Abstract

We demonstrate efficient schemes of deterministic entanglement generation and quantum state transfer (QST) with the nitrogen-vacancy (NV) centers in diamond confined in separated microtoroidal resonators via single-photon input-output process. Assisted by the polarization of input photon pulse and the electron spin state of NV center, high fidelity NV center entangled states and photonic entangled states can be generated, respectively. The analyses of experimental feasibility show that our schemes work well with low quality resonators and weak coupling between qubits, which may be beneficial for exploring large-scale quantum information processing with diamond-based solid-state devices.

© 2013 OSA

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    [CrossRef]
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    [CrossRef]
  36. G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
  39. K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A86, 020305(R) (2012).
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    [CrossRef]
  42. F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, Rolf-Simon Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond,” Phys. Rev. Lett.105, 040504 (2010).
    [CrossRef] [PubMed]
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    [CrossRef]
  44. P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
    [CrossRef]
  45. J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
    [CrossRef]
  46. C. Santori, P. E. Barclay, K.-M. C. Fu, and R. G. Beausoleil, “Vertical distribution of nitrogen-vacancy centers in diamond formed by ion implantation and annealing,” Phys. Rev. B79, 125313 (2009).
    [CrossRef]

2012 (2)

A. Zheng, J. Li, R. Yu, X.-Y. Lü, and Y. Wu, “Generation of Greenberger-Horne-Zeilinger state of distant diamond nitrogen-vacancy centers via nanocavity input-output process,” Opt. Express20, 16902–16912 (2012).
[CrossRef]

K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A86, 020305(R) (2012).
[CrossRef]

2011 (3)

J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
[CrossRef]

P.-B. Li, S.-Y. Gao, and F.-L. Li, “Quantum-information transfer with nitrogen-vacancy centers coupled to a whispering-gallery microresonator,” Phys. Rev. A83, 054306 (2011).
[CrossRef]

Q. Chen, W.-L. Yang, M. Feng, and J.-F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
[CrossRef]

2010 (8)

W.-L. Yang, Z.-Q. Yin, Z.-Y. Xu, M. Feng, and J.-F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett.96, 241113 (2010).
[CrossRef]

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London)466, 730–734 (2010).
[CrossRef]

R. J. Barbour, K. N. Dinyari, and H. Wang, “A composite microcavity of diamond nanopillar and deformed silica microsphere with enhanced evanescent decay length,” Opt. Express18, 18968–18974 (2010).
[CrossRef] [PubMed]

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett.97, 141108 (2010).
[CrossRef]

B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science330, 1212–1215 (2010).
[CrossRef] [PubMed]

X.-Q. Shao, L. Chen, S. Zhang, Y.-F. Zhao, and K.-H. Yeon, “Deterministic generation of arbitrary multi-atom symmetric Dicke states by a combination of quantum Zeno dynamics and adiabatic passage,” Europhys. Lett.90, 50003 (2010).
[CrossRef]

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, Rolf-Simon Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond,” Phys. Rev. Lett.105, 040504 (2010).
[CrossRef] [PubMed]

2009 (8)

C. Santori, P. E. Barclay, K.-M. C. Fu, and R. G. Beausoleil, “Vertical distribution of nitrogen-vacancy centers in diamond formed by ion implantation and annealing,” Phys. Rev. B79, 125313 (2009).
[CrossRef]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

H.-F. Wang and Shou Zhang, “Linear optical generation of multipartite entanglement with conventional photon detectors,” Phys. Rev. A79, 042336 (2009).
[CrossRef]

M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett.9, 1447–1450 (2009).
[CrossRef] [PubMed]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys.81, 865–942 (2009).
[CrossRef]

P. E. Barclay, K.-M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers” Opt. Express17, 9588–9601 (2009).
[CrossRef] [PubMed]

A. Young, C. Y. Hu, L. Marseglia, J. P. Harrison, J. L. O’Brien, and J. G. Rarity, “Cavity enhanced spin measurement of the ground state spin of an NV center in diamond,” New J. Phys.11, 013007 (2009).
[CrossRef]

