多粒子态及量子热纠缠信道中的隐形传态
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摘要
本论文主要讨论了用幺正变换和非最大纠缠信道实现量子隐形传态,分别用N对二粒子非最大纠缠态和一维海森堡链的热混合态作为量子信道实现纠缠传态,并讨论了不均匀磁场和温度对隐形传态的影响。
所谓量子隐形传态就是指:将甲地的某个粒子的未知量子态ψ传送到乙地的另一个粒子上,使得这个粒子处在ψ态上,而原来的未知粒子仍然留在原处。因为量子力学的不确定性原理,我们不能精确地将原量子态的所有信息全部提取出来,所以就将原来量子态的所有信息分为经典信息和量子信息两部分,它们分别由经典通道和量子通道传送到乙地。根据这些信息,在乙地构造出原量子态的全貌。
本文提出使用纠缠交换的方法,采用的是N对二粒子非最大纠缠的态作为量子通道来传输N粒子的GHZ态和W纠缠态的方案,比以往文献更具有一般意义。传输过程中,发送者对自己所拥有的粒子态进行Bell基测量(这样,原来的纠缠消失,产生新的纠缠,这就是所谓的纠缠交换。),并将测量结果通过经典通道通知接收者,接收者根据所获取的信息对她的粒子实行相应的幺正变换以恢复最初待传输的粒子态。从而,成功实现该隐形传输。与以前不同的是,本文只需采用一个共同的幺正矩阵来提取系数,实验上实现起来更加容易。
在量子通讯的实验中,由于外界环境的影响,我们很难得到最大的纠缠纯态。量子信道可能以混合纠缠态的形式出现。而固体材料中的热平衡态就是一种重要的混合纠缠态。本文还利用了两个独立的外加不均匀磁场的一维海森堡链的热纠缠态作为量子信道,实现了两粒子纠缠态的远程传送,分析了外界温度和磁场对纠缠和传输保真度的影响。我们发现纠缠会随温度的增高而降低,而当温度很低,外加反方向的磁场时,传输保真度大于经典通道的传输极限值2/3。
This thesis discusses the quantum teleportation with unitary variables and a non-maximally-entangled quantum channel. N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ state and W state via entanglement swapping.
The quantum teleportation means that when one teleports the unknown quantum stateψof a particle at place A to another one at place B, enable another particle to be the quantum stateψand the original particle remains at the primary place. Due to the uncertain principal of quantum mechanics, one can’t extract all information from the original quantum state exactly. Therefore, one divides all information of the original quantum state into two parts: general information and quantum information. A classical channel informs general information and quantum information is informed by quantum channel. According to these messages, one can configure all information of the original quantum state at place B.
In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ and W state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice’s different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ and W state are proposed.
In the experience of quantum communication, maximally entangled pure states are difficult to prepare due to the effects of environment. Therefore, a quantum channel is always represented by mixed states. The thermal equilibrium state in solid state materials is one essential mixed entangled state. In this dissertation, a two-particle entangled state can be teleported through the channel of thermal mixed states in two independent 1D Heisenberg chains. We study the effects of the non-uniform external magnetic field B and temperature T on the entanglement and fidelity. We found that the entanglement will decrease with the increasing of the temperature T. And when B1 and B 2 have different directions, the entanglement teleportation is better than the classical teleportation under low temperature. Because at that case the average fidelity is always greater than 2/3.
