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量子纠缠是实现量子计算和量子通信的核心基础，本文提出了在金刚石氮-空位色心（NV centers）自旋系综与超导量子电路耦合的混合系统中实现两个分离量子节点之间纠缠的理论方案.在该混合系统中，把金刚石NV centers自旋系综和与之耦合的超导共面谐振器视为一个量子节点，两个量子节点之间通过一个空的超导共面谐振器连接.具有较长相干时间的NV centers自旋系综作为一个量子存储器，用于制备、存储和发送量子信息；易于外部操控的超导量子电路可执行量子逻辑门操作，快速调控量子信息.为了实现两个分离量子节点之间的纠缠，首先对系统的哈密顿量进行正则变换，将其等价为两个NV centers自旋系综与同一个超导共面谐振器之间的JC耦合；然后采用NV centers自旋-光子混合比特编码的方式，通过调节超导共面谐振器的谐振频率，精确控制体系演化时间，高保真度地实现了两个分离量子节点之间的量子纠缠.本方案还可以进一步扩展和集成，用于构建多节点纠缠的分布式量子网络.Quantum entanglement is a kernel of quantum computation and quantum communication. We introduce a theoretical scheme to achieve the entanglement between two separated quantum nodes in a hybrid system. The proposed hybrid system based on diamond nitrogen-vacancy (NV) center spin ensemble is coherently coupled to a superconducting quantum circuit consisting of two quantum nodes and a quantum channel. Each node in our setup is composed of an NV center spin ensemble magnetically coupled to a superconducting coplanar resonator. The NV center spin ensemble composed of N identical and non-interacting NV spins, is placed in the magnetic field antinode of the superconducting coplanar resonator where the coupling is maximized. An array of superconducting quantum interference devices (SQUIDs) is inserted in the central conductor of resonator to make its frequency tunable with the magnetic flux threading through the SQUID loops. This flux is generated by passing current through an on-chip wire, so that the resonator can be brought in resonance with the NV center spins without changing their Zeeman splitting. Quantum qubits encoded into two separate nodes are connected by a vacuum superconducting coplanar resonator that is used as a quantum channel. This setup can potentially take the best elements of each individual system:NV center spin ensemble with longer coherence time capable of preparing, storing and releasing photonic quantum information, and the superconducting quantum circuits are easy to manipulate externally and can perform quantum logic gates to control quantum information rapidly. In order to realize the entanglement between two separated quantum nodes, firstly, we make a canonical transformation and obtain the Hamiltonian of the system that is reduced to two NV center spin ensembles resonantly coupled to a single mode of the superconducting coplanar resonator. Then we put forward the hybrid NV center spin-photon qubit encoding. In this hybrid encoding, the NV center spin and photon degrees of freedom enter on an equal footing into the definition of the qubit, in which case, quantum channel will switch on when three superconducting coplanar resonators are in resonance with each other, and all the manipulations can perform simply by tuning the frequencies of the superconducting coplanar resonators. Under the precise control of the evolution time, high fidelity entanglement between two separated quantum nodes is achieved. We show that this proposal can provide high fidelity quantum entanglement under realistic conditions, both in the resonant and the dispersive interaction cases. This hybrid quantum system will exhibit long coherence time and possess features like easy fabrication, integratability, and potential scalability. Furthermore, the quantum node composed of an NV center spin ensemble magnetically coupled to a superconducting coplanar resonator can be respectively integrated, which has practical applications in the realization of quantum information transmission and quantum entanglement among multiple quantum nodes.
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Keywords:
- diamond NV centers /
- superconducting quantum circuits /
- quantum nodes /
- quantum entanglement
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[1] Ladd T D, Jelezko F, Laflamme R, Nakamura Y, Monroe C, OBrien J L 2010 Nature 464 45
[2] Bennett C H, DiVincenzo D P 2000 Nature 404 247
[3] Childress L, Gurudev Dutt M V, Taylor J M, Zibrov A S, Jelezko F, Wrachtrup J, Hemmer P R, Lukin M D 2006 Science 314 281
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[5] Stoneham M 2009 Physics 2 34
[6] Englund D, Shields B, Rivoire K, Hatami F, Vuovi J, Park H, Lukin M D 2010 Nano Lett. 10 3922
[7] Santori C, Tamarat P, Neumann P, Wrachtrup J, Fattal D, Beausoleil R G, Rabeau J, Olivero P, Greentree A D, Prawer S, Jelezko F, Hemmer P 2006 Phys. Rev. Lett. 97 247401
[8] Harrison J, Sellars M J, Manson N B 2006 Diamond and Related Materials 15 586
[9] Fuchs G D, Dobrovitski V V, Toyli D M, Heremans F J, Awschalom D D 2009 Science 326 1520
[10] Fuchs G D, Dobrovitski V V, Hanson R, Batra A, Weis C D, Schenkel T, Awschalom D D 2008 Phys. Rev. Lett. 101 117601
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[12] Xiao Y F, Zou C L, Li B B, Li Y, Dong C H, Han Z F, Gong Q H 2010 Phys. Rev. Lett. 105 153902
[13] Kubo Y, Ong F R, Bertet P, Vion D, Jacques V, Zheng D, Drau A, Roch J F, Auffeves A, Jelezko F, Wrachtrup J, Barthe M F, Bergonzo P, Esteve D 2010 Phys. Rev. Lett. 105 140502
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[15] DiCarlo L, Chow J M, Gambetta J M, Bishop L S, Johnson B R, Schuster D I, Majer J, Blais A, Frunzio L, Girvin S M, Schoelkopf R J 2009 Nature 460 240
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[17] Xiang Z L, Ashhab S, You J Q, Nori F 2013 Rev. Mod. Phys. 85 623
[18] Kubo Y, Grezes C, Dewes A, Umeda T, Isoya J, Sumiya H, Morishita N, Abe H, Onoda S, Ohshima T, Jacques V, Drau A, Roch J F, Diniz I, Auffeves A, Vion D, Esteve D, Bertet P 2011 Phys. Rev. Lett. 107 220501
[19] Chen Q, Yang W L, Feng M 2012 Phys. Rev. A 86 022327
[20] Xiang Z L, L X Y, Li T F, You J Q, Nori F 2013 Phys. Rev. B 87 144516
[21] Carretta S, Chiesa A, Troiani F, Gerace D, Amoretti G, Santini P 2013 Phys. Rev. Lett. 111 110501
[22] Zou L J, Marcos D, Diehl S, Putz S, Schmiedmayer J, Majer J, Rabl P 2014 Phys. Rev. Lett. 113 023603
[23] Felicetti S, Sanz M, Lamata L, Romero G, Johansson G, Delsing P, Solano E 2014 Phys. Rev. Lett. 113 093602
[24] Hammerer K, Srensen A S, Polzik E S 2010 Rev. Mod. Phys. 82 1041
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