光场性质的研究与量子态的隐形传送
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摘要
量子光学是研究光场的相干性和量子统计特性以及光与物质相互作用的量子特征的学科。研究发现在光场与原子相互作用过程中，特别是非线性过程中，会出现某些经典场所不允许存在的量子效应，它们是光是量子场的本质反映，我们称之为非经典效应。现实验上已证实，量子光场主要存在三种非经典效应：光子反聚束、亚泊松分布和压缩态。这些效应不仅利于对光的本质进一步认识，而且在光学领域中有着重要的实际应用价值。比如：具有压缩效应的量子态，由于其某一分量的量子涨落小于相干态相应分量的量子涨落，使得它在光通讯等领域有着广阔的应用前景。所以研究光场的量子特性是量子光学的一个重要课题。
另外，在1994年之后兴起并在国际上蓬勃发展起来的新生学科——量子信息，是以量子态作为量子信息的载体，其对量子信息的处理实质上是对各种量子态的制备与操纵。在本文中，一方面我们研究光场的特性，其中包括相干光场与空间反演对称非线性介质相互作用后，介质对光场性质的影响(如压缩性质、分布特性和相干性)，以及压缩奇偶相干光场的量子特性；另一方面，我们在量子态的制备与操纵方面作一定研究，如压缩奇偶相干态的制备及如何利用[Ⅰ]型三能级原子与腔场的非共振相互作用来传送未知的薛定谔猫态。
Quantum optics is a subject on the coherence properties of radiation field, quantum statistical properties and quantum characters of light interacting with matter. The research has showed that there have appeared quantum effects in the interaction of light with atoms, especially in the nonlinear process. The effects peculiar to quantum field, do not exist in classical field, which reveals the quantum nature of light, then called non-classical effects. Now it has been proved by experiments, that quantum states of cavity field can exhibit three main non-classical features, i.e. photon antibunching effect, sub-Poissonian statistics distribution, and squeezed states, which not only benefit our further understanding of light nature, but also have significant applied value in the optics field. For instance in quantum states which have squeezing effect, one quadrature phase may have reduced quantum fluctuations compared with what the relative quadrature phase does in coherent states, then this make it have differen
t applications in optical communication systems, and so on. Therefore, the study on quantum characters of cavity field is an important topic in quantum optics.
In addition, quantum information as a newly emerging subject has had a rapid development in the world since 1994, in which carries of quantum information are quantum states, so that disposal of quantum information virtually is preparation and manipulation of diversified quantum states. In this paper, on one hand, we have studied characters of cavity field, including the influence of a nonlinear medium of inversion symmetry on the properties of coherent light field (such as squeezed property, distribution of light field and coherent property) after interacting with the medium, as well as the quantum properties of the fields
in squeezed even and squeezed odd coherent states; on the other hand, we have also done some research as to preparation and manipulation of quantum states, i.e. how to generate squeezed even and squeezed odd coherent states and how to teleport an unknown schroding cat state via ?-type three-level atom with cavity field through non-resonance process ,etc.
另外，在1994年之后兴起并在国际上蓬勃发展起来的新生学科——量子信息，是以量子态作为量子信息的载体，其对量子信息的处理实质上是对各种量子态的制备与操纵。在本文中，一方面我们研究光场的特性，其中包括相干光场与空间反演对称非线性介质相互作用后，介质对光场性质的影响(如压缩性质、分布特性和相干性)，以及压缩奇偶相干光场的量子特性；另一方面，我们在量子态的制备与操纵方面作一定研究，如压缩奇偶相干态的制备及如何利用[Ⅰ]型三能级原子与腔场的非共振相互作用来传送未知的薛定谔猫态。
Quantum optics is a subject on the coherence properties of radiation field, quantum statistical properties and quantum characters of light interacting with matter. The research has showed that there have appeared quantum effects in the interaction of light with atoms, especially in the nonlinear process. The effects peculiar to quantum field, do not exist in classical field, which reveals the quantum nature of light, then called non-classical effects. Now it has been proved by experiments, that quantum states of cavity field can exhibit three main non-classical features, i.e. photon antibunching effect, sub-Poissonian statistics distribution, and squeezed states, which not only benefit our further understanding of light nature, but also have significant applied value in the optics field. For instance in quantum states which have squeezing effect, one quadrature phase may have reduced quantum fluctuations compared with what the relative quadrature phase does in coherent states, then this make it have differen
t applications in optical communication systems, and so on. Therefore, the study on quantum characters of cavity field is an important topic in quantum optics.