所谓量子隐形传态就是指:将甲地的某个粒子的未知量子态ψ传送到乙地的另一个粒子上,使得这个粒子处在ψ态上,而原来的未知粒子仍然留在原处。因为量子力学的不确定性原理,我们不能精确地将原量子态的所有信息全部提取出来,所以就将原来量子态的所有信息分为经典信息和量子信息两部分,它们分别由经典通道和量子通道传送到乙地。根据这些信息,在乙地构造出原量子态的全貌。
本文提出使用纠缠交换的方法,采用的是N对二粒子非最大纠缠的态作为量子通道来传输N粒子的GHZ态和W纠缠态的方案,比以往文献更具有一般意义。传输过程中,发送者对自己所拥有的粒子态进行Bell基测量(这样,原来的纠缠消失,产生新的纠缠,这就是所谓的纠缠交换。),并将测量结果通过经典通道通知接收者,接收者根据所获取的信息对她的粒子实行相应的幺正变换以恢复最初待传输的粒子态。从而,成功实现该隐形传输。与以前不同的是,本文只需采用一个共同的幺正矩阵来提取系数,实验上实现起来更加容易。
在量子通讯的实验中,由于外界环境的影响,我们很难得到最大的纠缠纯态。量子信道可能以混合纠缠态的形式出现。而固体材料中的热平衡态就是一种重要的混合纠缠态。本文还利用了两个独立的外加不均匀磁场的一维海森堡链的热纠缠态作为量子信道,实现了两粒子纠缠态的远程传送,分析了外界温度和磁场对纠缠和传输保真度的影响。我们发现纠缠会随温度的增高而降低,而当温度很低,外加反方向的磁场时,传输保真度大于经典通道的传输极限值2/3。
This thesis discusses the quantum teleportation with unitary variables and a non-maximally-entangled quantum channel. N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ state and W state via entanglement swapping.
The quantum teleportation means that when one teleports the unknown quantum stateψof a particle at place A to another one at place B, enable another particle to be the quantum stateψand the original particle remains at the primary place. Due to the uncertain principal of quantum mechanics, one can’t extract all information from the original quantum state exactly. Therefore, one divides all information of the original quantum state into two parts: general information and quantum information. A classical channel informs general information and quantum information is informed by quantum channel. According to these messages, one can configure all information of the original quantum state at place B.
In this scheme, N non-maximally entangled particle pairs are used as quantum channel to teleport an unknown N-particle entangled GHZ and W state via entanglement swapping. In order to realize this teleportation, the sender Alice operates Bell-state measurement on particles belonging to herself. Then she informs the results to the receiver Bob through classical communication. According to the results, Bob operates corresponding transformation to reconstruct the initial state. The advantage of this scheme is that it needs only one common unitary matrix for Alice’s different results, which has a more general meaning. As a special case, teleporting an unknown three-particle entangled GHZ and W state are proposed.
In the experience of quantum communication, maximally entangled pure states are difficult to prepare due to the effects of environment. Therefore, a quantum channel is always represented by mixed states. The thermal equilibrium state in solid state materials is one essential mixed entangled state. In this dissertation, a two-particle entangled state can be teleported through the channel of thermal mixed states in two independent 1D Heisenberg chains. We study the effects of the non-uniform external magnetic field B and temperature T on the entanglement and fidelity. We found that the entanglement will decrease with the increasing of the temperature T. And when B1 and B 2 have different directions, the entanglement teleportation is better than the classical teleportation under low temperature. Because at that case the average fidelity is always greater than 2/3.
引文
[1]Bennett C.H., Crepeau C., Jozsa R., Peres A., Wootters W.K., Teleporting an unknown quantum state via dual classical and Einstein- Podolsky-Rosen channels. [J]. Phys. Rev. Lett. 1993,70(13):1895-1899
[2] Lu H., Guo G.C., Teleportation of a two-particle entangled state via entanglement swapping. [J]. Phys. Lett. A. 2000, 276:209-212
[3] Gu Y.J., Zheng Y.Z., Guo G.C. Probablistic teleportation of an arbitrary two-particle entangled state. [J]. Chin. Phys. Lett. 2001, 18 (12): 1543- 1545.
[4] Shi B.S., Jiang Y.K., Guo G.C. Probablistic teleportation of an arbitrary two-particle entangled state. [J]. Phys. Lett. A. 2000,268:161-164.
[5] Fang J.X., Ling Y.S., Zhu S.Q., Chen X.F.,Probablistic teleportation of a three-particle state via three pairs of entangled particles. [J]. Phys. Rev. A. 2003,67(1):014305-1-014305-4.
[6] Gao T., Wang Z.X., Yan F.L. Quantum logic network for probabilistic teleportation of two-particle state in a general form. Chin. Phys. Lett. 2003,12:2094.
