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Dynamics of multipartite quantum coherence in asymmetric spin-orbit coupled system

## Dynamics of multipartite quantum coherence in asymmetric spin-orbit coupled system

Shao Ya-Ting, Yan Kai, Wu Yin-Zhong, Hao Xiang
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• #### Abstract

The time evolution of multipartite quantum coherence is studied in a three-body spin system with an asymmetric interaction. The l1 norm measurement is used to estimate the degree of quantum coherence in the spin system. The decoherence of all components of quantum coherence in the three-body spin system is analyzed by the exact diagnolization and numerical method based on quantum master equation. The environmental noise induced by the spontaneous decay can be simulated by the quantum amplitude damping model. It is found that the time evolution of quantum coherence component is closely related to the quantum property of the whole initial state. When the initial state is a separable pure one, the asymmetric interactions can conduce to the enhancement of the degree of multipartite quantum coherence in a short time interval. Under the influence of quantum noise, the degree of quantum coherence decreases gradually. We pay much attention to the spatial distribution of the degree of quantum coherence in a many-body system. The additivity relationship of bipartite component and tripartite coherence can exist if the initial state is chosen to be a Werner-like state. This kind of the coherence additivity between all bipartite components and global coherence can be extended to an arbitrary N-body Werner-like state. But this additivity relationship depends on the l1 norm coherence measurement. Owing to the asymmetric interaction and noise, the degree of tripartite quantum coherence is more than the sum of all degrees of bipartite quantum coherence. The difference between the degree of tripartite coherence and the sum of all degrees of bipartite coherence is increased in a short time interval. The environmental noise can also suppress the difference in the coherence degree. The degree of the nearest neighboring bipartite coherence decreases more quickly than those of other bipartite coherences. The asymmetric interaction gives rise to the improvement in the degree of bipartite coherence and tripartite coherence. The coherence of the next-nearest neighboring two systems can be robust against the environmental noise. These results are helpful in preparing the multipartite quantum resources. We can utilize the system of coupled micro-cavities to realize the quantum spin system with controllable asymmetric interaction. In this way, the global coherence and bipartite coherence can be manipulated effectively by the quantum electromagnetic technology.