J.-H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
[CrossRef]

2008 (4)

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B78, 125318 (2008).
[CrossRef]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef]

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
[CrossRef]

2007 (3)

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nat. Phys.3, 253–255 (2007).
[CrossRef]

A. J. Shields, “Semiconductor quantum light sources,” Nat. Photon.1215–223 (2007).
[CrossRef]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science316, 1312–1316 (2007).
[CrossRef]

2006 (6)

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express14, 7986–7994 (2006).
[CrossRef] [PubMed]

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett.6, 2075–2079 (2006).
[CrossRef] [PubMed]

H. Walther, B. T. H. Varcoe, B. G. Englert, and T. Becker, “Cavity quantum electrodynamics,” Rep. Prog. Phys.69, 1325–1382 (2006).
[CrossRef]

R. Hanson, O. Gywat, and D. D. Awschalom, “Room-temperature manipulation and decoherence of a single spin in diamond,” Phys. Rev. B74, 161203(R) (2006).
[CrossRef]

N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B74, 104303 (2006).
[CrossRef]

2004 (2)

J. A. Sauer, K. M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman, “Cavity QED with optically transported atoms,” Phys. Rev. A69, 051804(R) (2004).
[CrossRef]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett.93, 130501 (2004).
[CrossRef] [PubMed]

2003 (2)

X.-B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A67, 044301 (2003).
[CrossRef]

G. Vidal, “Efficient Classical Simulation of Slightly Entangled Quantum Computations,” Phys. Rev. Lett.91, 147902 (2003).
[CrossRef] [PubMed]

2002 (1)

A. Vaziri, G. Weihs, and A. Zeilinger, “Experimental two-photon, three-dimensional entanglement for quantum communication,” Phys. Rev. Lett.89, 240401 (2002).
[CrossRef] [PubMed]

2000 (2)

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
[CrossRef]

S.-B. Zheng and G.-C. Guo, “Efficient scheme for two-atom entanglement and quantum information processing in cavity QED,” Phys. Rev. Lett.85, 2392–2395 (2000).
[CrossRef] [PubMed]

1995 (1)

A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: theory,” Phys. Rev. B53, 13441–13455 (1995).
[CrossRef]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

1991 (1)

A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett.67, 661–663 (1991).
[CrossRef] [PubMed]

1911 (1)

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett.95, 191115 (2009).

Achard, J.

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

An, J.-H.

J.-H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
[CrossRef]

Aoki, T.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

Awschalom, D. D.

B. B. Buckley, G. D. Fuchs, L. C. Bassett, and D. D. Awschalom, “Spin-light coherence for single-spin measurement and control in diamond,” Science330, 1212–1215 (2010).
[CrossRef] [PubMed]

R. Hanson, O. Gywat, and D. D. Awschalom, “Room-temperature manipulation and decoherence of a single spin in diamond,” Phys. Rev. B74, 161203(R) (2006).
[CrossRef]

Balasubramanian, G.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

Barbour, R. J.

Barclay, P. E.

P. E. Barclay, K.-M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers” Opt. Express17, 9588–9601 (2009).
[CrossRef] [PubMed]

C. Santori, P. E. Barclay, K.-M. C. Fu, and R. G. Beausoleil, “Vertical distribution of nitrogen-vacancy centers in diamond formed by ion implantation and annealing,” Phys. Rev. B79, 125313 (2009).
[CrossRef]

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett.95, 191115 (2009).

Barth, M.