[7] Lu H. Probablistic teleportation of a three-particle state via entanglement swapping. [J]. Chin. Phys. Lett. 2001,18(8):1004-1006.
[8] Chen L.B. Teleportation of an arbitrary three-particle state. [J]. Chin.Phys. 2002,11(10):0999-1003.
[9] Dai H.Y.,Li C.Z., Chen P.X. probabilistic teleportation of the three- particle entangled state by the partial three-particle entangled state and the three-particle entangled W state. [J]. Chin. Phys. Lett. 2003, 20(8): 1196- 1198.
[10] 席拥军,方建兴,朱士群,王一奇,“N粒子量子纠缠态的隐形传送”[J]量子光学学报,第 11 卷第 1 期,2005(25-28)。
[11] L. Davidovich et al. Teleportation of an atomic state between two cavities using nonlocal microwave fields. Phys. Rev . A , 1994,50,R895.
[12] G. Brassard , A. Mann, Measurement of the Bell operator and quantum teleportation.[J]. Phys. Rev. A. 1995,51,R1727.
[13] L. Vaidman , Teleportation of quantum states. [J]. Phys. Rev . A , 1994, 49 ,1473.
[14] A. Barenco et al. ,. Conditional quantum dynamics and logic gates.[J]. Phys. Rev . Lett. 1995, 74,4083.
[15] J . I. Cirac , A. S. Parkins , Schemes for atomic-state teleportation. [J]. Phys. Rev . A , 1994, 50 ,R4441.
[16] M. H. Y. Moussa , Teleportation of a cavity-radition-field state: An alternative scheme. [J]. Phys. Rev. A , 1996, 54 ,4661.
[17] S. B. Zheng , G. C. Guo. Teleportation of an unknown atomic state through the Raman atom-cavity-field interaction.[J].Phys. Lett . A , 1997, 232 ,171.
[18] S. B. Zheng , G. C. Guo. Teleportation of superpositions of macroscopic states of a cavity field. [J]. Phy . Lett . A , 1997, 236 ,180.
[19] Bouwmeester D, Pan J W, Mattle K, et al. Nature, 1997, 390(6660):575-579.
[20] Boschi D, Branca S, De Martini F, et al. Phys Rev Lett, 1998, 80(6 ):1121-1125.
[21] Furusawa A, Sorensen J L, Braunstein S L, et al. Science, 1998, 282(5389):706-709.
[22]Nielsen M A, Knill E, Laflamme R. Nature, 1998, 396(6706):52-55.
[23] Kim Y H, Kulik S P, Shih Y H. Phys Rev Lett, 2001, 86(7):1370-1373.
[24] Lombardi E, Sciarrino F, Popescu S, et al. Phys Rev Lett, 2002, 88(7):070402.
[1] C.H. Bennett, et al., Teleportation an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 (1993) 1895.
[2] A. Ekert,Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67 (1991) 661.
[3] M.A. Neilsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, New York, 2000, pp. 171-211.
[4] Zhan You-Bang, Teleportation of N-particle entangled W state via entanglement swapping, Chin. Phys. Vol 13 No 11, November 2004.
[5] Xi Yong-jun, Fang Jian-xing, Zhu Shi-qun and Wang Yi-qi. Teleportation of n-particle entangled state . Acta Sinica Quantum Optica 11(1) 2005 25-28.
[6] Fang Jian-xing, Zhu Shi-qun, Zhang Rong, and Chen Xian-feng. Probabilistic teleportation of a three-particle state. Commun. Theor. Phys. 40 (2003). pp.519-522.
[7] Jianxing Fang, Yinshen Lin, Shiqun Zhu, and Xianfeng Chen. Probabilistic teleportation of a three-particle state via three pairs of entangled particles. Phys. Rev. A 67, (2003) 014305.
[8] Hong Lu, Guang-can Guo. Teleportation of a two-particle entangled state via entanglement swapping. Phys. Lett. A 276 (2000) 209-212.
