双模压缩真空态光场与纠缠态原子相互作用系统中的纠缠特性
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摘要
纠缠态是量子光学中十分重要的研究课题,近年来一直引起人们的极大兴趣。双模压缩真空态具有良好的模间纠缠性质,理论上可以作为量子通讯的信息载体。本文利用描述原子与光场相互作用的典型理论模型Jaynes-Cummings模型,研究了双模压缩真空光场与纠缠态原子的作用,分别讨论了腔外原子旋转角θ和两原子态中相位角(?)对系统纠缠性质的影响。
研究表明,旋转角θ和相位角(?)不破坏场与原子和光场两模之间纠缠的周期性演化规律。当相位角(?)一定时,腔外原子旋转角θ对场与原子纠缠以及场的模间纠缠有着重要影响。随着腔外原子旋转角θ的增大,场与原子纠缠度最大值减小,场的模间纠缠度最小值增大。当相位角(?) =0时,选择适当的旋转角θ,可以使场与原子处于退纠缠状态,模间纠缠度趋于定值。当腔外原子旋转角θ≠nπ/ 2时,相位角(?)对场与原子纠缠以及场的模间纠缠有着很大影响。随着相位角(?)的增大,场与原子纠缠度最大值增大,光场的模间纠缠度最小值减小。而且,当场与原子纠缠度最大值越小(即模间纠缠度最小值越大)时,这种影响越显著。
Entangled states are very important topics in quantum optics, which attract huge interest nowadays. Light field at the two-mode squeezing vacuum state has the dominant property in the entanglement between the two modes. Theoretically, such light field can be used as information carrier in quantum teleportation. In this paper, by using the J-C Model, we study the interaction of entangled atoms with the light field at the two-mode squeezing vacuum state, and discuss the entangled properties of the system influenced by the rotation angleθoutside the cavity and the phase(?) in the two-atom state.
The rotation angleθand the phase(?) do not destroy the periodicity of the entanglement between the atom and the cavity as well as the two modes of the cavity. When the phase(?) is certain, the rotation angleθplays an important role in the entanglement between the atom and the cavity as well as the two modes. With the increase of the rotation angleθ, the maximum of the entanglement between atom and cavity reduces while the minimum of the entanglement between the two modes of the cavity increases. When (?) =0, by choosing the proper rotation angleθ, the atom and the cavity can be disentangled and the entanglement between the two modes of the cavity becomes a constant. When the rotation angle isθ≠nπ/ 2, the phase (?) has great influence on the entanglement of the atom and the cavity as well as the two modes. With the increase of the rotation angleθ, the maximum of the entanglement between the atom and the cavity increases while the minimum of the entanglement between the two modes of the cavity decreases. When the maximum of the entanglement between the atom and the cavity becomes smaller (or the minimum of the entanglement between the two modes becomes larger), the influence is enhanced.
研究表明,旋转角θ和相位角(?)不破坏场与原子和光场两模之间纠缠的周期性演化规律。当相位角(?)一定时,腔外原子旋转角θ对场与原子纠缠以及场的模间纠缠有着重要影响。随着腔外原子旋转角θ的增大,场与原子纠缠度最大值减小,场的模间纠缠度最小值增大。当相位角(?) =0时,选择适当的旋转角θ,可以使场与原子处于退纠缠状态,模间纠缠度趋于定值。当腔外原子旋转角θ≠nπ/ 2时,相位角(?)对场与原子纠缠以及场的模间纠缠有着很大影响。随着相位角(?)的增大,场与原子纠缠度最大值增大,光场的模间纠缠度最小值减小。而且,当场与原子纠缠度最大值越小(即模间纠缠度最小值越大)时,这种影响越显著。
Entangled states are very important topics in quantum optics, which attract huge interest nowadays. Light field at the two-mode squeezing vacuum state has the dominant property in the entanglement between the two modes. Theoretically, such light field can be used as information carrier in quantum teleportation. In this paper, by using the J-C Model, we study the interaction of entangled atoms with the light field at the two-mode squeezing vacuum state, and discuss the entangled properties of the system influenced by the rotation angleθoutside the cavity and the phase(?) in the two-atom state.
