B, Franco R L, Compagno G 2007 Phys. Rev. Lett. 99 160502 Cao X F , Zheng H 2008 Phys. Rev. A 77 022320
[9] Santos M F , Milman P, Davidovich L, Zagury N 2006 Phys. Rev. A 73 040305(R) Almeida M P, de Melo F, Hor-Meyll M, Salles A , Walborn S P, Souto Ribeiro P H, Davidovich L 2007 Science 316 579
[10] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059 John S 1987 Phys. Rev. Lett. 58 2486 Ho K M , Chan C T ,Soukoulis C M 1990 Phys. Rev. Lett. 65 3152 Yablonovitch E, Gmitter T J 1991 Phys. Rev. Lett. 67 2295
[11] John S, Quang T 1994 Phys. Rev. A 50 1764 Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805 Yang Y P, Fleischhauer M , Zhu S Y 2003 Phys. Rev. A 68 043805 Zhu S Y, Chen H, Huang H 1997 Phys. Rev. Lett. 79 205 Zhu S Y, Yang Y P , Chen H , Zheng H, Zubairy M S 2000 Phys. Rev. Lett. 84 2136
[12] Wang F Q , Zhang Z M , Liang R S 2008 Phys. Rev. A 78 042320
[13] Phoenix S J D, Knight P L 1988 Ann. Phys. (N. Y.) 186 381 Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023 Phoenix S J D, Knight P L 1991 Phys. Rev. Lett. 66 2833
[14] Grobe R, Rzazewski K, Eberly J H 1994 J. Phys. B 27 L503 Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge,Cambridge University Press) P101
[15] Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805
[16] Araki H, Lieb E 1970 Commun. Math. Phys. 18 160
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[1] Einstein A, Podolsky B, Rosen N 1935 Phys. Rev. 47 777
[2] Pereira S F , Ou Z Y ,Kimble H J 2000 Phys. Rev. A 62 042311
[3] Grover L K 1997 Phys. Rev. Lett. 79 325
[4] Bouwmeaster D, Pan J W, Mattle K, Elbl M, Weinfurter H, Zeilinger A 1997 Nature 390 575 Bennett C H, Brassard G, Crepeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 Zhang Q , Li F L, Li H R 2006 Acta Phys. Sin. 55 2275 (in Chinese)[张 茜、李福利、李宏荣 2006 55 2275]
[5] Deutsch D, Ekert A, Jozsa R, Macchiavello C, Popescu S, Sanpera A 1996 Phys. Rev. Lett. 77 2818 Ekert A K 1991 Phys. Rev. Lett. 67 661
[6] Fang M F, Zhu S Y 2006 Physica A 369 475 Cheng Q L, Xie S Y, Yang Y P 2008 Acta Phys. Sin. 57 6968 (in Chinese)[成秋丽、谢双媛、羊亚平 2008 57 6968] Guo L, Liang X T 2009 Acta Phys. Sin. 58 0050 (in Chinese)[郭 亮、梁先庭 2009 58 0050] Zhang L H, Li G X, Gan Z W 2003 Acta Phys. Sin. 52 1168 (in Chinese)[张立辉、李高翔、甘仲惟 2003 52 1168] Zhang Y J, Zhou Y,Xia Y J 2008 Acta Phys. Sin. 57 0021 (in Chinese)[张英杰、周 原、夏云杰 2008 57 0021] Huang C J, He H Y, Zhou M,Fang J Y,Huang Z H 2006 Acta Phys. Sin. 55 1764 (in Chinese)[黄春佳、贺慧勇、周 明、方家元、黄祖洪 2006 55 1764] Wang J X, Yang Z Y, An Y Y 2007 Acta Phys. Sin. 56 6420 (in Chinese)[王菊霞、杨志勇、安毓英 2007 56 6420]
[7] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[8] Bellomo B, Franco R L, Compagno G 2007 Phys. Rev. Lett. 99 160502 Cao X F , Zheng H 2008 Phys. Rev. A 77 022320
[9] Santos M F , Milman P, Davidovich L, Zagury N 2006 Phys. Rev. A 73 040305(R) Almeida M P, de Melo F, Hor-Meyll M, Salles A , Walborn S P, Souto Ribeiro P H, Davidovich L 2007 Science 316 579
[10] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059 John S 1987 Phys. Rev. Lett. 58 2486 Ho K M , Chan C T ,Soukoulis C M 1990 Phys. Rev. Lett. 65 3152 Yablonovitch E, Gmitter T J 1991 Phys. Rev. Lett. 67 2295
[11] John S, Quang T 1994 Phys. Rev. A 50 1764 Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805 Yang Y P, Fleischhauer M , Zhu S Y 2003 Phys. Rev. A 68 043805 Zhu S Y, Chen H, Huang H 1997 Phys. Rev. Lett. 79 205 Zhu S Y, Yang Y P , Chen H , Zheng H, Zubairy M S 2000 Phys. Rev. Lett. 84 2136
[12] Wang F Q , Zhang Z M , Liang R S 2008 Phys. Rev. A 78 042320
[13] Phoenix S J D, Knight P L 1988 Ann. Phys. (N. Y.) 186 381 Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023 Phoenix S J D, Knight P L 1991 Phys. Rev. Lett. 66 2833
[14] Grobe R, Rzazewski K, Eberly J H 1994 J. Phys. B 27 L503 Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge,Cambridge University Press) P101
[15] Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805
[16] Araki H, Lieb E 1970 Commun. Math. Phys. 18 160
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