In addition, quantum information as a newly emerging subject has had a rapid development in the world since 1994, in which carries of quantum information are quantum states, so that disposal of quantum information virtually is preparation and manipulation of diversified quantum states. In this paper, on one hand, we have studied characters of cavity field, including the influence of a nonlinear medium of inversion symmetry on the properties of coherent light field (such as squeezed property, distribution of light field and coherent property) after interacting with the medium, as well as the quantum properties of the fields
in squeezed even and squeezed odd coherent states; on the other hand, we have also done some research as to preparation and manipulation of quantum states, i.e. how to generate squeezed even and squeezed odd coherent states and how to teleport an unknown schroding cat state via ?-type three-level atom with cavity field through non-resonance process ,etc.
引文
1. C. M. Caves. Quantum-mechanical noise in an interferometer[J]. Phys. Rev. (D), 1981, 23(8): 1693～1708
2. J. Gea-banacloche, G. Leuchs. Squeezed states for interferometric gravitational-wave detectors[J]. J. Mod. Opt., 1987, 34(6,7):793～811
3．雷敏生，杨千里，刘世炳．类科尔介质中受激辐射场的量子统计性质[J]．光子学报，1996，25(12)：1057～1061
4．刘三秋，刘金明．Kerr介质中三能级原子与压缩光场相互作用的光子统计分布特性[J]．光子学报，1999，28 (3)：193～197
5. T. K. Liu, J. S. Peng. N-th squeezing of the field amplitude in the multiphoto Jaynes-Commings model in a kerr medium[J]. Acta photonica sinica (光子学报), 1997, 26(1):21～26 (in Chinese)
6. D. R. He. Squeezing of the two-photon Jaynes-Cummings model in a kerr medium[J]. Chinese J. Quant. Electron(量子电子学报), 1999, 16(2):122～129(in Chinese)
7. S. Q. Liu, L. wan, S. M. Liu. Squeezing effect of two coupling atoms interacting with a single mode light field in kerr medium[J]. Acta Optica Sinica(光学学报), 2002, 22(8):902～906(in Chinese)
8. K. Sundar. Highly amplitude-squeezed states of the radiation field[J]. Phys. Rev. Lett., 1995, 75(11):2116～2119
9．万琳，陶向阳等．Kerr介质中“耦合双原子-单模光场”模型的反聚束效应[J]．量子电子学报，2002，19 (4)，337～342
10. Anirban pathak, Swapan Mandal. Phase fluctuations of coherent light coupled to a nonlinear medium of inversion symmetry[J]. Phys. Lett. A, 2000, 272:346～352
11．彭金生，李高翔．近代量子光学导论[M]．科学出版社，1996：165
12. Li Hongcai, Wu Longquan. Generation of superposition of squeezed states via Raman interaction[J]. Opt. Comm., 2001, 197:97-101
13．李洪才，吴龙泉．利用简并∧型三能级原子与单模腔场的Raman相互作用制备压缩态的叠加态．光子学报，2001，30(9)：1060～1063
14．李洪才，吴龙泉．在腔场与可移动镜子系统中对镜子位置的测量．光子学报，2002，31(10)：1169～1173
15. Carl M. Bender, Luis M. A. Bettencourt. Multiple-scale analysis of the quantum anharmonic oscillator[J]. Phys. Rev. Lett., 1996, 77(20):4114～4117
16. Swapan Mandal. Quantum oscillator of quartic anharmonicity[J]. J. Phys. A, 1998, 31: L501～L505
17. Liao J, Wang X G, Wu L A, Pan S H. Superposition of negative binomial states. Journal of optics. B. Quantum and semiclassical optics, 2000, 2(4):541～544
18．李洪才，陈翔．相干光与空间反演对称介质作用的压缩性质．中国激光(已录用，待发表)
19. Zhu. K,. Wang. Q, Li. X. Nonclassical statistical properties of field in squeezed even and squeezed odd coherent states[J]. Opt. Soc. Am. B 10, 1993, 10(7): 1297—1291
20. Zheng. S. B, Guo. G. C. Generation of superposition of squeezed coherent states[J]. Chin. Phys. Lett., 1997, 14(4):273—276
21．林秀，李洪才，利用∨型三能级原子与光场Raman相互作用制备多原子[J]．物理学报，2001，50(09)：1689—1692