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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett.93, 130501 (2004).
[CrossRef] [PubMed]

Jiang, L.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London)466, 730–734 (2010).
[CrossRef]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science316, 1312–1316 (2007).
[CrossRef]

Jozsa, R.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

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J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
[CrossRef]

Kewes, G.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett.97, 141108 (2010).
[CrossRef]

Kielpinski, D.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
[CrossRef]

Kimble, H. J.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

King, B. E.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
[CrossRef]

Kniepert, J.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, Rolf-Simon Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond,” Phys. Rev. Lett.105, 040504 (2010).
[CrossRef] [PubMed]

Kolesov, R.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
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K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A86, 020305(R) (2012).
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Kuhn, A.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nat. Phys.3, 253–255 (2007).
[CrossRef]

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C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
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M. Larsson, K. N. Dinyari, and H. Wang, “Composite optical microcavity of diamond nanopillar and silica microsphere,” Nano Lett.9, 1447–1450 (2009).
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A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: theory,” Phys. Rev. B53, 13441–13455 (1995).
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P.-B. Li, S.-Y. Gao, and F.-L. Li, “Quantum-information transfer with nitrogen-vacancy centers coupled to a whispering-gallery microresonator,” Phys. Rev. A83, 054306 (2011).
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Li, J.

Li, P.-B.

P.-B. Li, S.-Y. Gao, and F.-L. Li, “Quantum-information transfer with nitrogen-vacancy centers coupled to a whispering-gallery microresonator,” Phys. Rev. A83, 054306 (2011).
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J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett.97, 141108 (2010).
[CrossRef]

Lü, X.-Y.

Lukin, M. D.

J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
[CrossRef]

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London)466, 730–734 (2010).
[CrossRef]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science316, 1312–1316 (2007).
[CrossRef]

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P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
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N. B. Manson, J. P. Harrison, and M. J. Sellars, “Nitrogen-vacancy center in diamond: Model of the electronic structure and associated dynamics,” Phys. Rev. B74, 104303 (2006).
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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

Markham, M. L.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

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A. Young, C. Y. Hu, L. Marseglia, J. P. Harrison, J. L. O’Brien, and J. G. Rarity, “Cavity enhanced spin measurement of the ground state spin of an NV center in diamond,” New J. Phys.11, 013007 (2009).
[CrossRef]

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X.-B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A67, 044301 (2003).
[CrossRef]

Matsuzaki, Y.

K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A86, 020305(R) (2012).
[CrossRef]

Maze, J.

E. Togan, Y. Chu, A. S. Trifonov, L. Jiang, J. Maze, L. Childress, M. V. G. Dutt, A. S. Sørensen, P. R. Hemmer, A. S. Zibrov, and M. D. Lukin, “Quantum entanglement between an optical photon and a solid-state spin qubit,” Nature (London)466, 730–734 (2010).
[CrossRef]

M. V. Gurudev Dutt, L. Childress, L. Jiang, E. Togan, J. Maze, F. Jelezko, A. S. Zibrov, P. R. Hemmer, and M. D. Lukin, “Quantum register based on individual electronic and nuclear spin qubits in diamond,” Science316, 1312–1316 (2007).
[CrossRef]

Maze, J. R.

J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
[CrossRef]

McMurtrie, R. L.

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
[CrossRef]

Meijer, J.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

Meyer, V.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
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D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag1994).

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G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef]

Monroe, C.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
[CrossRef]

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C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B78, 125318 (2008).
[CrossRef]

Myatt, C. J.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
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Naydenov, B.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
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Neumann, P.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
[CrossRef] [PubMed]

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
[CrossRef]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

Neumman, P.

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef]

Nizovtsev, A.

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
[CrossRef]

Nüsse, N.

J. Wolters, A. W. Schell, G. Kewes, N. Nüsse, M. Schoengen, H. Döscher, T. Hannappel, B. Löchel, M. Barth, and O. Benson, “Enhancement of the zero phonon line emission from a single nitrogen vacancy center in a nanodiamond via coupling to a photonic crystal cavity,” Appl. Phys. Lett.97, 141108 (2010).
[CrossRef]

O’Brien, J. L.

A. Young, C. Y. Hu, L. Marseglia, J. P. Harrison, J. L. O’Brien, and J. G. Rarity, “Cavity enhanced spin measurement of the ground state spin of an NV center in diamond,” New J. Phys.11, 013007 (2009).
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J.-H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
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Olivero, P.

