Abstract

We propose efficient schemes for universal quantum gates with the photon polarization states and electron spin states of nitrogen-vacancy (NV) centers in diamond embedded in optical microcavity. A hybrid polarization-spin controlled-NOT gate and a two-qubit controlled phase gate between NV centers in separated cavities are demonstrated in the weak-coupling regime without complex devices or interaction. The gates presented here are deterministic and can be applied directly to a variety of quantum information processing tasks. The feasibility analyses show that our schemes can be accomplished with high fidelity under current technologies and have wide potential applications in quantum communication and computation fields.

© 2013 Optical Society of America

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  36. P. Delaney, J. C. Greer, and J. A. Larsson, “Spin-polarization mechanisms of the nitrogen-vacancy center in diamond,” Nano Lett. 10, 610–614 (2010).
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  44. K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon–photon SWAP gate using a Λ system,” Phys. Rev. A 82, 010301(R) (2010).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  48. L.-M. Duan, A. Kuzmich, and H. J. Kimble, “Cavity QED and quantum-information processing with “hot” trapped atoms,” Phys. Rev. A 67, 032305 (2003).
    [CrossRef]
  49. L.-M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
    [CrossRef]
  50. K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A 86, 020305(R) (2012).
    [CrossRef]
  51. R. Hanson, O. Gywat, and D. D. Awschalom, “Room-temperature manipulation and decoherence of a single spin in diamond,” Phys. Rev. B 74, 161203(R) (2006).
    [CrossRef]
  52. 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]
  53. F. Shi, X. Rong, N. Xu, Y. Wang, J. Wu, B. Chong, X. Peng, J. Kniepert, R.-S. 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]

2013 (1)

A. B. Young, C. Y. Hu, and J. G. Rarity, “Generating entanglement with low Q-factor microcavities,” Phys. Rev. A 87, 012332 (2013).
[CrossRef]

2012 (4)

K. Koshino and Y. Matsuzaki, “Entangling homogeneously broadened matter qubits in the weak-coupling cavity-QED regime,” Phys. Rev. A 86, 020305(R) (2012).
[CrossRef]

X. Xu, Z. Wang, C. Duan, P. Huang, P. Wang, Y. Wang, N. Xu, X. Kong, F. Shi, X. Rong, and J. Du, “Coherence-protected quantum gate by continuous dynamical decoupling in diamond,” Phys. Rev. Lett. 109, 070502 (2012).
[CrossRef]

T. van der Sar, Z. H. Wang, M. S. Blok, H. Bernien, T. H. Taminiau, D. M. Toyli, D. A. Lidar, D. D. Awschalom, R. Hanson, and V. V. Dobrovitski, “Decoherence-protected quantum gates for a hybrid solid-state spin register,” Nature 484, 82–86 (2012).
[CrossRef]

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. Express 20, 16902–16912 (2012).
[CrossRef]

2011 (6)

S. Zhang, X.-Q. Shao, L. Chen, Y.-F. Zhao, and K.-H. Yeon, “Robust SWAP gate on nitrogen-vacancy centres via quantum Zeno dynamics,” J. Phys. B 44, 075505 (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. A 83, 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. A 83, 054305 (2011).
[CrossRef]

M. W. Doherty, N. B. Manson, P. Delaney, and L. C. L. Hollenberg, “The negatively charged nitrogen-vacancy centre in diamond: the electronic solution,” New J. Phys. 13, 025019 (2011).
[CrossRef]

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]

W.-L. Yang, Z.-Q. Yin, Z.-Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
[CrossRef]

2010 (13)

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 466, 730–734 (2010).
[CrossRef]

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]

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]

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with Rydberg atoms,” Rev. Mod. Phys. 82, 2313–2363 (2010).
[CrossRef]

L.-M. Duan and C. Monroe, “Quantum networks with trapped ions,” Rev. Mod. Phys. 82, 1209–1224 (2010).
[CrossRef]

Y. Ma, M. Rohlfing, and A. Gali, “Excited states of the negatively charged nitrogen-vacancy color center in diamond,” Phys. Rev. B 81, 041204 (2010).
[CrossRef]

P. Delaney, J. C. Greer, and J. A. Larsson, “Spin-polarization mechanisms of the nitrogen-vacancy center in diamond,” Nano Lett. 10, 610–614 (2010).
[CrossRef]

V. M. Acosta, A. Jarmola, E. Bauch, and D. Budker, “Optical properties of the nitrogen-vacancy singlet levels in diamond,” Phys. Rev. B 82, 201202 (2010).
[CrossRef]

C. Bonato, F. Haupt, S. S. R. Oemrawsingh, J. Gudat, D. Ding, M. P. van Exter, and D. Bouwmeester, “CNOT and Bell-state analysis in the weak-coupling cavity QED regime,” Phys. Rev. Lett. 104, 160503 (2010).
[CrossRef]

J.-J. Chen, J.-H. An, M. Feng, and G. Liu, “Teleportation of an arbitrary multipartite state via photonic Faraday rotation,” J. Phys. B 43, 095505 (2010).
[CrossRef]

K. Koshino, S. Ishizaka, and Y. Nakamura, “Deterministic photon–photon SWAP gate using a Λ system,” Phys. Rev. A 82, 010301(R) (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, R.-S. 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]

2009 (5)

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. A 79, 032303 (2009).
[CrossRef]

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]

Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input–output process,” Phys. Rev. A 79, 064304 (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).
[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]

