## Deterministic generation of multiparticle entanglement in a coupled cavity-fiber system |

Optics Express, Vol. 19, Issue 2, pp. 1207-1216 (2011)

http://dx.doi.org/10.1364/OE.19.001207

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### Abstract

We develop a one-step scheme for generating multiparticle entangled states between two cold atomic clouds in distant cavities coupled by an optical fiber. We show that, through suitably choosing the intensities and detunings of the fields and precisely tuning the time evolution of the system, multiparticle entanglement between the separated atomic clouds can be engineered deterministically, in which quantum manipulations are insensitive to the states of the cavity and losses of the fiber. The experimental feasibility of this scheme is analyzed based on recent experimental advances in the realization of strong coupling between cold ^{87}Rb clouds and fiber-based cavity. This scheme may open up promising perspectives for implementing quantum communication and networking with coupled cavities connected by optical fibers.

© 2011 Optical Society of America

## 1. Introduction

*and |111···111〉*

_{j}*(*

_{j}*N*terms) are product states describing

*N*atoms in the j

*th*cavity which are all in the (same) internal state |0〉 or |1〉. This method can be implemented in one step and in a deterministic fashion. Through suitably choosing the intensities and detunings of the fields and precisely controlling the dynamics of the system, the target entangled states can be engineered, which are immune to the spontaneous emission of the atoms and losses of the fiber, and independent of the states of the cavities. As an application, we also discuss how to use the produced entangled atomic state |

*ψ*〉 to generate the so called NOON state of the cavity modes [30

_{s}30. K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. **99**, 053602 (2007). [CrossRef] [PubMed]

*n*〉

*(*

_{j}*j*= 1, 2) is Fock state for the respective cavity mode. This state is important for quantum lithography and Heisenberg-limited interferometry with photons. We should emphasize that the NOON state, which is mode-entangled, is different from the multiparticle atomic entangled states proposed in this scheme. The generated NOON state in itself is a two-mode entangled state, in which the entanglement is between two different cavity modes. However, the generated atomic entangled states are particle-entangled. The experimental feasibility and technical demands of this scheme are analyzed based on recent experimental advances in the strong coupling between cold

^{87}Rb clouds and fiber-based cavity. Implementing the proposal in experiment would be an important step toward quantum communication and networking with atomic clouds in distant cavities connected by optical fibers.

## 2. Generation of the entangled states

*lν*̄/2

*πc*, where

*l*is the length of the fiber and

*ν*̄ is the decay rate of the cavity fields into the continuum of the fiber modes. If we consider the short fiber limit

*lν*̄/2

*πc*≤ 1, then only one resonant mode

*b*of the fiber interacts with the cavity modes [24

24. A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. **96**, 010503 (2006). [CrossRef] [PubMed]

*ν*is the cavity-fiber coupling strength, and

*φ*is the phase due to propagation of the field through the fiber. Define three normal bosonic modes

*c*,

*c*

_{1},

*c*

_{2}by the canonical transformations

24. A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. **96**, 010503 (2006). [CrossRef] [PubMed]

*c*,

*c*

_{1}and

*c*

_{2}, the interaction Hamiltonian ℋ

_{c,f}is diagonal. We rewrite this Hamiltonian as

_{0}+ ℋ

_{1}.

*e*

^{iℋ0t}, which leads to

*e*

^{i𝒱0t}, with

*β*| ≫ |

*δ*|, |Λ|, |

*ν*|, we can bring the effective Hamiltonian (5) to a new form under the rotating-wave approximation [14

14. E. Solano, G. S. Agarwal, and H. Walther, “Strong-driving-assisted multipartite entanglement in cavity QED,” Phys. Rev. Lett. **90**, 027903 (2003). [CrossRef] [PubMed]

*ν*| ≫ {|

*δ*|, |Λ|}, we can take the rotating-wave approximation and safely neglect the nonresonant modes

*c*

_{1},

*c*

_{2}. At present, we can obtain the effective Hamiltonian with

*c*has no contribution from the fiber mode

*b*, the system gets in this instance insensitive to fiber losses. By using the magnus formula, the evolution operator 𝒰 (