Ostby, E. P.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
[CrossRef] [PubMed]

Pahlke, K.

X.-B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A67, 044301 (2003).
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Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett.6, 2075–2079 (2006).
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Parkins, A. S.

B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. I. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008).
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Peng, X.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, Rolf-Simon Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond,” Phys. Rev. Lett.105, 040504 (2010).
[CrossRef] [PubMed]

Peres, A.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett.70, 1895–1899 (1993).
[CrossRef] [PubMed]

Pezzagna, S.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

Popa, I.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, and J. Wrachtrup, “Observation of coherent oscillation of a single nuclear spin and realization of a two-qubit conditional quantum gate,” Phys. Rev. Lett.93, 130501 (2004).
[CrossRef] [PubMed]

Prawer, S.

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
[CrossRef]

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express14, 7986–7994 (2006).
[CrossRef] [PubMed]

Rabeau, J. R.

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express14, 7986–7994 (2006).
[CrossRef] [PubMed]

T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
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Rand, S. C.

A. Lenef and S. C. Rand, “Electronic structure of the N-V center in diamond: theory,” Phys. Rev. B53, 13441–13455 (1995).
[CrossRef]

Rarity, J. G.

A. Young, C. Y. Hu, L. Marseglia, J. P. Harrison, J. L. O’Brien, and J. G. Rarity, “Cavity enhanced spin measurement of the ground state spin of an NV center in diamond,” New J. Phys.11, 013007 (2009).
[CrossRef]

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B78, 125318 (2008).
[CrossRef]

Reichart, P.

Rempe, G.

M. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and G. Rempe, “A single-photon server with just one atom,” Nat. Phys.3, 253–255 (2007).
[CrossRef]

Rempp, F.

P. Neumann, R. Kolesov, B. Naydenov, J. Beck, F. Rempp, M. Steiner, V. Jacques, G. Balasubramanian, M. L. Markham, D. J. Twitchen, S. Pezzagna, J. Meijer, J. Twamley, F. Jelezko, and J. Wrachtrup, “Quantum register based on coupled electron spins in a room-temperature solid,” Nat. Phys.6, 249–253 (2010).
[CrossRef]

P. Neumman, N. Mizuochi, F. Rempp, P. Hemmer, H. Watanabe, S. Yamasaki, V. Jacques, T. Gaebel, F. Jelezko, and J. Wrachtrup, “Multipartite entanglement among single spins in diamond,” Science320, 1326–1329 (2008).
[CrossRef]

Rong, X.

F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, Rolf-Simon Schoenfeld, W. Harneit, M. Feng, and J. Du, “Room-Temperature Implementation of the Deutsch-Jozsa Algorithm with a Single Electronic Spin in Diamond,” Phys. Rev. Lett.105, 040504 (2010).
[CrossRef] [PubMed]

Rowe, M.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
[CrossRef]

Rubanov, S.

Sackett, C. A.

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
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Santori, C.

P. E. Barclay, K.-M. Fu, C. Santori, and R. G. Beausoleil, “Hybrid photonic crystal cavity and waveguide for coupling to diamond NV-centers” Opt. Express17, 9588–9601 (2009).
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C. Santori, P. E. Barclay, K.-M. C. Fu, and R. G. Beausoleil, “Vertical distribution of nitrogen-vacancy centers in diamond formed by ion implantation and annealing,” Phys. Rev. B79, 125313 (2009).
[CrossRef]

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
[CrossRef]

C. Santori, D. Fattal, S. M. Spillane, M. Fiorentino, R. G. Beausoleil, A. D. Greentree, P. Olivero, M. Draganski, J. R. Rabeau, P. Reichart, S. Rubanov, D. N. Jamieson, and S. Prawer, “Coherent population trapping in diamond N-V centers at zero magnetic field,” Opt. Express14, 7986–7994 (2006).
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Appl. Phys. Lett. (3)

P. E. Barclay, K.-M. C. Fu, C. Santori, and R. G. Beausoleil, “Chip-based microcavities coupled to nitrogen-vacancy centers in single crystal diamond,” Appl. Phys. Lett.95, 191115 (2009).