2008 (6)

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,” Science 320, 1326–1329 (2008).
[CrossRef]

R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008).
[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]

L. J. Rogers, S. Armstrong, M. J. Sellars, and N. B. Manson, “Infrared emission of the NV centre in diamond: Zeeman and uniaxial stress studies,” New J. Phys. 10, 103024 (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,” Science 319, 1062–1065 (2008).
[CrossRef]

C. Y. Hu, W. J. Munro, and J. G. Rarity, “Deterministic photon entangler using a charged quantum dot inside a microcavity,” Phys. Rev. B 78, 125318 (2008).
[CrossRef]

2007 (5)

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. Photonics 1, 215–223 (2007).
[CrossRef]

P. Kok, W. J. Munro, K. Nemoto, T. C. Ralph, J. P. Dowling, and G. J. Milburn, “Linear optical quantum computing with photonic qubits,” Rev. Mod. Phys. 79, 135–174 (2007).
[CrossRef]

R. Hanson, L. P. Kouwenhoven, J. R. Petta, S. Tarucha, and L. M. K. Vandersypen, “Spins in few-electron quantum dots,” Rev. Mod. Phys. 79, 1217–1265 (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,” Science 316, 1312–1316 (2007).
[CrossRef]

2006 (5)

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

R. Hanson, O. Gywat, and D. D. Awschalom, “Room-temperature manipulation and decoherence of a single spin in diamond,” Phys. Rev. B 74, 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. B 74, 104303 (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. Express 14, 7986–7994 (2006).
[CrossRef]

2004 (3)

L.-M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. 92, 127902 (2004).
[CrossRef]

K. Nemoto and W. J. Munro, “Nearly deterministic linear optical controlled-NOT gate,” Phys. Rev. Lett. 93, 250502 (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]

2003 (1)

L.-M. Duan, A. Kuzmich, and H. J. Kimble, “Cavity QED and quantum-information processing with “hot” trapped atoms,” Phys. Rev. A 67, 032305 (2003).
[CrossRef]

2001 (1)

J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. 73, 565–582 (2001).
[CrossRef]

1999 (1)

A. Imamog¯lu, D. D. Awschalom, G. Burkard, D. P. DiVincenzo, D. Loss, M. Sherwin, and A. Small, “Quantum information processing using quantum dot spins and cavity QED,” Phys. Rev. Lett. 83, 4204–4207 (1999).
[CrossRef]

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]

Acosta, V. M.

V. M. Acosta, A. Jarmola, E. Bauch, and D. Budker, “Optical properties of the nitrogen-vacancy singlet levels in diamond,” Phys. Rev. B 82, 201202 (2010).
[CrossRef]

An, J.-H.

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W.-L. Yang, Z.-Q. Yin, Z.-Y. Xu, M. Feng, and C. H. Oh, “Quantum dynamics and quantum state transfer between separated nitrogen-vacancy centers embedded in photonic crystal cavities,” Phys. Rev. A 84, 043849 (2011).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Basic model containing an NV center confined to a cavity with quantized WGM and a single photon pulse introduced to interact with the NV center. (b) Electron energy level configuration of the NV center and relevant transition coupling with corresponding photon polarization. | and |+ are used as qubits while |e is auxiliary.

Fig. 2.
Fig. 2.

Scheme for generation of entanglement in distant NV centers. CNOT indicates the hybrid polarization-spin CNOT gate. HWP, half-wave plate; PBS, circular polarization beam splitter; D, detector.

Fig. 3.
Fig. 3.

Illustration of setups for the controlled phase gate on two distant NV centers. CPF indicates the controlled phase flip gate in Fig. 1(a). P45 is a 45° polarizer.

Fig. 4.
Fig. 4.

Reflection coefficient as functions of parameters variation under the resonant condition ω0=ωC=ωp. (a) r(ωp) against g/κ for γ=1.5×105κ, κs0. The dotted lines indicate r(ωp)=0.95. (b) r(ωp) against κs/κ for γ=1.5×105κ, g=0.01κ.

Fig. 5.
Fig. 5.

Fidelity of the presented controlled phase gate on two distant NV centers as a function of the reflectances r(ωp) and r0(ωp).

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

dadt=[i(ωpωC)κ2κs2]a(t)gσ(t)κain(t)+Γ,
dσdt=[i(ωpω0)γ2]σ(t)gσz(t)a(t)+ϒ,
r(ωp)=aout(t)ain(t)=[i(ωcωp)κ2+κs2][i(ω0ωp)+γ2]+g2[i(ωcωp)+κ2+κs2][i(ω0ωp)+γ2]+g2.
r0(ωp)=i(ωcωp)κ2+κs2i(ωcωp)+κ2+κs2.
r(ωp)=(κsκ)γ+4g2(κs+κ)γ+4g2,r0(ωp)=κsκκs+κ.
|R+|L2(α|0+β|1)|R2(α|0+β|1)+|L2(α|1+β|0).
12(|R+|L)|001212[|R(|0012+|1112)+|L(|0012|1112)].
12(|R+|L)(α|+++β|++γ|++δ|)CPF1,HWP|R(α|+++β|+)+|L(γ|++δ|)CPF2,P4512(|R+|L)(α|+++β|++γ|+δ|).
|++|2(α|R+β|L)12|R[α(|++|)+β(|+|)]+12|L[α(|++|)β(|+|)].
F=|r2(ω)2r(ω)r0(ω)+5r02(ω)8|,

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