The rotation angleθand the phase(?) do not destroy the periodicity of the entanglement between the atom and the cavity as well as the two modes of the cavity. When the phase(?) is certain, the rotation angleθplays an important role in the entanglement between the atom and the cavity as well as the two modes. With the increase of the rotation angleθ, the maximum of the entanglement between atom and cavity reduces while the minimum of the entanglement between the two modes of the cavity increases. When (?) =0, by choosing the proper rotation angleθ, the atom and the cavity can be disentangled and the entanglement between the two modes of the cavity becomes a constant. When the rotation angle isθ≠nπ/ 2, the phase (?) has great influence on the entanglement of the atom and the cavity as well as the two modes. With the increase of the rotation angleθ, the maximum of the entanglement between the atom and the cavity increases while the minimum of the entanglement between the two modes of the cavity decreases. When the maximum of the entanglement between the atom and the cavity becomes smaller (or the minimum of the entanglement between the two modes becomes larger), the influence is enhanced.
引文
[1] 彭金生,李高翔,近代量子光学导论,北京:科学出版社, 1996.92~97,165~193.
[2] Phoenix S J D, Knight P L , Fluctuations and Entropy in Models of Quantum Optical Resonance , Ann. Phys. , 1988 , 186 : 381
[3] 黄春佳,周明,厉江帆,贺慧勇,单模辐射场与耦合双原子相互作用系统中场熵的压缩特性 , 物理学报 , 2002 ,51(4) : 805
[4] 宋同强,利用双模压缩真空态实现量子态的远程传输,物理学报,2004 ,53(10):3358-3362
[5] E. Schr?dinger, Naturwissenschaften 1935, 23 807~812, 823~828, 844~849, Die gegenw?rtige Situation in der Quantenmechanik . 英译本见 J. A. Wheeler , W. Zurek 主编,Quantum Theory of Measurement, Princeton Univ. Press. , Princeton , N. J. 1983.
[6] J.I. Cirac, P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. , 74 (1995) 4091~4094
[7] A.K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett., 67 (1991) 661~663
[8] L. Davidovich, N. Zagury, M. Brune, J.M. Raimond, S. Haroche, Teleportation of an atomic state between two cavities using nonlocal microwave fields, Phys. Rev. A 50 (1994) R895~R898
[9] B. Schumacher, Sending entanglement through noisy quantum channels, Phys. Rev. A 54 (1996) 2614~2628
[10] V. Buzek, M. Hillery, Quantum copying: Beyond the no-cloning theorem, Phys. Rev. A 54 (1996) 1844~1852
[11] Yang C P, Guo G C, Controllable emission properties of an atom inside a cavity by manipulating the atom outside the cavity, Chin. Phys. Lett. , 1997,14(7);485
[12] Liu T K, Wang J S, Feng J, Zhan M S, Controlling dipole squeezing of two atoms inside a cavity via manipulating an atom outside the cavity, Chin. Phys. Soc. 2004 13 (4 ) 497
[13] E. T. Jaynes , F. W. Cummings , Proc IEEE , 1963 , 51 : 89
[14] R. R. Puri and G. S. Agarwal , Collapse and revival phenomena in the Jaynes-Cummings model with cavity damping ,Phys. Rev. A , 1986 ,33(5) : 3610~3613.
[15] Shor P W, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52 (1995) 2493~2496
[16] 王成志,方卯发,双模压缩真空态与原子相互作用中的量子纠缠和退相干 ,物理学报 ,2002 ,51(9) : 1989~1995.
[17] V. Vedral , M. B. Rippin and P. L. Knight , Selective Study of Fe Atoms at the Interfaces of an Fe/Ir(100) Superlattice by means of Diffraction Anoncalous Fine Structure , Phys. Rev. Lett. , 1997 , 78(12) : 2275~2279.