W.-L. Yang, Z.-Q. Yin, Z.-Y. Xu, M. Feng, and J.-F. Du, “One-step implementation of multiqubit conditional phase gating with nitrogen-vacancy centers coupled to a high-Q silica microsphere cavity,” Appl. Phys. Lett.96, 241113 (2010).
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Europhys. Lett. (1)

X.-Q. Shao, L. Chen, S. Zhang, Y.-F. Zhao, and K.-H. Yeon, “Deterministic generation of arbitrary multi-atom symmetric Dicke states by a combination of quantum Zeno dynamics and adiabatic passage,” Europhys. Lett.90, 50003 (2010).
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Nano Lett. (2)

Y. S. Park, A. K. Cook, and H. Wang, “Cavity QED with diamond nanocrystals and silica microspheres,” Nano Lett.6, 2075–2079 (2006).
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Nat. Mater. (1)

G. Balasubramanian, P. Neumann, D. Twitchen, M. Markham, R. Kolesov, N. Mizuochi, J. Isoya, J. Achard, J. Beck, J. Tissler, V. Jacques, P. R. Hemmer, F. Jelezko, and J. Wrachtrup, “Ultralong spin coherence time in isotopically engineered diamond,” Nat. Mater.8, 383–387 (2009).
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A. J. Shields, “Semiconductor quantum light sources,” Nat. Photon.1215–223 (2007).
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Nat. Phys. (3)

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T. Gaebel, M. Domhan, I. Popa, C. Wittmann, P. Neumann, F. Jelezko, J. R. Rabeau, N. Stavrias, A. D. Greentree, S. Prawer, J. Meijer, J. Twamley, P. R. Hemmer, and J. Wrachtrup, “Room-temperature coherent coupling of single spins in diamond,” Nat. Phys.2, 408–413 (2006).
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Nature (London) (2)

C. A. Sackett, D. Kielpinski, B. E. King, C. Langer, V. Meyer, C. J. Myatt, M. Rowe, Q. A. Turchette, W. M. Itano, D. J. Wineland, and C. Monroe, “Experimental entanglement of four particles,” Nature (London)404, 256–259 (2000).
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New J. Phys. (3)

P. Tamarat, N. B. Manson, J. P. Harrison, R. L. McMurtrie, A. Nizovtsev, C. Santori, R. G. Beausoleil, P. Neumann, T. Gaebel, F. Jelezko, P. Hemmer, and J. Wrachtrup, “Spin-flip and spin-conserving optical transitions of the nitrogen-vacancy centre in diamond,” New J. Phys.10, 045004 (2008).
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J. R. Maze, A. Gali, E. Togan, Y. Chu, A. Trifonov, E. Kaxiras, and M. D. Lukin, “Properties of nitrogen-vacancy centers in diamond: the group theoretic approach,” New J. Phys.13, 025025 (2011).
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A. Young, C. Y. Hu, L. Marseglia, J. P. Harrison, J. L. O’Brien, and J. G. Rarity, “Cavity enhanced spin measurement of the ground state spin of an NV center in diamond,” New J. Phys.11, 013007 (2009).
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Opt. Express (4)

Phys. Rev. A (7)

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Q. Chen, W.-L. Yang, M. Feng, and J.-F. Du, “Entangling separate nitrogen-vacancy centers in a scalable fashion via coupling to microtoroidal resonators,” Phys. Rev. A83, 054305 (2011).
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J.-H. An, M. Feng, and C. H. Oh, “Quantum-information processing with a single photon by an input-output process with respect to low-Q cavities,” Phys. Rev. A79, 032303 (2009).
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X.-B. Zou, K. Pahlke, and W. Mathis, “Generation of an entangled state of two three-level atoms in cavity QED,” Phys. Rev. A67, 044301 (2003).
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Figures (3)

Fig. 1
Fig. 1

Diagrammatic illustration of basic model of single photon input-output process. (a) An NV center is confined to a MTR with quantized WGM and a single photon pulse is introduced to interact with the NV center. (b) The electron energy level configuration of an NV center and the relevant transition coupling with the input polarized photon. The sophisticated level splitting of the excited states is not shown.