22．林秀，李洪才．∨型原子与光子拉曼相互作用传送未知原子态[J]．光学学报，2001，21(12)：1451—1453
23. Yuan H. P. Two-photon coherent states of radiation field[J]. Phys. Rev. A13, 1976, 13(6): 2226—2243
24．郭光灿．量子光学[M]．北京：高等教育出版社，1990
25. S. M. Barnett and P. L. Knight. J. Opt. Soc. Am. B2, 1985:467; J. Mod. Opt, 34,1987:841
26. L. Xu and Z. M. Zhang. Modified effective Hamiltonian for degenerate Raman process[J]. Z. Phys. B, 1994, 95:507～510
27. G. C. Guo and S. B. Zheng. Generation of Schrdinger cat states via the Jaynes-Cummings model with large detuning[J]. Phys. Lett. A, 1996, 223:332～336
28. A. K. Ekert. Quantum cryptography based on Bell's theorem[J]. Phys. Lett. 1991, 67(5):661～663
29. C. H. Bennett, G.. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev.Lett., 1993, 70(13):1895～1899
30. L. Davidovich, N. Zagury, M. Brune, J. M. Raimond, S. Haroche. Telepotation of an atomic state between two cavities using nonlocal microwave fields[J]. Phys. Rev. A., 1994, 50(2):R895～898
31. S. B. Zheng, G. C. Guo. Teleportation of an unknown atomic state through the Raman atom-cavity-field interation[J]. Phys. Lett. A., 1997, 232(6): 171～174
32. N. G.. Almeida, L. P. Maia, C. J. Uillas-boas. One-cavity scheme for atomic-state teleportation through GHZ states[J]. Phys. Lett. A., 1998, 241 (4): 213～217
33. S. B. Zheng. Teleportation of atomic states via resonant atom-field interation[J]. J. Mod. Opt., 1999, 167(5): 111～113
34. S. B. Zheng, G. C. Guo. Efficient scheme for two-atom entanglement and quantum information processing in cavity QED[J]. Phys. Rev. Lett., 2000, 85(11):2392～2395
35．林秀、李洪才，利用Raman型的Jaynes-Cummings模型传送未知原子态，物理学报，2001，50 (4)，686～689
36. K. H. Song, W. J. Zhang. Proposal for teleporting an entangled coherent state via the dispersive atom-cavity-field interation[J]. Phys. Lett. A., 2001, 290:214～218
37. C. C. Gerry. Preparation of multiatom entangled states through dispersive atom-cavity-field interactions[J], Phys. Rev. A., 1996, 53(4):2857～2860
38．陈翔，李洪才．型原子与腔场的非共振作用实现量子逻辑门与猫态的传送[J]．福建师范大学学报(自然科学版)，2003，19(1)：45～47
39．林秀，李洪才．利用型三能级原子与腔场的非共振相互作用制备原子纠缠态[J]．福建师范大学学报(自然科学版)，2002，18(4)：30～34
40．陈翔，李洪才．压缩奇偶相干光场的量子特性[J]．福建师范大学学报(自然科学版)，2002，18(3)：38～41
2. J. Gea-banacloche, G. Leuchs. Squeezed states for interferometric gravitational-wave detectors[J]. J. Mod. Opt., 1987, 34(6,7):793～811
3．雷敏生，杨千里，刘世炳．类科尔介质中受激辐射场的量子统计性质[J]．光子学报，1996，25(12)：1057～1061
4．刘三秋，刘金明．Kerr介质中三能级原子与压缩光场相互作用的光子统计分布特性[J]．光子学报，1999，28 (3)：193～197
5. T. K. Liu, J. S. Peng. N-th squeezing of the field amplitude in the multiphoto Jaynes-Commings model in a kerr medium[J]. Acta photonica sinica (光子学报), 1997, 26(1):21～26 (in Chinese)
6. D. R. He. Squeezing of the two-photon Jaynes-Cummings model in a kerr medium[J]. Chinese J. Quant. Electron(量子电子学报), 1999, 16(2):122～129(in Chinese)
7. S. Q. Liu, L. wan, S. M. Liu. Squeezing effect of two coupling atoms interacting with a single mode light field in kerr medium[J]. Acta Optica Sinica(光学学报), 2002, 22(8):902～906(in Chinese)
8. K. Sundar. Highly amplitude-squeezed states of the radiation field[J]. Phys. Rev. Lett., 1995, 75(11):2116～2119
9．万琳，陶向阳等．Kerr介质中“耦合双原子-单模光场”模型的反聚束效应[J]．量子电子学报，2002，19 (4)，337～342
10. Anirban pathak, Swapan Mandal. Phase fluctuations of coherent light coupled to a nonlinear medium of inversion symmetry[J]. Phys. Lett. A, 2000, 272:346～352
11．彭金生，李高翔．近代量子光学导论[M]．科学出版社，1996：165
