## Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime |

Optics Express, Vol. 21, Issue 4, pp. 4093-4105 (2013)

http://dx.doi.org/10.1364/OE.21.004093

Acrobat PDF (940 KB)

### Abstract

We investigate an atomic entanglement purification protocol based on the coherent state input-output process by working in low-Q cavity in the atom-cavity intermediate coupling region. The information of entangled states are encoded in three-level configured single atoms confined in separated one-side optical micro-cavities. Using the coherent state input-output process, we design a two-qubit parity check module (PCM), which allows the quantum nondemolition measurement for the atomic qubits, and show its use for remote parities to distill a high-fidelity atomic entangled ensemble from an initial mixed state ensemble nonlocally. The proposed scheme can further be used for unknown atomic states entanglement concentration. Also by exploiting the PCM, we describe a modified scheme for atomic entanglement concentration by introducing ancillary single atoms. As the coherent state input-output process is robust and scalable in realistic applications, and the detection in the PCM is based on the intensity of outgoing coherent state, the present protocols may be widely used in large-scaled and solid-based quantum repeater and quantum information processing.

© 2013 OSA

## 1. Introduction

1. C. H. Bennett, G. Brassard, C. Crepeau, 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]

2. C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. **69**, 2881–2884 (1992). [CrossRef] [PubMed]

3. M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A **59**, 1829–1834 (1999). [CrossRef]

5. L. Xiao, G. L. Long, F. G. Deng, and J. W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A **69**, 052307 (2004). [CrossRef]

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

8. X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A **78**, 022321 (2008). [CrossRef]

9. G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A **65**, 032302 (2002). [CrossRef]

12. X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A **74**, 054302 (2006). [CrossRef]

*et al.*[13] in 1998, whose basic ideal is to divide the total transmission line into segments with a shorter length at the order of the attenuation length, then entanglement purification and entanglement swapping can be used to depress the effect of noise and extend the entanglement to longer distance. In 2001, Duan

*et al.*[14

14. L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature **414**, 413–418 (2001). [CrossRef] [PubMed]

*et al.*[15

15. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. **76**, 722–725 (1996). [CrossRef] [PubMed]

*et al.*[16

16. D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. **77**, 2818–2821 (1996). [CrossRef] [PubMed]

*et al.*[17

17. J. W. Pan, C. Simon, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) **410**, 1067–1070 (2001). [CrossRef]

18. J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature **423**, 417–422 (2003). [CrossRef] [PubMed]

19. C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. **89**, 257901 (2002). [CrossRef] [PubMed]

*et al.*[20

20. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A **77**, 042308 (2008). [CrossRef]

21. Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A **82**, 044305 (2010). [CrossRef]

23. F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A **83**, 062316 (2011). [CrossRef]

*et al.*[24] proposed an interesting EPP using cross-Kerr nonlinearity by identifying the intensity of probe coherent beams. There are also some important EPPs for multipartite systems in Ref. [25

25. M. Murao, M. B. Plenio, S. Popescu, V. Vedral, and P. L. Knight, “Multiparticle entanglement purification protocols,” Phys. Rev. A **57**, R4075–R4078 (1998). [CrossRef]

26. F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A **84**, 052312 (2011). [CrossRef]

*et al.*[27

27. C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A **53**, 2046 (1996). [CrossRef] [PubMed]

*et al.*[28

28. S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A **60**, 194–197 (1999). [CrossRef]

*et al.*[29

29. B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A **62**, 054301 (2000). [CrossRef]

*et al.*[30

30. Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A **64**, 014301 (2001). [CrossRef]

*et al.*[31

31. T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A **64**, 012304 (2001). [CrossRef]

*et al.*[32

32. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A **77**, 062325 (2008). [CrossRef]

33. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A **85**, 012307 (2012). [CrossRef]

34. F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A **85**, 022311 (2012). [CrossRef]

35. M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A **71**, 012308 (2005). [CrossRef]

36. M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A **71**, 044302 (2005). [CrossRef]

*et al.*[37

37. X. L. Feng, L. C. Kwek, and C. H. Oh, “Electronic entanglement purification scheme enhanced by charge detections,” Phys. Rev. A **71**, 064301 (2005). [CrossRef]