[9] Chen Li-bing. Teleportation of an arbitrary three-particle state. Chin. Phys., 2002,11(10):0999-1003
[10] Gu Y J, Zheng Y H, Guo G C, Probabilistic teleportation of an arbitrary two-particle state [J]. Chin. Phys. Lett. 2001,18 (12): 1543-1545.
[11]Yang C P, Guo G C, A proposal of teleportation for three-particle entangled state via entanglement swapping [J]. Chin. Phys. Lett. 1999,16 (9): 628-629.
[12]Lu H. Probabilistic teleportation of the three-particle entangled state via entanglement swapping . [J] Chin. Phys. Lett. , 2001,18 (8):1004-1006
[13] Shi Baosen, Jiang Yunkun, and Guo Guangcan. Probabilistic teleportation of two-particle entangled state. Phys. Lett. A. 268 (2000) 161-164.
[14]Dai Hongyi, Li Chengzu, and Chen Pingxing. Probabilistic teleportation of an arbitrary three-particle state via a partial entangled four-particle state and a partial entangled pair. Chin. Phys. 12 (2003) 1354.
[15]Gao Ting. Quantum logic networks for probabilistic and controlled teleportation of unknown quantum states. Quant-ph. (2003) 01312021.
[16]Cao Zhuoliang, Yang Ming. Probabilistic teleportation of unknown atomic state using W class states. Physica A. 337 (2004) 132-140.
[17] Boschi D et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80 (1998) 1121.
[18]Davidovich L, Zagury N, Brunee M et al. Teleportation of an atomic state between two cavities using nonlocal microwave fields. Phys. Rev. A. 50 (1994) R895.
[19] Cirac J I, and Parkins A S. Schemes for atomic-state teleportation. Phys. Rev. A. 50 (1994) R4441.
[20]Anders Karlsson, and Mohamed Bourennane. Quantum teleportation using three-particle entanglement. Phys. Rev. A. 58. (1998) 4394.
[1] C.H.Benett, G.Brassard, C.Crepeau, R.Jozsa, A.Peres, W.K.Wootters, Phys. Rev. Lett. 70 (1993) 1895.
[2] Jianxing Fang, Yinsheng Lin, Shiqun Zhu, and Xianfeng Chen. Phys. Rev. A 67 (2003) 014305.
[3] Anders. Karlsson and Mohamed Bourennane. Phys. Rev. A 58 (1998) 4394.
[4] Hong Lu, Guangcan Guo. Phys. Lett. A 276 (2000) 209-212.
[5] M.C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, (2001) 017901.
[6] X. Wang. Phys. Rev. A 66, (2002) 034302.
[7] X. Wang, Phys. Rev. A 64, (2001) 012313.
[8] Ye Yeo. Phys. Rev. A 66, (2002) 062312.
[9] Ye Yeo. Phys. Lett. A 309, (2003) 215.
[10] Xiang Hao, Shiqun Zhu. Phys. Lett. A. 338 (2005) 175-181.
[11] Zi Chong Kao, Jezreel Ng. And Ye Yeo. Phys.Rev. A 72 (2005) 062302.
[12] Yang Sun, Yuguang Chen, and Hong Chen. Phys. Rev. A 68 (2003) 044301.
[13] Guo-Feng Zhang and Shu-Shen Li. Phys. Rev. A 72, (2005) 034302.
[14] A. Peres, Phys. Rev. Lett. 77, (1996) 1413.
[15] J. Lee, M.S.Kim, Phys. Rev. Lett. 84, (2000) 4236.
[2] Lu H., Guo G.C., Teleportation of a two-particle entangled state via entanglement swapping. [J]. Phys. Lett. A. 2000, 276:209-212
[3] Gu Y.J., Zheng Y.Z., Guo G.C. Probablistic teleportation of an arbitrary two-particle entangled state. [J]. Chin. Phys. Lett. 2001, 18 (12): 1543- 1545.
[4] Shi B.S., Jiang Y.K., Guo G.C. Probablistic teleportation of an arbitrary two-particle entangled state. [J]. Phys. Lett. A. 2000,268:161-164.
[5] Fang J.X., Ling Y.S., Zhu S.Q., Chen X.F.,Probablistic teleportation of a three-particle state via three pairs of entangled particles. [J]. Phys. Rev. A. 2003,67(1):014305-1-014305-4.
