Kerr介质中非线性Jaynes-Cummings模型多光子跃迁的纠缠特性
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摘要
在线性和非线性Kerr介质Jaynes-Cummings(J-C)模型中,考虑多光子跃迁时原子和光场纠缠随时间的演化特性,给出原子和光场的纠缠度与跃迁光子数、失谐量、初始光子数、初始态参数及非线性项系数之间的解析关系,并分析其对原子和光场的纠缠度随时间演化的影响.结果表明,在非线性Kerr介质中,当光场与原子初始态接近最大纠缠态,且跃迁光子数较大时,纠缠态可稳定接近最大纠缠态,有利于量子纠缠态的远距离传输.
We considered the entanglement properties of multiphoton transition in the linear and nonlinear Kerr medium with Jaynes-Cummings(J-C)model.We gave the analytical relationship between the transition photon numbers,detuning quantity,initial photon numbers,initial state parameter,nonlinear coefficient and the entanglement degrees of atoms and light fields,and analyzed its effect on the entanglement degrees of atoms and light fields with time evolution.The results show that when the initial state is close to the maximum entangled state in the nonlinear Kerr medium,and the transition photon numbers are large,the entangled state is more stable near the maximum entangled state,which is beneficial to the long-distance transmission of quantum entangled states.
We considered the entanglement properties of multiphoton transition in the linear and nonlinear Kerr medium with Jaynes-Cummings(J-C)model.We gave the analytical relationship between the transition photon numbers,detuning quantity,initial photon numbers,initial state parameter,nonlinear coefficient and the entanglement degrees of atoms and light fields,and analyzed its effect on the entanglement degrees of atoms and light fields with time evolution.The results show that when the initial state is close to the maximum entangled state in the nonlinear Kerr medium,and the transition photon numbers are large,the entangled state is more stable near the maximum entangled state,which is beneficial to the long-distance transmission of quantum entangled states.
引文
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[9]樊开明,张国锋.阻尼Jaynes-Cummings模型中两原子的量子关联动力学[J].物理学报,2013,62(13):130301-1-130301-6.(FAN Kaiming,ZHANG Guofeng.The Dynamics of Quantum Correlation between Two Atoms in a Damping Jaynes-Cummings Model[J].Acta Phys Sin,2013,62(13):130301-1-130301-6.)
[10]白志达.Jaynes-Cummings模型中原子量子特性研究[J].大学物理,2017,36(5):78-80.(BAI Zhida.The Quantum Properties of Atom in Jaynes-Cummings Model[J].College Physics,2017,36(5):78-80.)
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[12]CHENG Jing,CHEN Xi,SHAN Chuanjia.Entanglement Evolution of Jaynes-Cummings Model in Resonance Case and Non-resonance Case[J].Int J Theor Phys,2018,57(6):1823-1828.
[13]XU Kai,HAN Wei,ZHANG Yingjie,et al.Non-Markovian Speedup Dynamics Control of the Damped JaynesCummings Model with Detuning[J].Chin Phys B,2018,27(1):010302-1-010302-6.
[14]丛红璐,任学藻,廖旭.非旋波近似下双光子Jaynes-Cummings模型的量子特性[J].光学学报,2015,35(7):0727002-1-0727002-7.(CONG Honglu,REN Xuezao,LIAO Xu.Quantum Properties of Two-Photon Jaynes-Cummings Model without Rotating Wave Approximation[J].Acta Optica Sinica,2015,35(7):0727002-1-0727002-7.)
[15]王菊霞.二能级原子与多模光场简并多光子共振相互作用系统中量子保真度的演化特性[J].物理学报,2014,63(18):184203-1-184203-8.(WANG Juxia.Evolution of the Quantum Fidelity in a System of Multimode Light Field Interacting Resonantly with a Two-Level Atom through Defenerate Multi-photon Process[J].Acta Phys Sin,2014,63(18):184203-1-184203-8.)
[16]刘王云,毕思文,豆西博.囚禁离子非线性Jaynes-Cummings模型量子场熵演化特性[J].物理学报,2010,59(3):1780-1785.(LIU Wangyun,BI Siwen,DOU Xibo.Evolution Properties of the Field Quantum Entropy in the Nonlinear Jaynes-Cummings Model of a Trapped Ion[J].Acta Phys Sin,2010,59(3):1780-1785.)
[17]刘晓静,刘继平,张晓茹,等.用多个光子晶体实现量子纠缠态的稳定性[J].吉林大学学报(理学版),2018,56(5):1224-1228.(LIU Xiaojing,LIU Jiping,ZHANG Xiaoru,et al.Stability of Quantum Entangled States with Multiple Photonic Crystals[J].Journal of Jilin University(Science Edition),2018,56(5):1224-1228.)
[2]ZHENG Shibiao,GUO Guangcan.Efficient Scheme for Two-Atom Entanglement and Quantum Information Processing in Cavity QED[J].Phys Rev Lett,2000,85(11):2392-2395.