*et al.*[38

38. Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A **73**, 014303 (2006). [CrossRef]

*et al.*[39

39. R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature **443**, 838–841 (2006). [CrossRef] [PubMed]

*et al.*[40

40. C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A **75**, 042325 (2007). [CrossRef]

*et al.*[41

41. C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A **84**, 032307 (2011). [CrossRef]

42. C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A **86**, 012323 (2012). [CrossRef]

*et al.*[43

43. Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A **86**, 034305 (2012). [CrossRef]

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

45. S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. **87**, 037902 (2001). [CrossRef] [PubMed]

53. F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A **80**, 042319 (2009). [CrossRef]

*et al.*[55

55. 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]

56. 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]

57. Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A **82**052329 (2010). [CrossRef]

58. 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]

43. Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A **86**, 034305 (2012). [CrossRef]

59. P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. **96**, 240501 (2006). [CrossRef] [PubMed]

60. T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. **8**, 184 (2006). [CrossRef]

*et al.*[61

61. F. Mei, Y. F. Yu, X. L. Feng, Z. M. Zhang, and C. H. Oh, “Quantum entanglement distribution with hybrid parity gate,” Phys. Rev. A **82**, 052315 (2010). [CrossRef]

## 2. Coherent state input-output process in low-Q cavity QED regime

54. C. Y. Hu, A. Young, J. L. OBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B **78**, 085307 (2008). [CrossRef]

55. 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]

54. C. Y. Hu, A. Young, J. L. OBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B **78**, 085307 (2008). [CrossRef]

55. 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]

*e*〉. The qubit is encoded by different hyperfine levels |0〉 and |1〉. The transition |1〉 ↔ |

*e*〉 for the atom is coupled to the cavity mode

*a*and driven by the input field

*a*, while the state |0〉 is decoupled from the cavity mode due to the large hyperfine splitting. The principle is shown in Fig. 1.

_{in}**79**, 032303 (2009). [CrossRef]

*κ*is large enough to guarantee there is only a weak excitation by the input optical pulse on the atom initially prepared in the ground state. When

*ω*

_{0}denotes the resonant frequency between excited state |

*e*〉 and ground state |1〉.

*ω*and

_{c}*ω*are frequencies of the cavity and the input state, respectively.

_{p}*g*is the atom-cavity coupling strength.

*γ*is the atomic decay rate.

*α*〉 and the atom is prepared in a superposition state

*θ*= arg(

_{i}*r*) (

_{i}*i*= 0, 1) are controlled by

*ω*

_{0},

*ω*,

_{c}*ω*and

_{p}*g*in the case of low-Q cavity (

*κ*≫

*γ*). Obviously, with the input-output process, a phase shift corresponds to the atomic state is generated on the output coherent state. By adjusting

61. F. Mei, Y. F. Yu, X. L. Feng, Z. M. Zhang, and C. H. Oh, “Quantum entanglement distribution with hybrid parity gate,” Phys. Rev. A **82**, 052315 (2010). [CrossRef]

## 3. Atomic entanglement purification using coherent input-output process in low-Q cavity

*ϕ*

^{+}〉

_{a1b1}|

*ϕ*

^{+}〉

_{a2b2}, the evolution of the whole system is

*X*basis measurement on both

*a*2 and

*b*2 atoms with the help of external classical field, respectively, then the original state |

*ϕ*

^{+}〉 can be recovered. In detail, if both the measurement results on Alice’s and Bob’s sides are |+

*X*〉 or |−

*X*〉, they will get the original state |

*ϕ*

^{+}〉 on

*a*1 and

*b*1 atoms. If the results are not in correspondence with each other, they need a phase-flip operation to recover the original state. On the contrary, if Alice and Bob get the result

*ϕ*

^{+}〉 with

*X*basis measurement and phase-flip operation in a similar way.