[6] Gao T., Wang Z.X., Yan F.L. Quantum logic network for probabilistic teleportation of two-particle state in a general form. Chin. Phys. Lett. 2003,12:2094.
[7] Lu H. Probablistic teleportation of a three-particle state via entanglement swapping. [J]. Chin. Phys. Lett. 2001,18(8):1004-1006.
[8] Chen L.B. Teleportation of an arbitrary three-particle state. [J]. Chin.Phys. 2002,11(10):0999-1003.
[9] Dai H.Y.,Li C.Z., Chen P.X. probabilistic teleportation of the three- particle entangled state by the partial three-particle entangled state and the three-particle entangled W state. [J]. Chin. Phys. Lett. 2003, 20(8): 1196- 1198.
[10] 席拥军,方建兴,朱士群,王一奇,“N粒子量子纠缠态的隐形传送”[J]量子光学学报,第 11 卷第 1 期,2005(25-28)。
[11] L. Davidovich et al. Teleportation of an atomic state between two cavities using nonlocal microwave fields. Phys. Rev . A , 1994,50,R895.
[12] G. Brassard , A. Mann, Measurement of the Bell operator and quantum teleportation.[J]. Phys. Rev. A. 1995,51,R1727.
[13] L. Vaidman , Teleportation of quantum states. [J]. Phys. Rev . A , 1994, 49 ,1473.
[14] A. Barenco et al. ,. Conditional quantum dynamics and logic gates.[J]. Phys. Rev . Lett. 1995, 74,4083.
[15] J . I. Cirac , A. S. Parkins , Schemes for atomic-state teleportation. [J]. Phys. Rev . A , 1994, 50 ,R4441.
[16] M. H. Y. Moussa , Teleportation of a cavity-radition-field state: An alternative scheme. [J]. Phys. Rev. A , 1996, 54 ,4661.
[17] S. B. Zheng , G. C. Guo. Teleportation of an unknown atomic state through the Raman atom-cavity-field interaction.[J].Phys. Lett . A , 1997, 232 ,171.
[18] S. B. Zheng , G. C. Guo. Teleportation of superpositions of macroscopic states of a cavity field. [J]. Phy . Lett . A , 1997, 236 ,180.
[19] Bouwmeester D, Pan J W, Mattle K, et al. Nature, 1997, 390(6660):575-579.
[20] Boschi D, Branca S, De Martini F, et al. Phys Rev Lett, 1998, 80(6 ):1121-1125.
[21] Furusawa A, Sorensen J L, Braunstein S L, et al. Science, 1998, 282(5389):706-709.
[22]Nielsen M A, Knill E, Laflamme R. Nature, 1998, 396(6706):52-55.
[23] Kim Y H, Kulik S P, Shih Y H. Phys Rev Lett, 2001, 86(7):1370-1373.
[24] Lombardi E, Sciarrino F, Popescu S, et al. Phys Rev Lett, 2002, 88(7):070402.
[1] C.H. Bennett, et al., Teleportation an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels, Phys. Rev. Lett. 70 (1993) 1895.
[2] A. Ekert,Quantum cryptography based on Bell’s theorem, Phys. Rev. Lett. 67 (1991) 661.
[3] M.A. Neilsen, I.L. Chuang, Quantum Computation and Quantum Information, Cambridge University Press, New York, 2000, pp. 171-211.
[4] Zhan You-Bang, Teleportation of N-particle entangled W state via entanglement swapping, Chin. Phys. Vol 13 No 11, November 2004.
[5] Xi Yong-jun, Fang Jian-xing, Zhu Shi-qun and Wang Yi-qi. Teleportation of n-particle entangled state . Acta Sinica Quantum Optica 11(1) 2005 25-28.
[6] Fang Jian-xing, Zhu Shi-qun, Zhang Rong, and Chen Xian-feng. Probabilistic teleportation of a three-particle state. Commun. Theor. Phys. 40 (2003). pp.519-522.