Fig. 2
Fig. 2

Diagrammatic illustration of setups for entanglement generation and QST. (a)Generating GHZ state of NV centers in three separated MTRs via single photon pulse. (b)Generating Bell state |Φ〉 using different polarization component of input photon. (c)Generating two-photon entangled state assisted by the NV center spin state. SPS: single-photon source; PBS: circular polarization beam splitter; HWP: half-wave plate; P45: 45° polarizer; D: detector.

Fig. 3
Fig. 3

The reflection coefficient as functions of parameters variation under the resonant condition ω0 = ωC = ωp. (a) r(ωp) against g / κ γ. (b) r(ωp) against g/κ for γ = 6 × 10−5κ (red curve) and γ = 6 × 10−4κ (blue curve). The dotted lines in (a) and (b) indicate |r(ωp)| = 0.95. (c) r(ωp) against g/γ for κ = 500γ (red curve), κ = 1000γ (blue curve) and κ = 1500γ (green curve). (d) r(ωp) against κ/γ for g = 300γ (red curve), g = 500γ (blue curve) and g = 800γ (green curve).

Equations (12)

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H = j = R , L [ ω j 0 2 σ j z + ω j C a j a j + i g j ( a j σ j + a j σ j ) ] + H R ,
d a j d t = [ i ( ω p ω C ) κ 2 ] a j ( t ) g σ j ( t ) κ a j , in ( t ) + ζ ,
d σ j d t = [ i ( ω p ω 0 ) γ 2 ] σ j ( t ) g σ j , z ( t ) a j ( t ) + ξ ,
r ( ω p ) = a j , out ( t ) a j , in ( t ) = [ i ( ω c ω p ) κ 2 ] [ i ( ω 0 ω p ) + γ 2 ] + g 2 [ i ( ω c ω p ) + κ 2 ] [ i ( ω 0 ω p ) + γ 2 ] + g 2 ,
r 0 ( ω p ) = i ( ω c ω p ) κ 2 i ( ω c ω p ) + κ 2 .
r ( ω p ) = κ γ + 4 g 2 κ γ + 4 g 2 , r 0 ( ω p ) = 1 .
| R | + | R | + , | R | | R | , | L | + | L | + , | L | | L | .
| R + | L 2 | 000 123 1 2 ( | R | 000 123 + | L | 111 123 ) 1 2 ( | R + | L ) ( | 000 123 + | 111 123 ) .
1 2 ( α 1 α 2 | R R + + α 1 α 2 | R R + α 1 β 2 | R L + α 1 β 2 | R L + + α 2 β 1 | L R + β 1 α 2 | L R + β 1 β 2 | L L + + β 1 β 2 | L L ) .
α 1 α 2 | R R + + α 1 β 2 | R L + α 2 β 1 | L R + β 1 β 2 | L L + = | + ( α 1 α 2 | R R + β 1 β 2 | L L ) + | ( α 1 β 2 | R L + α 2 β 1 | L R ) .
1 2 [ ( | R + | L ) ( α 1 | + + + β 1 | ) 12 + ( | R | L ) ( α 1 | + + β 1 | + ) 12 ] .
1 2 2 { ( | R + | L ) [ | + 1 ( α 1 | + + β 1 | ) 2 + | 1 ( α 1 | + β 1 | ) 2 ] + ( | R | L ) [ | + 1 ( α 1 | + β 1 | + ) 2 + | 1 ( α 1 | β 1 | + ) 2 ] } .

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