*ψ*

^{+}〉

_{a1b1}|

*ψ*

^{+}〉

_{a2b2}cannot be discarded as Alice and Bob can not distinguish the two cases that

*a*

_{1}

*b*

_{1}and

*a*

_{2}

*b*

_{2}both contain bit-flip errors. So the two cases |

*ϕ*

^{+}〉

_{a1b1}|

*ϕ*

^{+}〉

_{a2b2}and |

*ψ*

^{+}〉

_{a1b1}|

*ψ*

^{+}〉

_{a2b2}are preserved with probabilities of

*F*

^{2}and (1 −

*F*)

^{2}, respectively. That is, based on the post-selection principle according to the detected results on outgoing coherent states, Alice and Bob can eventually preserved a new mixed state ensemble with a fidelity

*F*′ =

*F*

^{2}/[

*F*

^{2}+ (1 −

*F*)

^{2}], which is larger than

*F*when

15. C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. **76**, 722–725 (1996). [CrossRef] [PubMed]

20. Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A **77**, 042308 (2008). [CrossRef]

*P*= exp(−2|

_{error}*α*|

^{2}). Such detector could be simple photodiode.

*N*rounds and numerically simulated them in Fig. 2(b). We can conclude that it is altered with the increment of

*N*and approximately approaches to 1 when

*N*≥ 4. Phase-flip errors may also occur during the interaction with environment noise. As discussed in Ref. [17

17. J. W. Pan, C. Simon, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) **410**, 1067–1070 (2001). [CrossRef]

18. J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature **423**, 417–422 (2003). [CrossRef] [PubMed]

## 4. Atomic entanglement concentration using coherent input-output process in low-Q cavity

*m*and

*n*beforehand, the ECP can be further simplified with an ancillary particle, by exploiting a previously known protocol in Ref. [33

33. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A **85**, 012307 (2012). [CrossRef]

*a*2 confined in a low-Q cavity

*A*2 on Alice’s side, whose parameters are same as the atom

*a*1 confined in cavity

*A*1 and the initial state is prepared in Based on the parity check operation on

*a*1 and

*a*2 atoms, the evolution of the whole state is

*mn*|

^{2}. Then Alice can perform

*X*basis measurement on the ancillary atom

*a*2. If the measurement result is |+

*X*〉, Alice and Bob will get the original state |

*ϕ*

^{+}〉 on

*a*1 and

*b*1 atoms. If the measurement result is |−

*X*〉, they need a phase-flip operation to recover the original state. On the contrary, if the detected result is

*X*basis measurement and phase-flip operation, which can be seen as another initial state and be concentrated in the next round by preparing a new ancillary atomic state. That is, Alice can iterate the concentration process several rounds to improve the success probability further. We have calculated the success probability in each iteration round and shown them in Fig. 3(b), which is essentially the same as figure 4 in Ref. [33

33. Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A **85**, 012307 (2012). [CrossRef]

*X*basis measurement are only needed on Alice’s side, there is no need to exchange any measurement results with Bob. This greatly simplifies the complication of classical communication. The parity check operation does not consume any entanglement resource, if we define the yield of maximally entangled states

*Y*as the ratio of the number of maximally entangled atom pairs and the number of initial less-entangled atom pairs, this modified ECP can obtain an optimal one.

## 5. Experimental feasibility

*ω*should be set to satisfy this condition when the atom and cavity mode have been adjusted in resonant interaction. Suppose the cavities in our protocols are Fabry-Perot (F-P) cavities, then the atom-cavity coupling strength depends on the atomic position, which can be described as here

_{p}*g*

_{0}is the peak coupling strength,

*r*

_{⊥}is the radial distance of the atoms with respect to the cavity axis,

*ω*and

_{c}*k*are the width and the wave vector of the Gaussian cavity mode, respectively. In 2005, Nu

_{c}*β*mann

*et al.*[63

63. S. Nuβmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. **95**, 173602 (2005). [CrossRef]

^{85}

*Rb*atoms coupled to a high-finesse optical cavity. In 2007, Fortier

*et al.*[64

64. K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. **98**, 233601 (2007). [CrossRef] [PubMed]

^{87}

*Rb*atoms into the cavity by incorporating a deterministic loaded atom conveyor. Colombe

*et al.*[65

65. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature **450**, 272–276 (2007). [CrossRef] [PubMed]