[7] Jianxing Fang, Yinshen Lin, Shiqun Zhu, and Xianfeng Chen. Probabilistic teleportation of a three-particle state via three pairs of entangled particles. Phys. Rev. A 67, (2003) 014305.
[8] Hong Lu, Guang-can Guo. Teleportation of a two-particle entangled state via entanglement swapping. Phys. Lett. A 276 (2000) 209-212.
[9] Chen Li-bing. Teleportation of an arbitrary three-particle state. Chin. Phys., 2002,11(10):0999-1003
[10] Gu Y J, Zheng Y H, Guo G C, Probabilistic teleportation of an arbitrary two-particle state [J]. Chin. Phys. Lett. 2001,18 (12): 1543-1545.
[11]Yang C P, Guo G C, A proposal of teleportation for three-particle entangled state via entanglement swapping [J]. Chin. Phys. Lett. 1999,16 (9): 628-629.
[12]Lu H. Probabilistic teleportation of the three-particle entangled state via entanglement swapping . [J] Chin. Phys. Lett. , 2001,18 (8):1004-1006
[13] Shi Baosen, Jiang Yunkun, and Guo Guangcan. Probabilistic teleportation of two-particle entangled state. Phys. Lett. A. 268 (2000) 161-164.
[14]Dai Hongyi, Li Chengzu, and Chen Pingxing. Probabilistic teleportation of an arbitrary three-particle state via a partial entangled four-particle state and a partial entangled pair. Chin. Phys. 12 (2003) 1354.
[15]Gao Ting. Quantum logic networks for probabilistic and controlled teleportation of unknown quantum states. Quant-ph. (2003) 01312021.
[16]Cao Zhuoliang, Yang Ming. Probabilistic teleportation of unknown atomic state using W class states. Physica A. 337 (2004) 132-140.
[17] Boschi D et al. Experimental realization of teleporting an unknown pure quantum state via dual classical and Einstein-Podolsky-Rosen channels. Phys. Rev. Lett. 80 (1998) 1121.
[18]Davidovich L, Zagury N, Brunee M et al. Teleportation of an atomic state between two cavities using nonlocal microwave fields. Phys. Rev. A. 50 (1994) R895.
[19] Cirac J I, and Parkins A S. Schemes for atomic-state teleportation. Phys. Rev. A. 50 (1994) R4441.
[20]Anders Karlsson, and Mohamed Bourennane. Quantum teleportation using three-particle entanglement. Phys. Rev. A. 58. (1998) 4394.
[1] C.H.Benett, G.Brassard, C.Crepeau, R.Jozsa, A.Peres, W.K.Wootters, Phys. Rev. Lett. 70 (1993) 1895.
[2] Jianxing Fang, Yinsheng Lin, Shiqun Zhu, and Xianfeng Chen. Phys. Rev. A 67 (2003) 014305.
[3] Anders. Karlsson and Mohamed Bourennane. Phys. Rev. A 58 (1998) 4394.
[4] Hong Lu, Guangcan Guo. Phys. Lett. A 276 (2000) 209-212.
[5] M.C. Arnesen, S. Bose, and V. Vedral, Phys. Rev. Lett. 87, (2001) 017901.
[6] X. Wang. Phys. Rev. A 66, (2002) 034302.
[7] X. Wang, Phys. Rev. A 64, (2001) 012313.
[8] Ye Yeo. Phys. Rev. A 66, (2002) 062312.
[9] Ye Yeo. Phys. Lett. A 309, (2003) 215.
[10] Xiang Hao, Shiqun Zhu. Phys. Lett. A. 338 (2005) 175-181.
[11] Zi Chong Kao, Jezreel Ng. And Ye Yeo. Phys.Rev. A 72 (2005) 062302.
[12] Yang Sun, Yuguang Chen, and Hong Chen. Phys. Rev. A 68 (2003) 044301.
[13] Guo-Feng Zhang and Shu-Shen Li. Phys. Rev. A 72, (2005) 034302.
[14] A. Peres, Phys. Rev. Lett. 77, (1996) 1413.
[15] J. Lee, M.S.Kim, Phys. Rev. Lett. 84, (2000) 4236.