[18] Vedral V , Plenio M B , Entanglement measures and purification procedures , Phys. Rev. A , 1998 , 57(3) : 1619~1633.
[19] Vedral V , Plenio M B , Entanglement measures and purification procedures , Phys. Rev. A , 1998 , 57(3) : 1619~1633.
[20] E. Rains , Bound on distillable entanglement , Phys. Rev. A , 1999 , 60(1) : 179~184.
[2] Phoenix S J D, Knight P L , Fluctuations and Entropy in Models of Quantum Optical Resonance , Ann. Phys. , 1988 , 186 : 381
[3] 黄春佳,周明,厉江帆,贺慧勇,单模辐射场与耦合双原子相互作用系统中场熵的压缩特性 , 物理学报 , 2002 ,51(4) : 805
[4] 宋同强,利用双模压缩真空态实现量子态的远程传输,物理学报,2004 ,53(10):3358-3362
[5] E. Schr?dinger, Naturwissenschaften 1935, 23 807~812, 823~828, 844~849, Die gegenw?rtige Situation in der Quantenmechanik . 英译本见 J. A. Wheeler , W. Zurek 主编,Quantum Theory of Measurement, Princeton Univ. Press. , Princeton , N. J. 1983.
[6] J.I. Cirac, P. Zoller, Quantum Computations with Cold Trapped Ions, Phys. Rev. Lett. , 74 (1995) 4091~4094
[7] A.K. Ekert, Quantum cryptography based on Bell's theorem, Phys. Rev. Lett., 67 (1991) 661~663
[8] L. Davidovich, N. Zagury, M. Brune, J.M. Raimond, S. Haroche, Teleportation of an atomic state between two cavities using nonlocal microwave fields, Phys. Rev. A 50 (1994) R895~R898
[9] B. Schumacher, Sending entanglement through noisy quantum channels, Phys. Rev. A 54 (1996) 2614~2628
[10] V. Buzek, M. Hillery, Quantum copying: Beyond the no-cloning theorem, Phys. Rev. A 54 (1996) 1844~1852
[11] Yang C P, Guo G C, Controllable emission properties of an atom inside a cavity by manipulating the atom outside the cavity, Chin. Phys. Lett. , 1997,14(7);485
[12] Liu T K, Wang J S, Feng J, Zhan M S, Controlling dipole squeezing of two atoms inside a cavity via manipulating an atom outside the cavity, Chin. Phys. Soc. 2004 13 (4 ) 497
[13] E. T. Jaynes , F. W. Cummings , Proc IEEE , 1963 , 51 : 89
[14] R. R. Puri and G. S. Agarwal , Collapse and revival phenomena in the Jaynes-Cummings model with cavity damping ,Phys. Rev. A , 1986 ,33(5) : 3610~3613.
[15] Shor P W, Scheme for reducing decoherence in quantum computer memory, Phys. Rev. A 52 (1995) 2493~2496
[16] 王成志,方卯发,双模压缩真空态与原子相互作用中的量子纠缠和退相干 ,物理学报 ,2002 ,51(9) : 1989~1995.
[17] V. Vedral , M. B. Rippin and P. L. Knight , Selective Study of Fe Atoms at the Interfaces of an Fe/Ir(100) Superlattice by means of Diffraction Anoncalous Fine Structure , Phys. Rev. Lett. , 1997 , 78(12) : 2275~2279.
[18] Vedral V , Plenio M B , Entanglement measures and purification procedures , Phys. Rev. A , 1998 , 57(3) : 1619~1633.
[19] Vedral V , Plenio M B , Entanglement measures and purification procedures , Phys. Rev. A , 1998 , 57(3) : 1619~1633.
[20] E. Rains , Bound on distillable entanglement , Phys. Rev. A , 1999 , 60(1) : 179~184.