非旋波近似下Tavis-Cummings模型的纠缠特性
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摘要
采用相干态正交化法研究了非旋波近似下Tavis-Cummings(TC)模型中两非全同量子比特间的纠缠动力学问题,分析了同一耦合强度下不同跃迁频率的量子比特和光场对两量子比特间纠缠演化的影响。研究结果表明,在弱耦合情况下,当其中一个量子比特的跃迁频率与光场频率相同而另一个量子比特的跃迁频率与光场频率对称失谐时,量子比特间的纠缠完全相同;当耦合强度较大时,两对称失谐情况下的量子比特间的纠缠演化由于非旋波项的作用不再完全相同。
The entanglement dynamics problem between two non-identical qubits in the Tavis-Cummings model without rotating wave approximation is discussed by the extended coherent state(ECS)method.The effects of the qubits with different transition frequencies but with a same coupling strength and the optical fields on the entanglement evolution between two qubits are investigated.The research results show that,in the case of the weak coupling,the entanglement evolution between two qubits is the same when the transition frequency of one qubit is identical to the optical field frequency but the transition frequency of another qubit is symmetric detuning from the optical field frequency.In contrast,in the case of the strong coupling,the entanglement evolution between two qubits is no longer same under the cases of two symmetric detuning due to the effect of the non-rotating wave term.
The entanglement dynamics problem between two non-identical qubits in the Tavis-Cummings model without rotating wave approximation is discussed by the extended coherent state(ECS)method.The effects of the qubits with different transition frequencies but with a same coupling strength and the optical fields on the entanglement evolution between two qubits are investigated.The research results show that,in the case of the weak coupling,the entanglement evolution between two qubits is the same when the transition frequency of one qubit is identical to the optical field frequency but the transition frequency of another qubit is symmetric detuning from the optical field frequency.In contrast,in the case of the strong coupling,the entanglement evolution between two qubits is no longer same under the cases of two symmetric detuning due to the effect of the non-rotating wave term.
引文
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[2] Wei J H,Shi L,Ma L H,et al.Remote preparation of an arbitrary multi-qubit state via two-qubit entangled states[J].Quantum Information Processing,2017,16(10):260.
[3] Wallraff A,Schuster D I,Blais A,et al.Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics[J].Nature,2004,431(7005):162-167.
[4] Chiorescu I,Bertet P,Semba K,et al.Coherent dynamics of a flux qubit coupled to a harmonic oscillator[J].Nature,2004,431(7005):159-162.
[5] Deppe F,Mariantoni M,Menzel E P,et al.Twophoton probe of the Jaynes-Cummings model and controlled symmetry breaking in circuit QED[J].Nature Physics,2008,4(9):686-691.
[6] Niemczyk T,Deppe F,Huebl H,et al.Circuit quantum electrodynamics in the ultrastrong-coupling regime[J].Nature Physics,2010,6(10):772-776.
[7] Xia J P,Ren X Z,Cong H L,et al.Quantum evolution of entanglement property in two-qubit and oscillator coupling system[J].Acta Physica Sinica,2012,61(1):014208.夏建平,任学藻,丛红璐,等.两量子比特与谐振子相耦合系统中的量子纠缠演化特性[J].物理学报,2012,61(1):014208.
[8] Cong H L,Ren X Z,Liao X.Quantum properties of two-photon Jaynes-Cummings model without rotating wave approximation[J].Acta Optica Sinica,2015,35(7):0727002.丛红璐,任学藻,廖旭.非旋波近似下双光子JaynesCummings模型的量子特性[J].光学学报,2015,35(7):0727002.
[9] Cong H L,Ren X Z.Exact solutions of energy spectrum and quantum entanglement in Tavis-Cummings model[J].Laser&Optoelectronics Progress,2017,54(9):092701.丛红璐,任学藻.Tavis-Cummings模型的能谱和量子纠缠的精确解[J].激光与光电子学进展,2017,54(9):092701.
[10] Mao L J,Huai S N,Zhang Y B.Tavis-Cummings model beyond the rotating wave approximation:Inhomogeneous coupling[EB/OL].(2014-03-24)[2018-03-29].https://arxiv.org/abs/1403.5893.
[11] Mao L J.Analytical solutions and dynamics of the Nqubit Rabi model[D].Taiyuan:Shanxi University,2016:13-18.毛丽君.多量子比特Rabi模型的解析解及动力学[D].太原:山西大学,2016:13-18.
[12] He S,Zhao Y,Chen Q H.Absence of collapse in quantum Rabi oscillations[J].Physical Review A,2014,90(5):053848.
[13] Xu Y H, Ren X Z, Liu X Y.Entanglement characteristics of quantum Rabi model with two arbitrary qubits[J].Acta Optica Sinica,2018,38(1):0127001.徐玉虎,任学藻,刘雪莹.两任意量子比特Rabi模型的纠缠演化特性[J].光学学报,2018,38(1):0127001.
[14] Wang K L,Chen Q H,Liu T.Extended coherent states in multibody physics and its application[M].Hefei:Press of University of Science and Technology of China,2012:38-46.汪克林,陈庆虎,刘涛.多体物理中的相干态正交化方法及其应用[M].合肥:中国科学技术大学出版社,2012:38-46.
[15] Wootters W K.Entanglement of formation of an arbitrary state of two qubits[J].Physical Review Letters,1998,80(10):2245-2248.
[16] Yin M.The entanglement of two atoms in a TavisCummings model driven by an external field[D].Wuhan:Huazhong University of Science and Technology of China,2007.尹淼.外场驱动下Tavis-Cummings模型中两原子的纠缠[D].武汉:华中科技大学,2007.
[17] Fujii K,Higashida K,Kato R,et al.Explicit form of solution of two atoms Tavis-Cummings model[J].Quantum Physics,2004,56(1):51-60.
[18] Wang C,Chen Q H.Quantum discord dynamics of two qubits in single-mode cavities[J]. Chinese Physics B,2013,22(4):040304.
[19] Zhai C H,Chu W J,Zhang L H,et al.Direct measurement of concurrence for two-qubit pure states[J].Acta Optica Sinica, 2016, 36(3):0327002.翟晨慧,储文静,章礼华,等.两比特纯态纠缠的直接测量[J].光学学报,2016,36(3):0327002.
[20] Liang H Q,Liu J M.Remote state preparation with bipartite entangled states in noisy environments[J].Acta Physica Sinica,2009,58(6):3692-3698.梁华秋,刘金明.噪声环境下基于两体纠缠态的远程态制备[J].物理学报,2009,58(6):3692-3698.
[21] SillanpaaM A,Park J I,Simmonds R W.Coherent quantum state storage and transfer between two phase qubits via a resonant cavity[J].Nature,2007,449(7161):438-442.
[22] Sun Y,Zhao S H,Dong C.Measurement device independent quantum key distribution network based on quantum memory and entangled photon sources[J].Acta Optica Sinica,2016,36(3):0327001.孙颖,赵尚弘,东晨.基于量子存储和纠缠光源的测量设备无关量子密钥分配网络[J].光学学报,2016,36(3):0327001.