*t*) is found as [33

33. A. Sørensen and K. Mølmer, “Entanglement and quantum computation with ions in thermal motion,” Phys. Rev. A **62**, 022311 (2000). [CrossRef]

34. S. L. Zhu, Z. D. Wang, and P. Zanardi, “Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity,” Phys. Rev. Lett. **94**, 100502 (2005). [CrossRef] [PubMed]

*γ*(

*t*) = −(Θ

^{2}/4

*δ*

^{2})(

*δt*− sin

*δt*), and

*α*(

*t*) = (Θ/2

*δ*)(1 −

*e*)

^{iδt}*e*

^{iθ0}. If the interaction time

*τ*satisfies

*δτ*= 2

*Kπ*, the evolution operator for the interaction Hamiltonian (7) can be expressed as where

*λ*= −Θ

^{2}/4

*δ*. Note that as this operator has no contribution from the cavity modes, thus in this instance the system gets insensitive to the states of the cavity modes, which allows the cavity modes to be in a thermal state.

_{1}, and in the second cavity is |111···111〉

_{2}. We now show how to prepare the multiatom maximally entangled state

*J*,

*M*〉 which is an eigenstate of the

*S*operator [35

_{z}35. K. Mølmer and A. Sørensen, “Multiparticle entanglement of hot trapped ions,” Phys. Rev. Lett. **82**, 1835–1838 (1999). [CrossRef]

*N*/2,−

*N*/2〉 and |

*N*/2,

*N*/2〉. Alternatively, we can expand the initial states in terms of the eigenstates of

*S*:|

_{x}*N*/2,−

*N*/2〉 = Σ

*c*|

_{M}*N*/2,

*M*〉

*and |*

_{x}*N*/2,

*N*/2〉 = Σ

*c*(−1)

_{M}^{N/2−M}|

*N*/2,

*M*〉

*. Then we can express the initial state of the whole system as |*

_{x}*N*/2,−

*N*/2〉

_{1}|

*N*/2,

*N*/2〉

_{2}= Σ[

*c*

_{M1cM2}(−1)

^{N/2−M2}|

*N/*2,

*M*

_{1}〉

*|*

_{x}*N*/2,

*M*

_{2}〉

*]. After applying the evolution operator*

_{x}*U*(

*τ*), the final state will be If we choose

*λτ*=

*π*/2, then we have

*τ*), the final state will be If we choose

*λτ*=

*π*/2, then we have

*N*is odd or even, which is quite different from previous studies [33

33. A. Sørensen and K. Mølmer, “Entanglement and quantum computation with ions in thermal motion,” Phys. Rev. A **62**, 022311 (2000). [CrossRef]

34. S. L. Zhu, Z. D. Wang, and P. Zanardi, “Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity,” Phys. Rev. Lett. **94**, 100502 (2005). [CrossRef] [PubMed]

*N*00

*N*〉. It is known that these entangled states are important for quantum lithography and Heisenberg-limited interferometry with photons. Using the generated atomic entangled state |

*ψ*〉, we wish to produce the state |

_{s}*N*00

*N*〉. To this aim, we employ the stimulated Raman transitions between the atomic ground states |0〉 and |1〉. After preparing the two atomic clouds in the target entangled state |

*ψ*〉, we switch off the driving laser fields of frequencies

_{s}*ω*

_{1},

*ω*

_{2}and the couplings of the cavity modes to the fiber modes. Then we have two entangled atomic clouds trapped in two separated cavities, where the couplings of the atoms to the driving laser field and cavity modes are the type. Starting from the state

*→ |111···111〉|*

_{j}*N*〉

*.*

_{j}## 3. Technical considerations

^{87}Rb atoms cooled in the |

*F*= 1〉 ground state and trapped inside an optical cavity, this cloud can be prepared in the |

*F*= 2〉 ground state employing either the optical pumping or adiabatic population transfer techniques [36

36. K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. **70**, 1003–1025 (1997). [CrossRef]

^{87}Rb atoms positioned deterministically anywhere within the cavity and localized entirely within a single antinode of the standing-wave cavity field [20