^{87}

*Rb*BEC can be positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field. These excellent experiments have proved that we can manipulate the position of a single atom and tune the atom-cavity coupling strength, and then control the reflectivity of the input coherent state to obtain the desired phase shifts. In our proposed protocols, if

*r*

_{⊥}= 0, the atom-cavity coupling strength

*g*=

*g*

_{0}cos(

*k*) should be matched with the cavity decay rate

_{z}c*κ*as

^{87}

*Rb*atom resonant frequency

*λ*= 780

*nm*. Parameters of the cavity are same as in Ref. [65

65. Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature **450**, 272–276 (2007). [CrossRef] [PubMed]

*L*= 38.6

*μm*, cavity decay rate

*κ*= 2

*π*× 53

*MHz*, peak coupling strength

*g*

_{0}= 2

*π*× 215

*MHz*, finesse

*f*= 37000 which correspond to a longitudinal mode number

*n*= 99. We can estimate the appropriate atomic longitudinal coordinate

*ω*∼

_{c}*ω*

_{0}). The variation of the atomic position in the cavity may lead to the mismatch of the coupling strength (

*θ*

_{0}and

*θ*

_{1}in the coherent state input-output process. We detect the intensity of outgoing coherent state instead of the direct homodyne measurement to overcome this imperfection. Experimental schemes, such as optical lattice [67

67. J. A. Sauer, K. M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman, “Cavity QED with optically transported atoms,” Phys. Rev. A **69**, 051804(R) (2004). [CrossRef]

68. A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. **89**, 103001(2002). [CrossRef] [PubMed]

*η*and the efficiency of the detectors

*η*, the error probability coming from the detections can be defined to

_{D}*P*

_{e1}= exp[−2

*η*(1 −

_{D}*η*)|

*α*|

^{2}]. Moreover, the atomic decay rate

*γ*may also effect the success probability of the protocols. The error probability caused by atomic decay rate in the intermediate coupling region in low-Q cavity is

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

56. 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]

62. F. Mei, Y. F. Yu, X. L. Feng, S. L. Zhu, and Z. M. Zhang, “Optical quantum computation with cavities in the intermediate coupling region,” Europhys. Lett. **91**, 10001 (2010). [CrossRef]

*η*= 0.7,

_{D}*α*= 3, the transmission rate through other optical components is 0.9, then we can numerically simulated the success probability in the present EPP and ECP with respect to

*F*

^{2}+ (1 −

*F*)

^{2}. After considering the error probabilities

*P*

_{e1}and

*P*

_{e2}, the success probability will decrease as shown in Fig. 4(a). However, is does not affect the fidelity of the mixed state based on the post-selection principle. In our ECP, the success probability 2|

*mn*|

^{2}will decrease such as shown in Fig. 4(b), while we can utilize our modified protocol by introducing ancillary atoms in cavity QED to improve the success probability further.

36. M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A **71**, 044302 (2005). [CrossRef]

38. Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A **73**, 014303 (2006). [CrossRef]

40. C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A **75**, 042325 (2007). [CrossRef]

36. M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A **71**, 044302 (2005). [CrossRef]

40. C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A **75**, 042325 (2007). [CrossRef]

## 6. Summary

## Acknowledgments

## References and links

1. | C. H. Bennett, G. Brassard, C. Crepeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and Einstein-Podolsky-Rosen channels,” Phys. Rev. Lett. |

2. | C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett. |

3. | M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A |

4. | A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A |

5. | L. Xiao, G. L. Long, F. G. Deng, and J. W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A |

6. | A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett. |

7. | C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys.Rev. Lett. |

8. | X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A |

9. | G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A |

10. | F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A |

11. | C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A |

12. | X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A |

13. | H, J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. Lett. |

14. | L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature |

15. | C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett. |

16. | D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett. |

17. | J. W. Pan, C. Simon, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London) |

18. | J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature |

19. | C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett. |

20. | Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A |

21. | Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A |

22. | X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A |

23. | F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A |

24. | C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput. |

25. | M. Murao, M. B. Plenio, S. Popescu, V. Vedral, and P. L. Knight, “Multiparticle entanglement purification protocols,” Phys. Rev. A |

