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The time evolutions of the entanglement between a two-level atom and its spontaneous emission field in free space, cavity, isotropic and anisotropic photonic crystal are studied by using quantum entropy. It is found that the evolution properties of the atom-field entanglement are directly related to the nature of the structured reservoir,specifically, to the distribution of the density of modes. In free space and cavity, as the density of the modes varies smoothly with frequency, the atom-field entanglement decays to zero in a finite time. However in an isotropic and anisotropic photonic crystal, the atom-field entanglement can keep steady due to the existence of a photonic band gap in the density of the modes. Thus, we can control the time evolution of the entanglement between the atom and its spontaneous emission field by changing the density of the modes of the structured reservoirs.
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Keywords:
- entanglement /
- quantum entropy /
- structured reservoir /
- density of modes
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[27] Fang M F, Zhu S Y 2006 Physica A 369 475
[28] Xie S Y, Hu X 2010 Acta Phys. Sin. 59 6172 (in Chinese)[谢双媛, 胡翔 2010 物理学报 59 6172]
[29] Roshan Entezar S 2009 Phys Lett. A 373 3413
[30] 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 物理学报 57 6968]
[31] 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 物理学报 52 1168]
[32] Wang C Z, Fang M F 2002 Acta Phys. Sin. 51 1989 (in Chinese) [王成志, 方卯发 2002 物理学报 51 1989]
[33] Wooters W K 1998 Phys. Rev. Lett. 80 2245
[34] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) p101
[35] Vidal G, Werner R F 2002 Phys. Rev. A 65 032314
[36] Phoenix S J D, Knight P L 1988 Ann. Phys. 186 381
[37] Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023
[38] Phoenix S J D, Knight P L 1991 Phys. Rev. Lett. 66 2833
[39] Araki H, Lieb E 1970 Commum. Math. Phys. 18 160
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[1] Purcell E M 1946 Phys. Rev. 69 681
[2] Kleppner D 1981 Phys. Rev. Lett. 47 233
[3] Yablonovitch E 1987 Phys. Rev. Lett. 58 2059
[4] John S 1987 Phys. Rev. Lett. 58 2486
[5] John S, Quang T 1995 Phys. Rev. Lett. 74 3419
[6] John S, Wang J 1991 Phys. Rev. B 43 12772
[7] John S, Quang T 1994 Phys. Rev. A 50 1764
[8] John S, Wang J 1990 Phys. Rev. Lett. 64 2418
[9] Yang Y P, Zhu S Y 2000 Phys. Rev. A 61 043809
[10] Yang Y P, Zhu S Y 2000 Phys. Rev. A 62 013805
[11] Lambropoulos P, Nikolopoulos G M, Nielsen T R, Bay S 2000 Rep. Prog. Phys. 63 455
[12] Zheng Y Z, Dai L Y, Guo G C 2003 Acta Phys. Sin. 52 2678 (in Chinese)[郑亦庄, 戴玲玉, 郭光灿 2003 物理学报 52 2678]
[13] 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 物理学报 55 2275]
[14] Zhang J X, Dong R F, Xie C D 2001 Physics 30 43 (in Chinese) [张俊香, 董瑞芳, 谢常德 2001 物理 30 43]
[15] Pereira S F, Ou Z Y, Kimble H J 2000 Phys. Rev. A 62 042311
[16] Grover L K 1997 Phys. Rev. Lett. 79 325
[17] Su X L, Jia X J, Xie C D, Peng K C 2010 Physics 39 746 (in Chinese) [苏晓龙, 贾晓军, 谢常德, 彭堃墀 2010 物理 39 746]
[18] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
[19] Han F, Xia Y J 2009 Chin. Phys. B 18 5144
[20] Wang F Q, Zhang Z M, Liang R S 2008 Phys. Rev. A 78 042320
[21] Bellomo B, Franco R L, Maniscalco S, Compagno G 2008 Phys. Rev. A 78 060302
[22] Zhang Y J, Yang X Q, Han W, Xia Y J 2013 Chin. Phys. B 22 090307
[23] Cui C C, Xie S Y, Yang Y P 2012 Acta Phys. Sin. 61 124206 (in Chinese)[崔丛丛, 谢双媛, 羊亚平 2012 物理学报 61 124206]
[24] Cummings N I, Hu B L 2008 Phys. Rev. A 77 053823
[25] Lazarou C, Luoma K, Maniscalco S, Piilo J, Garraway B M 2012 Phys. Rev. A 86 012331
[26] Guo L, Liang X T 2009 Acta Phys. Sin. 58 50 (in Chinese)[郭亮, 梁先庭 2009 物理学报 58 50]
[27] Fang M F, Zhu S Y 2006 Physica A 369 475
[28] Xie S Y, Hu X 2010 Acta Phys. Sin. 59 6172 (in Chinese)[谢双媛, 胡翔 2010 物理学报 59 6172]
[29] Roshan Entezar S 2009 Phys Lett. A 373 3413
[30] 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 物理学报 57 6968]
[31] 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 物理学报 52 1168]
[32] Wang C Z, Fang M F 2002 Acta Phys. Sin. 51 1989 (in Chinese) [王成志, 方卯发 2002 物理学报 51 1989]
[33] Wooters W K 1998 Phys. Rev. Lett. 80 2245
[34] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) p101
[35] Vidal G, Werner R F 2002 Phys. Rev. A 65 032314
[36] Phoenix S J D, Knight P L 1988 Ann. Phys. 186 381
[37] Phoenix S J D, Knight P L 1991 Phys. Rev. A 44 6023
[38] Phoenix S J D, Knight P L 1991 Phys. Rev. Lett. 66 2833
[39] Araki H, Lieb E 1970 Commum. Math. Phys. 18 160
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