#### References

 [1] 吕为民 2019 博士学位论文 (北京: 中国科学技术大学) Lv W M 2019 Ph. D. Dissertation (Beijing: University of Science and Technology of China) (in Chinese) [2] Barney R D, Huele J F S V 2019 Phys. Scr. 94 105105 [3] Ding Z Y, Yang H, Yuan H, Wang D, Yang J, Ye L 2019 Phys. Rev. A 100 022308 [4] Kouzakov K A, Chotorlishvili L, Wtzel J, Berakdar J, Ernst A 2019 Phys. Rev. A 100 022311 [5] Guo W J, Wei L F 2017 Chin. Phys. B 26 010303 [6] Liu Z, Qiu L, Pan F 2017 Quantum Inf. Process. 16 109 [7] Khmelinskii I, Makarov V I 2020 Chem. Phys. 532 110671 [8] Afsaneh E, Bagheri H M, Jafari M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 145502 [9] 高明 2011 博士学位论文 (湖南: 国防科学技术大学) Gao M 2011 Ph. D. Dissertation (Hunan: National University of Defense Technology) (in Chinese) [10] Chuchem M, Cohen D 2010 Physica E 42 555 [11] Trushechkin A S 2019 Math Notes 106 986 [12] Rodriguez-Rosario C A, Frauenheim T, Aspuru-Guzik A 2019 Open Syst. Inf. Dyn. 26 1950022 [13] Balazadenh L, Najarbashi G, Tavana A 2018 Sci. Rep. 8 17789 [14] Escalera-Moreno L, Gaita-Ariño A, Coronado E 2019 Phys. Rev. B 100 064405 [15] Lin C W, Sels D, Wang Y B 2020 Phys. Rev. A 101 022320 [16] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 [17] Zhao M J, Ma T, Quan Q, Fan H, Pereira R 2019 Phys. Rev. A 100 012315 [18] Hu M L, Fan H 2018 Phys. Rev. A 98 022312 [19] Gao D M, Lv T H 2019 Int. J. Theor. Phys. 58 1195 [20] Sargolzahi I, Mirafzali S Y 2019 Phys. Rev. A 100 042121 [21] 张志君 2017 硕士学位论文 (南京: 南京邮电大学) Zhang Z J 2017 M. S. Thesis (Nanjing: Nanjing University of Posts and Telecommunications) (in Chinese) [22] 范洪义 2014 物理学报 63 020302 Fan H Y 2014 Acta Phys. Sin. 63 020302 [23] 田聪, 鹿翔, 张英杰, 夏云杰 2019 物理学报 68 150301 Tian C, Lu X, Zhang Y J, Xia Y J 2019 Acta Phys. Sin. 68 150301 [24] Yuan Z G, Zhang P, Li S S, Jian J 2016 Ann. Phys. 365 223 [25] Karpat G, Cakmak B, Fanchini F F 2014 Phys. Rev. B 90 104431 [26] Malvezzi A L, Karpat G, Cakmak B, Fanchini F F, Debarba T, Vianna R O 2016 Phys. Rev. B 93 184428 [27] Korenic A, Perovic S, Cirkovic M M, Miquel P A 2020 Prog. Biophys. Mol. Biol. 150 1 [28] Xu P, Hu Y H, Hou X W 2018 Physica A 491 282 [29] Peng H P, Fang M F, Yu M, Zou H M 2018 Int. J. Theor. Phys. 57 1872 [30] Ming F, Wang D, Shi W N, Huang A J, Du M M, Sun W Y, Ye L 2018 Quantum Inf. Process. 17 267 [31] Xie Y X, Gao Y Y 2019 Laser Phys. Lett. 16 045202 [32] Radhakrishnan C, Ermakov I, Byrnes T 2017 Phys. Rev. A 96 012341 [33] Hui N J, Xu Y Y, Wang J, Zhang Y, Hu Z D 2017 Physica B 510 7 [34] Feldman K E 2006 J. Phys. A: Math. Gen. 39 1039 [35] Levitov L S, Rashba E I 2001 Phys. Rev. B 67 115324 [36] Dzyaloshinskii I 1958 Phys. Chem. Solids 4 241 [37] Moriya T 1960 Phys. Rev. 120 91 [38] De Raedt H, Miyashita S, Michielsen K and Machida M 2004 Phys. Rev. B 70 064401 [39] Hartmann M J, Brand O F G S L, Plenio M B 2007 Phys. Rev. Lett. 99 160501 [40] Chen Z X, Zhou Z W, Zhou X, Zhou X F, Guo G C 2010 Phys. Rev. A 81 022303 [41] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404

#### Cited By

• 图 1  当初态为$\left| {001} \right\rangle$时, 量子相干组分演化, 参量选取为$D = 0.2,$ $\gamma = 0.2,$ $\varGamma = 0.5,$ $n = 0.2$, 黑色实线为${C_{123}}$, 红色虚线和绿色点划线分别为${C_{12}}, {C_{13}}$, 蓝色点线为${C_{23}}$

Figure 1.  The dynamics of all fractions of quantum coherence for the initial state $\left| {001} \right\rangle$. The parameters are chosen to be$D = 0.2,$ $\gamma = 0.2,$ $\varGamma = 0.5,$ $n = 0.2$. The black solid line denotes ${C_{123}}$, the red dashed and green dot-dashed line are ${C_{12}}, {C_{13}}$ respectively, and the blue dotted line represents ${C_{23}}$.

图 2  当初态为$\left| {001} \right\rangle$时, 量子相干组分差值的演化, 参量选取为$\varGamma = 0.5,$ $n = 0.2$　(a) 当$\gamma = 0.2$时, 黑色实线对应参数$D = 0.3,$ 红色虚线对应$D = 0.5;$ (b)当$D = 0.2$时, 黑色实线对应参数$\gamma = 0.3,$ 红色虚线对应$\gamma = 0.7$

Figure 2.  The dynamics of the difference of quantum coherence for the initial state $\left| {001} \right\rangle$. The parameters are chosen to be $\varGamma = 0.5,$ $n = 0.2$: (a) When $\gamma = 0.2$, the black solid line denotes $D = 0.3$ the red dashed line is $D = 0.5;$ (b) When $D = 0.2$, the black solid line denotes$\gamma = 0.3,$ the red dashed line is $\gamma = 0.7$.