26. | F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A |

27. | C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A |

28. | S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A |

29. | B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A |

30. | Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A |

31. | T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A |

32. | Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A |

33. | Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A |

34. | F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A |

35. | M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A |

36. | M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A |

37. | X. L. Feng, L. C. Kwek, and C. H. Oh, “Electronic entanglement purification scheme enhanced by charge detections,” Phys. Rev. A |

38. | Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A |

39. | R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature |

40. | C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A |

41. | C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A |

42. | C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A |

43. | Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A |

44. | J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys. |

45. | S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett. |

46. | L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett. |

47. | Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A |

48. | K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature (London) |

49. | J. Cho and H. W. Lee, “Generation of atomic cluster states through the cavity input-output process,” Phys. Rev. Lett. |

50. | J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darqui, G. Messin, A. Browaeys, and P. Grangier, “Quantum interference between two single photons emitted by independently trapped atoms,” Nature |

51. | H. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and R. Gerhard, “A single-photon server with just one atom,” Nat. Phys. |

52. | T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science |

53. | F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A |

54. | C. Y. Hu, A. Young, J. L. OBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B |

55. | 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 |

56. | Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A |

57. | Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A |

58. | J. J. Chen, J. H. An, M. Feng, and G. Liu, “Teleportation of an arbitrary multipartite state via photonic Faraday rotation,” J. Phys. B |

59. | P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett. |

60. | T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys. |

61. | F. Mei, Y. F. Yu, X. L. Feng, Z. M. Zhang, and C. H. Oh, “Quantum entanglement distribution with hybrid parity gate,” Phys. Rev. A |

62. | F. Mei, Y. F. Yu, X. L. Feng, S. L. Zhu, and Z. M. Zhang, “Optical quantum computation with cavities in the intermediate coupling region,” Europhys. Lett. |

63. | S. Nuβmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett. |

64. | K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett. |

65. | Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature |

66. | B. Dayan, A. S. Parkins, E. Takao Aoki, P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science |

67. | J. A. Sauer, K. M. Fortier, M. S. Chang, C. D. Hamley, and M. S. Chapman, “Cavity QED with optically transported atoms,” Phys. Rev. A |

68. | A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett. |

**OCIS Codes**

(270.0270) Quantum optics : Quantum optics

(270.5568) Quantum optics : Quantum cryptography

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: December 3, 2012

Revised Manuscript: January 17, 2013

Manuscript Accepted: January 18, 2013

Published: February 11, 2013

**Citation**

Cong Cao, Chuan Wang, Ling-yan He, and Ru Zhang, "Atomic entanglement purification and concentration using coherent state input-output process in low-Q cavity QED regime," Opt. Express **21**, 4093-4105 (2013)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-21-4-4093