[3]WONG A,CHRISTENSEN N.Potential Multiparticle Entanglement Measure[J].Phys Rev A,2001,63(4):44301-44304.
[4]饶志明,谢方森,胡利云,等.双光子J-C模型中原子与光场的纠缠及纠缠度[J].江西师范大学学报(自然科学版),2004,28(5):387-390.(RAO Zhiming,XIE Fangsen,HU Liyun,et al.The Entangled of Cavity Field and Atom in the Two-Photon Jaynes-Cummings Model and the Degree of Entanglement[J].Journal of Jiangxi Normal University(Natural Science),2004,28(5):387-390.)
[5]TAN Lei,ZHU Zhonghua,ZHANG Yuqing.Entanglement Dynamics of a Moving Multi-photon JaynesCummings Model in Mixed States[J].Chin Phys B,2011,20(7):070303-1-070303-11.
[6]JAYNES E T,CUMMINGS F W.Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser[J].Proc IEEE,1963,51(1):89-109.
[7]SINGH S,SINHA A.Solutions of Two-Mode Jaynes-Cummings Models[J].Pramana,2008,70(5):887-900.
[8]饶金同,王家驷,梁军.强度依赖Jaynes-Cummings模型中的量子态保真度[J].激光技术,2012,36(5):708-712.(RAO Jintong,WANG Jiasi,LIANG Jun.Fidelities of Quantum States in Intensity-Dependent JaynesCummings Model[J].Laser Technology,2012,36(5):708-712.)
[9]樊开明,张国锋.阻尼Jaynes-Cummings模型中两原子的量子关联动力学[J].物理学报,2013,62(13):130301-1-130301-6.(FAN Kaiming,ZHANG Guofeng.The Dynamics of Quantum Correlation between Two Atoms in a Damping Jaynes-Cummings Model[J].Acta Phys Sin,2013,62(13):130301-1-130301-6.)
[10]白志达.Jaynes-Cummings模型中原子量子特性研究[J].大学物理,2017,36(5):78-80.(BAI Zhida.The Quantum Properties of Atom in Jaynes-Cummings Model[J].College Physics,2017,36(5):78-80.)
[11]王艳清,萨楚尔夫,王亚男.阻尼Jaynes-Cummings模型下两原子与双模真空态光场相互作用系统中量子态的保真度[J].内蒙古师范大学学报(自然科学汉文版),2015,44(3):352-358.(WANG Yanqing,SA Chuerfu,WANG Yanan.The Fidelity of Quantum State in a System Interacting Two Atoms with Two-Mode Vacuum Field in a Damping Jaynes-Cummings Model[J].Journal of Inner Mongolia Normal University(Natural Science Edition),2015,44(3):352-358.)
[12]CHENG Jing,CHEN Xi,SHAN Chuanjia.Entanglement Evolution of Jaynes-Cummings Model in Resonance Case and Non-resonance Case[J].Int J Theor Phys,2018,57(6):1823-1828.
[13]XU Kai,HAN Wei,ZHANG Yingjie,et al.Non-Markovian Speedup Dynamics Control of the Damped JaynesCummings Model with Detuning[J].Chin Phys B,2018,27(1):010302-1-010302-6.
[14]丛红璐,任学藻,廖旭.非旋波近似下双光子Jaynes-Cummings模型的量子特性[J].光学学报,2015,35(7):0727002-1-0727002-7.(CONG Honglu,REN Xuezao,LIAO Xu.Quantum Properties of Two-Photon Jaynes-Cummings Model without Rotating Wave Approximation[J].Acta Optica Sinica,2015,35(7):0727002-1-0727002-7.)
[15]王菊霞.二能级原子与多模光场简并多光子共振相互作用系统中量子保真度的演化特性[J].物理学报,2014,63(18):184203-1-184203-8.(WANG Juxia.Evolution of the Quantum Fidelity in a System of Multimode Light Field Interacting Resonantly with a Two-Level Atom through Defenerate Multi-photon Process[J].Acta Phys Sin,2014,63(18):184203-1-184203-8.)
[16]刘王云,毕思文,豆西博.囚禁离子非线性Jaynes-Cummings模型量子场熵演化特性[J].物理学报,2010,59(3):1780-1785.(LIU Wangyun,BI Siwen,DOU Xibo.Evolution Properties of the Field Quantum Entropy in the Nonlinear Jaynes-Cummings Model of a Trapped Ion[J].Acta Phys Sin,2010,59(3):1780-1785.)
[17]刘晓静,刘继平,张晓茹,等.用多个光子晶体实现量子纠缠态的稳定性[J].吉林大学学报(理学版),2018,56(5):1224-1228.(LIU Xiaojing,LIU Jiping,ZHANG Xiaoru,et al.Stability of Quantum Entangled States with Multiple Photonic Crystals[J].Journal of Jilin University(Science Edition),2018,56(5):1224-1228.)