图 3  当初态为W态时, 量子相干组分演化, 参量$D = 0.2,$ $\gamma = 0.2,$ $\varGamma = 0.5,$ $n = 0.2$, 　黑色实线为${C_{123}}$, 红色虚线和绿色点划线分别为${C_{12}}, {C_{13}}$, 蓝色点线为${C_{23}}$

Figure 3.  The dynamics of all fractions of quantum coherence for the initial W state. The parameters are chosen to be $D = 0.2,$ $\gamma = 0.2,$ $\varGamma = 0.5,$ $n = 0.2$. The black solid line denotes ${C_{123}}$, the red dashed and green dot-dashed line are ${C_{12}}, {C_{13}}$ respectively, and the blue dotted line represents ${C_{23}}$.

图 4  当初态为W态时, 量子相干组分差值的演化, 参量选取为$\varGamma = 0.5,$ $n = 0.2$　(a) 当$\gamma = 0.2$时, 黑色实线对应参数$D = 0.3,$ 红色虚线对应$D = 0.5;$ (b)当$D = 0.2$时, 黑色实线对应参数$\gamma = 0.3,$ 红色虚线对应$\gamma = 0.7$

Figure 4.  The dynamics of the difference of quantum coherence for the initial W state. The parameters are chosen to be $\varGamma = 0.5,$ $n = 0.2$; (a) When $\gamma = 0.2$, the black solid line denotes $D = 0.3$ the red dashed line is $D = 0.5;$ (b) When $D = 0.2$, the black solid line denotes$\gamma = 0.3,$ the red dashed line is $\gamma = 0.7$.

•  [1] 吕为民 2019 博士学位论文 (北京: 中国科学技术大学) Lv W M 2019 Ph. D. Dissertation (Beijing: University of Science and Technology of China) (in Chinese) [2] Barney R D, Huele J F S V 2019 Phys. Scr. 94 105105 [3] Ding Z Y, Yang H, Yuan H, Wang D, Yang J, Ye L 2019 Phys. Rev. A 100 022308 [4] Kouzakov K A, Chotorlishvili L, Wtzel J, Berakdar J, Ernst A 2019 Phys. Rev. A 100 022311 [5] Guo W J, Wei L F 2017 Chin. Phys. B 26 010303 [6] Liu Z, Qiu L, Pan F 2017 Quantum Inf. Process. 16 109 [7] Khmelinskii I, Makarov V I 2020 Chem. Phys. 532 110671 [8] Afsaneh E, Bagheri H M, Jafari M 2018 J. Phys. B: At. Mol. Opt. Phys. 51 145502 [9] 高明 2011 博士学位论文 (湖南: 国防科学技术大学) Gao M 2011 Ph. D. Dissertation (Hunan: National University of Defense Technology) (in Chinese) [10] Chuchem M, Cohen D 2010 Physica E 42 555 [11] Trushechkin A S 2019 Math Notes 106 986 [12] Rodriguez-Rosario C A, Frauenheim T, Aspuru-Guzik A 2019 Open Syst. Inf. Dyn. 26 1950022 [13] Balazadenh L, Najarbashi G, Tavana A 2018 Sci. Rep. 8 17789 [14] Escalera-Moreno L, Gaita-Ariño A, Coronado E 2019 Phys. Rev. B 100 064405 [15] Lin C W, Sels D, Wang Y B 2020 Phys. Rev. A 101 022320 [16] Baumgratz T, Cramer M, Plenio M B 2014 Phys. Rev. Lett. 113 140401 [17] Zhao M J, Ma T, Quan Q, Fan H, Pereira R 2019 Phys. Rev. A 100 012315 [18] Hu M L, Fan H 2018 Phys. Rev. A 98 022312 [19] Gao D M, Lv T H 2019 Int. J. Theor. Phys. 58 1195 [20] Sargolzahi I, Mirafzali S Y 2019 Phys. Rev. A 100 042121 [21] 张志君 2017 硕士学位论文 (南京: 南京邮电大学) Zhang Z J 2017 M. S. Thesis (Nanjing: Nanjing University of Posts and Telecommunications) (in Chinese) [22] 范洪义 2014 物理学报 63 020302 Fan H Y 2014 Acta Phys. Sin. 63 020302 [23] 田聪, 鹿翔, 张英杰, 夏云杰 2019 物理学报 68 150301 Tian C, Lu X, Zhang Y J, Xia Y J 2019 Acta Phys. Sin. 68 150301 [24] Yuan Z G, Zhang P, Li S S, Jian J 2016 Ann. Phys. 365 223 [25] Karpat G, Cakmak B, Fanchini F F 2014 Phys. Rev. B 90 104431 [26] Malvezzi A L, Karpat G, Cakmak B, Fanchini F F, Debarba T, Vianna R O 2016 Phys. Rev. B 93 184428 [27] Korenic A, Perovic S, Cirkovic M M, Miquel P A 2020 Prog. Biophys. Mol. Biol. 150 1 [28] Xu P, Hu Y H, Hou X W 2018 Physica A 491 282 [29] Peng H P, Fang M F, Yu M, Zou H M 2018 Int. J. Theor. Phys. 57 1872 [30] Ming F, Wang D, Shi W N, Huang A J, Du M M, Sun W Y, Ye L 2018 Quantum Inf. Process. 17 267 [31] Xie Y X, Gao Y Y 2019 Laser Phys. Lett. 16 045202 [32] Radhakrishnan C, Ermakov I, Byrnes T 2017 Phys. Rev. A 96 012341 [33] Hui N J, Xu Y Y, Wang J, Zhang Y, Hu Z D 2017 Physica B 510 7 [34] Feldman K E 2006 J. Phys. A: Math. Gen. 39 1039 [35] Levitov L S, Rashba E I 2001 Phys. Rev. B 67 115324 [36] Dzyaloshinskii I 1958 Phys. Chem. Solids 4 241 [37] Moriya T 1960 Phys. Rev. 120 91 [38] De Raedt H, Miyashita S, Michielsen K and Machida M 2004 Phys. Rev. B 70 064401 [39] Hartmann M J, Brand O F G S L, Plenio M B 2007 Phys. Rev. Lett. 99 160501 [40] Chen Z X, Zhou Z W, Zhou X, Zhou X F, Guo G C 2010 Phys. Rev. A 81 022303 [41] Yu T, Eberly J H 2004 Phys. Rev. Lett. 93 140404
•  Citation:
##### Metrics
• Abstract views:  547
• Cited By: 0
##### Publishing process
• Received Date:  26 July 2020
• Accepted Date:  24 August 2020
• Available Online:  22 October 2020
• Published Online:  05 January 2021