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### References

- C. H. Bennett, G. Brassard, C. Crepeau, 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]
- C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on Einstein-Podolsky-Rosen states,” Phys. Rev. Lett.69, 2881–2884 (1992). [CrossRef] [PubMed]
- M. Hillery, V. Buzek, and A. Berthiaume, “Quantum secret sharing,” Phys. Rev. A59, 1829–1834 (1999). [CrossRef]
- A. Karlsson, M. Koashi, and N. Imoto, “Quantum entanglement for secret sharing and secret splitting,” Phys. Rev. A59, 162–168 (1999). [CrossRef]
- L. Xiao, G. L. Long, F. G. Deng, and J. W. Pan, “Efficient multiparty quantum-secret-sharing schemes,” Phys. Rev. A69, 052307 (2004). [CrossRef]
- A. K. Ekert, “Quantum cryptography based on Bells theorem,” Phys. Rev. Lett.67, 661–663 (1991). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard, and N. D. Mermin, “Quantum cryptography without Bells theorem,” Phys.Rev. Lett.68, 557–559 (1992). [CrossRef] [PubMed]
- X. H. Li, F. G. Deng, and H. Y. Zhou, “Efficient quantum key distribution over a collective noise channel,” Phys. Rev. A78, 022321 (2008). [CrossRef]
- G. L. Long and X. S. Liu, “Theoretically efficient high-capacity quantum-key-distribution scheme,” Phys. Rev. A65, 032302 (2002). [CrossRef]
- F. G. Deng, G. L. Long, and X. S. Liu, “Two-step quantum direct communication protocol using the Einstein-Podolsky-Rosen pair block,” Phys. Rev. A68, 042317 (2003). [CrossRef]
- C. Wang, F. G. Deng, Y. S. Li, X. S. Liu, and G. L. Long, “Quantum secure direct communication with high-dimension quantum superdense coding,” Phys. Rev. A71, 044305 (2005). [CrossRef]
- X. H. Li, F. G. Deng, and H. Y. Zhou, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. A74, 054302 (2006). [CrossRef]
- H, J. Briegel, W. Dr, J. I. Cirac, and P. Zoller, “Improving the security of secure direct communication based on the secret transmitting order of particles,” Phys. Rev. Lett.81, 5932–5935 (1998).
- L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, “Long-distance quantum communication with atomic ensembles and linear optics,” Nature414, 413–418 (2001). [CrossRef] [PubMed]
- C. H. Bennett, G. Brassard, S. Popescu, B. Schumacher, J. A. Smolin, and W. K. Wootters, “Purification of noisy entanglement and faithful teleportation via noisy channels,” Phys. Rev. Lett.76, 722–725 (1996). [CrossRef] [PubMed]
- D. Deutsch, A. Ekert, R. Jozsa, C. Macchiavello, S. Popescu, and A. Sanpera, “Quantum privacy amplification and the security of quantum cryptography over noisy channels,” Phys. Rev. Lett.77, 2818–2821 (1996). [CrossRef] [PubMed]
- J. W. Pan, C. Simon, and A. Zellinger, “Entanglement purification for quantum communication,” Nature (London)410, 1067–1070 (2001). [CrossRef]
- J. W. Pan, S. Gasparonl, R. Ursin, G. Weihs, and A. zellinger, “Experimental entanglement purification of arbitrary unknown states,” Nature423, 417–422 (2003). [CrossRef] [PubMed]
- C. Simon and J. W. Pan, “Polarization entanglement purification using spatial entanglement,” Phys. Rev. Lett.89, 257901 (2002). [CrossRef] [PubMed]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Efficient polarization-entanglement purification based on parametric down-conversion sources with cross-Kerr nonlinearity,” Phys. Rev. A77, 042308 (2008). [CrossRef]
- Y. B. Sheng and F. G. Deng, “One-step deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A82, 044305 (2010). [CrossRef]
- X. H. Li, “Deterministic polarization-entanglement purification using spatial entanglement,” Phys. Rev. A82, 044304 (2010). [CrossRef]
- F. G. Deng, “One-step error correction for multipartite polarization entanglement,” Phys. Rev. A83, 062316 (2011). [CrossRef]
- C. Wang, Y. Zhang, and G. S. Jin, “Polarization-entanglement purification and concentration using cross-Kerr nonlinearity,” Quantum Inf. Comput.11, 0988–1002 (2011).
