基于退相干环境克尔介质的贝尔型纠缠相干.doc
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1、精品论文基于退相干环境克尔介质的贝尔型纠缠相干态的产生宋思谕1,2, 王书浩1,2, 许国富1,2 , 龙桂鲁1,21 清华大学物理学院低维量子物理国家重点实验室,北京 1000842 清华大学清华信息科学技术国家实验室,北京 100084 摘要:我们提出了两个产生贝尔型纠缠相干态的方案。一个是利用单光子,另一个是利用纠缠 光子对。对比与以前的方案,方案仅应用线性光学器件,单光子探测器,和克尔介质来完成 的,并且整个的产生过程考虑了克尔介质的退相干效应的影响。代替相干叠加态,我们选择相 干态作为输入态。文中进行了产生的贝尔纠缠相干态的保真度与退相干效应的作用的数值研 究,并且讨论了光子的损耗对
2、产生的成功率和保真度的影响。我们的方案也适用于多模 GHZ 态的产生关键词:贝尔型纠缠相干态,态产生,克尔介质中图分类号: O43Generation of Bell-type entangled coherent states with realistic cross-Kerr nonlinearitySi Yu Song1,2 , Shuhao Wang1,2 , Guo Fu Xu1,2 , Gui Lu Long1,21 State Key Laboratory of Low-Dimensional Quantum Physics and Department of Physics,
3、Tsinghua University, Beijing, 1000842 Tsinghua National Laboratory For Information Science and Technology, TsinghuaUniversity, Beijing, 100084Abstract: We propose two protocols for generating Bell-type entangled coherent states (ECSs). One uses a single photon; the other one uses an entangled photon
4、 pair. In contrast to previous works, the protocols are completed merely using linear optical elements,single-photon detectors, and the cross-Kerr nonlinearity, where the decoherence eect of the cross-Kerr nonlinearity is imposed onto the generation process. Considering the diculty in generating a c
5、oherent super-positioned state with large amplitude, the input state is taken as the coherent state. The delity of the generated ECSs in the presence of decoherence of weak nonlinearity is numerical studied. Photon loss is found to aect only the probability, and not the delity, of the generation pro
6、cess. The protocol is also proved to be easily applicable forthe generation of multi-mode GHZ-type ECSs.基金项目: National Natural Science Foundation (11175094),National Basic Research Program (2009CB929402), Na- tional Basic Research Program (2011CB9216002)作者简介: Song Si Yu(1986-),female,PHD,major resea
7、rch direction:quantum information. Correspondence author:Long Gui Lu (1962-),male,professor,major research direction:quantum information.- 20 -Key words: Bell-type entangled coherent states, state generation, cross-Kerr nonlinearityEntanglement is a signicant ingredient of quantum systems dierent fr
8、om classical sys- tems, and is thus important in studying non-local and non-classical behaviors. Using entangled states, many schemes have been proposed to implement the tasks in quantum information processing (QIP) 1. One of the most important states exhibiting quantum entanglement is the entangled
9、 coherent state (ECS). The ECS was rst shown in Ref. 2, and the theoretical generation process of ECS was subsequently proposed through the optical system 3. Soon after, ECSs have been theoretically achieved by trapped ions 4, nanomechanical systems 5, quantum dots 6, microwave cavity quantum electr
10、odynamics 7, Bose-Einstein condensation systems 8, and superconducting systems 9. ECSs exhibit several advantages, such as ro- bustness against absorption and decoherence of the environment 10, which leads to the better performance of small-amplitude ECSs than photon systems in teleportation 11. Mea
11、nwhile, the four Bell-type ECSs can be simply discriminated by a beam splitter (BS) and two photon- number-resolving detectors 12, which is a great advantage in designing quantum computing protocols 11. ECSs are widely applied in quantum communication and quantum computation 3, 13, 14, 15, 16, 17, 1
12、8, 19, 20, 21, such as quantum teleportation 15, 21, 22, entanglement purication 23, quantum error corrections 24, 25, etc.The generation of a two-mode ECS in an optical system can be simply realized by injecting a coherent superposition state (CSS) into one port of a BS 22, 26, 27. The explicit for
13、m ofthe CSS is|CSS = N (| | ), (1)where the subscripts “+” and “” correspond to even and odd CSSs, respectively, and N =212(1 e2| ) 2 are the normalization constants. In the following context, for simplicity, thestates are not necessarily normalized, and “” is used instead of “=” to denote non-norma
14、lizedstates. The output state is the Bell-type ECS |Bell |, | , . Similarly, theGreenberger-Horne-Zeilinger (GHZ)-type ECS of N modes can be obtained by passing a CSS of the form of N (|N | N ) through a sequence of N 1 BSs with reectivityr1 = 1/N , r2 = 1/N 1, , and rN = 1/2 20. However, the protoc
15、ols introducedabove can only obtain ECSs with small amplitudes, which is mainly due to the diculty ofgenerating CSSs with large amplitudes. Although considerable eorts have been devoted to the enlargement of the amplitudes of CSSs and improving the delity in the generation process 26, 28, 29, 30, 31
16、, 32, the generation of CSSs with large amplitudes is still an open question.The scheme in Ref. 30 can produce CSSs with 2.2 using a squeezed single-photon state,and then is improved to be close to 3.4 with high delity using the cavity-assisted interaction31. In Ref. 32, they obtained CSSs with high
17、 delity ( 4), where double cross-phasemodulations are applied. The amplitude of ECSs obtained by BSs and a vacuum state is atmost CSS , which still cannot satisfy the requirements of QIP.2 ! !图 1: Schematic of the generation of Bell-type ECSs with realistic cross-Kerr nonlinearity. BSand PBS denote
18、beam splitter and polarization splitter, respectively. D1 and D2 denote the single-photon detectors. The four cross-Kerr nonlinearities give one mode of coherent state a phase shift .In this paper, we simply generate two-mode ECSs using the coherent state assisted by the photon states without using
19、CSSs. Our protocols are completed by BSs, a polarization beam splitter (PBS), single-photon detectors, and the cross-Kerr nonlinearity 33. The cross- Kerr nonlinearity has been used to generate entanglement and CSSs 26, 27, 34, 35, 36, 37; it has also been used in quantum computation 28, 38, 39, 40,
20、 41. Experimentally, a strong Kerr nonlinearity is extremely dicult to obtain because the nonlinear eects in a nonlinear mediumare suciently weak (3 1022 m2 V 2 ) 43, 42, even with the method of electromagneticallyinduced transparency 29, 44. Thus far, the achieved phase shift at the single-photon l
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