## Dynamics of multipartite quantum coherence in asymmetric spin-orbit coupled system

###### Corresponding author: Hao Xiang, xhao@mail.usts.edu.cn
• School of Physical Science and Technology, Suzhou University of Science and Technology, Suzhou 215009, China

Abstract: The time evolution of multipartite quantum coherence is studied in a three-body spin system with an asymmetric interaction. The l1 norm measurement is used to estimate the degree of quantum coherence in the spin system. The decoherence of all components of quantum coherence in the three-body spin system is analyzed by the exact diagnolization and numerical method based on quantum master equation. The environmental noise induced by the spontaneous decay can be simulated by the quantum amplitude damping model. It is found that the time evolution of quantum coherence component is closely related to the quantum property of the whole initial state. When the initial state is a separable pure one, the asymmetric interactions can conduce to the enhancement of the degree of multipartite quantum coherence in a short time interval. Under the influence of quantum noise, the degree of quantum coherence decreases gradually. We pay much attention to the spatial distribution of the degree of quantum coherence in a many-body system. The additivity relationship of bipartite component and tripartite coherence can exist if the initial state is chosen to be a Werner-like state. This kind of the coherence additivity between all bipartite components and global coherence can be extended to an arbitrary N-body Werner-like state. But this additivity relationship depends on the l1 norm coherence measurement. Owing to the asymmetric interaction and noise, the degree of tripartite quantum coherence is more than the sum of all degrees of bipartite quantum coherence. The difference between the degree of tripartite coherence and the sum of all degrees of bipartite coherence is increased in a short time interval. The environmental noise can also suppress the difference in the coherence degree. The degree of the nearest neighboring bipartite coherence decreases more quickly than those of other bipartite coherences. The asymmetric interaction gives rise to the improvement in the degree of bipartite coherence and tripartite coherence. The coherence of the next-nearest neighboring two systems can be robust against the environmental noise. These results are helpful in preparing the multipartite quantum resources. We can utilize the system of coupled micro-cavities to realize the quantum spin system with controllable asymmetric interaction. In this way, the global coherence and bipartite coherence can be manipulated effectively by the quantum electromagnetic technology.

Reference (41)

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