- M. Murao, M. B. Plenio, S. Popescu, V. Vedral, and P. L. Knight, “Multiparticle entanglement purification protocols,” Phys. Rev. A57, R4075–R4078 (1998). [CrossRef]
- F. G. Deng, “Efficient multipartite entanglement purification with the entanglement link from a subspace,” Phys. Rev. A84, 052312 (2011). [CrossRef]
- C. H. Bennett, H. J. Bernstein, S. Popescu, and B. Schumacher, “Concentrating partial entanglement by local operations,” Phys. Rev. A53, 2046 (1996). [CrossRef] [PubMed]
- S. Bose, V. Vedral, and P. L. Knight, “Purification via entanglement swapping and conserved entanglement,” Phys. Rev. A60, 194–197 (1999). [CrossRef]
- B. S. Shi, Y. K. Jiang, and G. C. Guo, “Optimal entanglement purification via entanglement swapping,” Phys. Rev. A62, 054301 (2000). [CrossRef]
- Z. Zhao, J. W. Pan, and M. S. Zhan, “Practical scheme for entanglement concentration,” Phys. Rev. A64, 014301 (2001). [CrossRef]
- T. Yamamoto, M. Koashi, and N. Imoto, “Concentration and purification scheme for two partially entangled photon pairs,” Phys. Rev. A64, 012304 (2001). [CrossRef]
- Y. B. Sheng, F. G. Deng, and H. Y. Zhou, “Nonlocal entanglement concentration scheme for partially entangled multipartite systems with nonlinear optics,” Phys. Rev. A77, 062325 (2008). [CrossRef]
- Y. B. Sheng, L. Zhou, S. M. Zhao, and B. Y. Zheng, “Efficient single-photon-assisted entanglement concentration for partially entangled photon pairs,” Phys. Rev. A85, 012307 (2012). [CrossRef]
- F. G. Deng, “Optimal nonlocal multipartite entanglement concentration based on projection measurements,” Phys. Rev. A85, 022311 (2012). [CrossRef]
- M. Yang, W. Song, and Z. L. Cao, “Entanglement purification for arbitrary unknown ionic states via linear optics,” Phys. Rev. A71, 012308 (2005). [CrossRef]
- M. Yang, Y. Zhao, W. Song, and Z. L. Cao, “Entanglement concentration for unknown atomic entangled states via entanglement swapping,” Phys. Rev. A71, 044302 (2005). [CrossRef]
- X. L. Feng, L. C. Kwek, and C. H. Oh, “Electronic entanglement purification scheme enhanced by charge detections,” Phys. Rev. A71, 064301 (2005). [CrossRef]
- Z. L. Cao, L. H. Zhang, and M. Yang, “Concentration for unknown atomic entangled states via cavity decay,” Phys. Rev. A73, 014303 (2006). [CrossRef]
- R. Reichle, D. Leibfried, E. Knill, J. Britton, R. B. Blakestad, J. D. Jost, C. Langer, R. Ozeri, S. Seidelin, and D. J. Wineland, “Experimental purification of two-atom entanglement,” Nature443, 838–841 (2006). [CrossRef] [PubMed]
- C. D. Ogden, M. Paternostro, and M. S. Kim, “Concentration and purification of entanglement for qubit systems with ancillary cavity fields,” Phys. Rev. A75, 042325 (2007). [CrossRef]
- C. Wang, Y. Zhang, and G. S. Jin, “Entanglement purification and concentration of electron-spin entangled states using quantum-dot spins in optical microcavities,” Phys. Rev. A84, 032307 (2011). [CrossRef]
- C. Wang, “Efficient entanglement concentration for partially entangled electrons using a quantum-dot and microcavity coupled system,” Phys. Rev. A86, 012323 (2012). [CrossRef]
- Z. H. Peng, J. Zou, X. J. Liu, Y. J. Xiao, and L. M. Kuang, “Atomic and photonic entanglement concentration via photonic Faraday rotation,” Phys. Rev. A86, 034305 (2012). [CrossRef]
- J. M. Raimond, M. Brune, and S. Haroche, “Manipulating quantum entanglement with atoms and photons in a cavity,” Rev. Mod. Phys.73, 565 (2001). [CrossRef]
- S. Osnaghi, P. Bertet, A. Auffeves, P. Maioli, M. Brune, J. M. Raimond, and S. Haroche, “Coherent control of an atomic collision in a cavity,” Phys. Rev. Lett.87, 037902 (2001). [CrossRef] [PubMed]
- L. M. Duan and H. J. Kimble, “Scalable photonic quantum computation through cavity-assisted interactions,” Phys. Rev. Lett.92, 127902 (2004). [CrossRef] [PubMed]
