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Quantum entanglement plays a key role in quantum information and quantum computation and thus attracts much attention in many branches of physics both in theory and in experiment. But recent studies revealed that some separable states (non-entangled state) may speed up certain tasks over their classical counterparts and may also possess certain kinds of quantum correlations. For example, geometric quantum discord, which is a more general quantum correlation measure than entanglement, can be nonzero for some separable states. From a practical point of view, it is proposed that the geometric quantum discord be responsible for the power of many quantum information processing tasks. In order to capture such correlations, Ollivier and Zurek introduced quantum discord, which measures the discrepancy between two natural yet different quantum analogues of two classically equivalent expressions of mutual information. However, the calculation of quantum discord is based on numerical maximization procedure, and there are few analytical expressions even for a two-qubit state. In order to obtain the analytical results of quantum discord, a geometric measure of quantum discord which measures the quantum correlations through the minimum Hilbert-Schmidt distance between the given state and zero discord state is introduced. Geometric quantum discord is defined as an effective measure of quantum correlation, and the geometric quantum discord through the minimal distance between the quantum state and the set of zero-discord states in a bipartite quantum system can be worked out. In this paper, by using the geometric quantum discord measurement method, the geometric quantum discord in Tavis-Cummings model is investigated, and the influences of the initial state purity, entanglement degree, dipole-dipole coupling intensity between two atoms, and field in the Fock state on the evolution characteristic of geometric quantum discord are analyzed. The results show that the geometric quantum discord appears periodically. It initially decreases to a minimum value, and then turns out to be increased for different initial states. The rigorous analysis and numerical results reveal that when we take a suitable initial state, the geometric quantum discord of two atoms can be kept in correlation. When the atoms are in the different initial states, the quantum properties of the system are significant. The photon number of the field can lead the quantum discord to be weakened. Geometric quantum discord can be increased by increasing the cavity photon number and the dipole-dipole coupling intensity. Geometric quantum discord can be enhanced obviously by increasing the strength of the dipole-dipole coupling interaction. The conclusions may conduce to the understanding of quantum correlation for the other systems from the view of geometric quantum discord.
[1] Ekert A K 1991 Phys. Rev. Lett. 67 661
[2] Bennett C H, Brassard G, Grepean C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[3] Shor P W 1992 Phys. Rev. Lett. 52 2493
[4] Bogoliubov N M, Bulloughz R K, Timonenx 1996 J. Phys. A: Math. Gen. 19 6305
[5] Zuo Z C, Xia Y J 2003 Acta Phys. Sin. 52 2687(in Chinese) [左战春, 夏云杰 2003 52 2687]
[6] Guo L, Liang X T 2009 Acta Phys. Sin. 58 50(in Chinese) [郭亮, 梁先庭 2009 58 50]
[7] Zhang G F, Bu J J 2010 Acta Phys. Sin. 59 1462(in Chinese) [张国锋, 卜晶晶 2010 59 1462]
[8] Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017910
[9] Hu Y H, Tan Y G, Liu Q 2013 Acta Phys. Sin. 62 074202(in Chinese) [胡要花, 谭勇刚, 刘强 2013 62 074202]
[10] He Z, Li L W 2013 Acta Phys. Sin. 18 180301(in Chinese) [贺志, 李龙武 2013 18 180301]
[11] Ali M, Rau A R P, Alber G 2010 Phys. Rev. A 81 359
[12] Dakic B, Vedral V, Brukner C 2010 Phys. Rev. Lett. 105 4649
[13] Fan K M, Zhang G F 2013 Acta Phys. Sin. 62 130301(in Chinese) [樊开明, 张国锋 2013 62 130301]
[14] Hu M L, Tian D P 2014 Ann. Phys. 343 132
[15] LI Y J, Liu J M, Zhang Y 2014 Chin. Phys. B 23 110306
[16] Chang L, Luo S 2013 Phys. Rev. A 82 034302
[17] Zhu H J, Zhang G F 2014 Chin. Phys. B 23 120306
[18] Song W, Yu L B, Dong P, Li D C, Yang M, Cao Z L 2013 Sci. China: Phys. Mech. Astron. 56 737
[19] Xiao Y L, Li T, Fei S M, Jing N, Wang Z X 2016 Chin. Phys. B 25 030301
[20] Zou H M, Fang M F 2016 Chin. Phys. B 25 090302
[21] Shan C J, Xia Y J 2006 Acta Phys. Sin. 55 1585(in Chinese) [单传家, 夏云杰 2006 55 1585]
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[1] Ekert A K 1991 Phys. Rev. Lett. 67 661
[2] Bennett C H, Brassard G, Grepean C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895
[3] Shor P W 1992 Phys. Rev. Lett. 52 2493
[4] Bogoliubov N M, Bulloughz R K, Timonenx 1996 J. Phys. A: Math. Gen. 19 6305
[5] Zuo Z C, Xia Y J 2003 Acta Phys. Sin. 52 2687(in Chinese) [左战春, 夏云杰 2003 52 2687]
[6] Guo L, Liang X T 2009 Acta Phys. Sin. 58 50(in Chinese) [郭亮, 梁先庭 2009 58 50]
[7] Zhang G F, Bu J J 2010 Acta Phys. Sin. 59 1462(in Chinese) [张国锋, 卜晶晶 2010 59 1462]
[8] Ollivier H, Zurek W H 2001 Phys. Rev. Lett. 88 017910
[9] Hu Y H, Tan Y G, Liu Q 2013 Acta Phys. Sin. 62 074202(in Chinese) [胡要花, 谭勇刚, 刘强 2013 62 074202]
[10] He Z, Li L W 2013 Acta Phys. Sin. 18 180301(in Chinese) [贺志, 李龙武 2013 18 180301]
[11] Ali M, Rau A R P, Alber G 2010 Phys. Rev. A 81 359
[12] Dakic B, Vedral V, Brukner C 2010 Phys. Rev. Lett. 105 4649
[13] Fan K M, Zhang G F 2013 Acta Phys. Sin. 62 130301(in Chinese) [樊开明, 张国锋 2013 62 130301]
[14] Hu M L, Tian D P 2014 Ann. Phys. 343 132
[15] LI Y J, Liu J M, Zhang Y 2014 Chin. Phys. B 23 110306
[16] Chang L, Luo S 2013 Phys. Rev. A 82 034302
[17] Zhu H J, Zhang G F 2014 Chin. Phys. B 23 120306
[18] Song W, Yu L B, Dong P, Li D C, Yang M, Cao Z L 2013 Sci. China: Phys. Mech. Astron. 56 737
[19] Xiao Y L, Li T, Fei S M, Jing N, Wang Z X 2016 Chin. Phys. B 25 030301
[20] Zou H M, Fang M F 2016 Chin. Phys. B 25 090302
[21] Shan C J, Xia Y J 2006 Acta Phys. Sin. 55 1585(in Chinese) [单传家, 夏云杰 2006 55 1585]
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