12. Li Hongcai, Wu Longquan. Generation of superposition of squeezed states via Raman interaction[J]. Opt. Comm., 2001, 197:97-101
13．李洪才，吴龙泉．利用简并∧型三能级原子与单模腔场的Raman相互作用制备压缩态的叠加态．光子学报，2001，30(9)：1060～1063
14．李洪才，吴龙泉．在腔场与可移动镜子系统中对镜子位置的测量．光子学报，2002，31(10)：1169～1173
15. Carl M. Bender, Luis M. A. Bettencourt. Multiple-scale analysis of the quantum anharmonic oscillator[J]. Phys. Rev. Lett., 1996, 77(20):4114～4117
16. Swapan Mandal. Quantum oscillator of quartic anharmonicity[J]. J. Phys. A, 1998, 31: L501～L505
17. Liao J, Wang X G, Wu L A, Pan S H. Superposition of negative binomial states. Journal of optics. B. Quantum and semiclassical optics, 2000, 2(4):541～544
18．李洪才，陈翔．相干光与空间反演对称介质作用的压缩性质．中国激光(已录用，待发表)
19. Zhu. K,. Wang. Q, Li. X. Nonclassical statistical properties of field in squeezed even and squeezed odd coherent states[J]. Opt. Soc. Am. B 10, 1993, 10(7): 1297—1291
20. Zheng. S. B, Guo. G. C. Generation of superposition of squeezed coherent states[J]. Chin. Phys. Lett., 1997, 14(4):273—276
21．林秀，李洪才，利用∨型三能级原子与光场Raman相互作用制备多原子[J]．物理学报，2001，50(09)：1689—1692
22．林秀，李洪才．∨型原子与光子拉曼相互作用传送未知原子态[J]．光学学报，2001，21(12)：1451—1453
23. Yuan H. P. Two-photon coherent states of radiation field[J]. Phys. Rev. A13, 1976, 13(6): 2226—2243
24．郭光灿．量子光学[M]．北京：高等教育出版社，1990
25. S. M. Barnett and P. L. Knight. J. Opt. Soc. Am. B2, 1985:467; J. Mod. Opt, 34,1987:841
26. L. Xu and Z. M. Zhang. Modified effective Hamiltonian for degenerate Raman process[J]. Z. Phys. B, 1994, 95:507～510
27. G. C. Guo and S. B. Zheng. Generation of Schrdinger cat states via the Jaynes-Cummings model with large detuning[J]. Phys. Lett. A, 1996, 223:332～336
28. A. K. Ekert. Quantum cryptography based on Bell's theorem[J]. Phys. Lett. 1991, 67(5):661～663
29. C. H. Bennett, G.. Brassard, C. Crepeau, R. Jozsa, A. Peres, W. Wootters. Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels[J]. Phys. Rev.Lett., 1993, 70(13):1895～1899
30. L. Davidovich, N. Zagury, M. Brune, J. M. Raimond, S. Haroche. Telepotation of an atomic state between two cavities using nonlocal microwave fields[J]. Phys. Rev. A., 1994, 50(2):R895～898
31. S. B. Zheng, G. C. Guo. Teleportation of an unknown atomic state through the Raman atom-cavity-field interation[J]. Phys. Lett. A., 1997, 232(6): 171～174
32. N. G.. Almeida, L. P. Maia, C. J. Uillas-boas. One-cavity scheme for atomic-state teleportation through GHZ states[J]. Phys. Lett. A., 1998, 241 (4): 213～217
33. S. B. Zheng. Teleportation of atomic states via resonant atom-field interation[J]. J. Mod. Opt., 1999, 167(5): 111～113
34. S. B. Zheng, G. C. Guo. Efficient scheme for two-atom entanglement and quantum information processing in cavity QED[J]. Phys. Rev. Lett., 2000, 85(11):2392～2395
35．林秀、李洪才，利用Raman型的Jaynes-Cummings模型传送未知原子态，物理学报，2001，50 (4)，686～689
36. K. H. Song, W. J. Zhang. Proposal for teleporting an entangled coherent state via the dispersive atom-cavity-field interation[J]. Phys. Lett. A., 2001, 290:214～218
37. C. C. Gerry. Preparation of multiatom entangled states through dispersive atom-cavity-field interactions[J], Phys. Rev. A., 1996, 53(4):2857～2860
38．陈翔，李洪才．型原子与腔场的非共振作用实现量子逻辑门与猫态的传送[J]．福建师范大学学报(自然科学版)，2003，19(1)：45～47
39．林秀，李洪才．利用型三能级原子与腔场的非共振相互作用制备原子纠缠态[J]．福建师范大学学报(自然科学版)，2002，18(4)：30～34
40．陈翔，李洪才．压缩奇偶相干光场的量子特性[J]．福建师范大学学报(自然科学版)，2002，18(3)：38～41
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