- Y. F. Xiao, X. M. Lin, J. Gao, Y. Yang, Z. F. Han, and G. C. Guo, “Realizing quantum controlled phase flip through cavity QED,” Phys. Rev. A70, 042314 (2004). [CrossRef]
- K. M. Birnbaum, A. Boca, R. Miller, A. D. Boozer, T. E. Northup, and H. J. Kimble, “Photon blockade in an optical cavity with one trapped atom,” Nature (London)436, 87 (2005). [CrossRef]
- J. Cho and H. W. Lee, “Generation of atomic cluster states through the cavity input-output process,” Phys. Rev. Lett.95, 160501 (2005). [CrossRef] [PubMed]
- J. Beugnon, M. P. A. Jones, J. Dingjan, B. Darqui, G. Messin, A. Browaeys, and P. Grangier, “Quantum interference between two single photons emitted by independently trapped atoms,” Nature440, 779–782 (2006). [CrossRef] [PubMed]
- H. Hijlkema, B. Weber, H. P. Specht, S. C. Webster, A. Kuhn, and R. Gerhard, “A single-photon server with just one atom,” Nat. Phys.3, 253–255 (2007). [CrossRef]
- T. Wilk, S. C. Webster, A. Kuhn, and G. Rempe, “Single-atom single-photon quantum interface,” Science317, 488–490 (2007). [CrossRef] [PubMed]
- F. Mei, M. Feng, Y. F. Yu, and Z. M. Zhang, “Scalable quantum information processing with atomic ensembles and flying photons,” Phys. Rev. A80, 042319 (2009). [CrossRef]
- C. Y. Hu, A. Young, J. L. OBrien, W. J. Munro, and J. G. Rarity, “Giant optical Faraday rotation induced by a single-electron spin in a quantum dot: Applications to entangling remote spins via a single photon,” Phys. Rev. B78, 085307 (2008). [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]
- Q. Chen and M. Feng, “Quantum gating on neutral atoms in low-Q cavities by a single-photon input-output process,” Phys. Rev. A79064304 (2009). [CrossRef]
- Q. Chen and M. Feng, “Quantum-information processing in decoherence-free subspace with low-Q cavities,” Phys. Rev. A82052329 (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. B43, 095505 (2010). [CrossRef]
- P. van Loock, T. D. Ladd, K. Sanaka, F. Yamaguchi, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater using bright coherent light,” Phys. Rev. Lett.96, 240501 (2006). [CrossRef] [PubMed]
- T. D. Ladd, P. van Loock, K. Nemoto, W. J. Munro, and Y. Yamamoto, “Hybrid quantum repeater based on dispersive CQED interactions between matter qubits and bright coherent light,” New J. Phys.8, 184 (2006). [CrossRef]
- F. Mei, Y. F. Yu, X. L. Feng, Z. M. Zhang, and C. H. Oh, “Quantum entanglement distribution with hybrid parity gate,” Phys. Rev. A82, 052315 (2010). [CrossRef]
- F. Mei, Y. F. Yu, X. L. Feng, S. L. Zhu, and Z. M. Zhang, “Optical quantum computation with cavities in the intermediate coupling region,” Europhys. Lett.91, 10001 (2010). [CrossRef]
- S. Nuβmann, M. Hijlkema, B. Weber, F. Rohde, G. Rempe, and A. Kuhn, “Submicron positioning of single atoms in a microcavity,” Phys. Rev. Lett.95, 173602 (2005). [CrossRef]
- K. M. Fortier, S. Y. Kim, M. J. Gibbons, P. Ahmadi, and M. S. Chapman, “Deterministic loading of individual atoms to a high-finesse optical cavity,” Phys. Rev. Lett.98, 233601 (2007). [CrossRef] [PubMed]
- Y. Colombe, T. Steinmetz, G. Dubois, F. Linke, D. Hunger, and J. Reichel, “Strong atom-field coupling for Bose-Einstein condensates in an optical cavity on a chip,” Nature450, 272–276 (2007). [CrossRef] [PubMed]
- B. Dayan, A. S. Parkins, E. Takao Aoki, P. Ostby, K. J. Vahala, and H. J. Kimble, “A photon turnstile dynamically regulated by one atom,” Science319, 1062–1065 (2008). [CrossRef] [PubMed]
- 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]
- A. B. Mundt, A. Kreuter, C. Becher, D. Leibfried, J. Eschner, F. Schmidt-Kaler, and R. Blatt, “Coupling a single atomic quantum bit to a high finesse optical cavity,” Phys. Rev. Lett.89, 103001(2002). [CrossRef] [PubMed]

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