20. 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 (London) **450**, 272–276 (2007). [CrossRef]

*ρ*(

**r**) is the atomic density distribution,

*z*and

*r*

_{⊥}are respectively the longitudinal and transverse atomic coordinates, and

*w*and

*k*are respectively the mode radius and wave vector). For a Gaussian cloud centered on a single lattice site with

_{c}*N*< 10

^{3}, in which the distribution can be considered point-like, an average atom-field coupling strength

*ḡ*/2

*π*≃ 200 MHz can be obtained [20

20. 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 (London) **450**, 272–276 (2007). [CrossRef]

*δg*/

*ḡ*≪ 1, or

*k*≪ 1 and

_{c}δz*δr*

_{⊥}≪

*w*. Therefore, under these conditions all the atoms in the cavity have the nearly same coupling strength and then collectively interact with the cavity field. On the other hand, to avoid the direct interaction between the atoms being in the ground state, the mean atom-atom distance should be larger than the radius of the atom in the ground state. For a combined trap with the shape of flat disk employed in the experiment, the mean atom-atom distance may be estimated as

*ns*state. The orbit radius of the valence electron is approximately as

*r*∼

_{g}*n*

^{2}

*a*

_{0}, where

*a*

_{0}is the Bohr radius. This imposes a condition on the atomic number, i.e.,

*n*= 5,

*δr*

_{⊥}≃ 2

*μ*m, when

*N*< 10

^{3}, we have

*d ≫ r*, which implies the single-particle approximation or no-direct interaction condition is valid.

_{g}*E⃗*= ℰ⃗

_{t}_{i}

*e*

^{i[k⃗i⋅r⃗−ωit]}(

*i*= 0, 1, 2, 3). Then the actual coupling coefficients between the atoms and the laser fields have the spatial phases

*e*

^{ik⃗i⋅r⃗n}for the individual atom with the position coordinate

*r⃗*. Therefore, the effective Hamiltonian (2) should be in a more general form as After performing a time-independent unitary transformation

_{n}37. I. E. Linington and N. V. Vitanov, “Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage,” Phys. Rev. A **77**, 062327 (2008). [CrossRef]

*k⃗*

_{3}−

*k⃗*

_{1}+

*k⃗*

_{2}= 0, then the spatial phase terms will not appear in the effective Hamiltonian. Thus our discussion in the above section still holds. The only difference is that the state vector for each atom should be redefined as

37. I. E. Linington and N. V. Vitanov, “Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage,” Phys. Rev. A **77**, 062327 (2008). [CrossRef]

*r⃗*≈

_{n}*R̄*+

*δr*, and the deviation from the mean position is much smaller than the wavelength of the laser—Lamb-Dicke regime, i.e.,

_{n}*δ r*≪

_{n}*λ*, then the spatial phase terms are global and can be absorbed into the complex Rabi frequencies.

_{L}_{0}= 100|

*g*

_{0}|, Δ

_{1}= − 100|

*g*

_{0}|, |Ω

_{0}| = |

*g*

_{0}|, |Ω

_{1}| = 10|

*g*

_{0}|, |Ω

_{2}| = 10|

*g*

_{0}|,

*ν*= 0.1|

*g*

_{0}|,

*δ*= 0.01|

*g*

_{0}|. The probability for the Raman transition |0〉 ↔ |1〉 induced by the classical field and the normal modes

*c*

_{1},

*c*

_{2}is on the order of 𝒫

*∼ |Ω*

_{f}_{0}

*g*

_{0}|

^{2}/(Δ

_{0}

*ν*)

^{2}. For fiber loss at a rate

*κ*, we get the effective loss rate Γ

_{f}*=*

_{f}*κ*|Ω

_{f}_{0}

*g*

_{0}|

^{2}/(Δ

_{0}

*ν*)

^{2}∼ 0.01

*κ*. The occupation of the excited state |

_{f}*e*〉 can be estimated to be 𝒫

*∼ |Ω*

_{e}_{1}|

^{2}/|Δ

_{1}|

^{2}. Spontaneous emission from the excited state at a rate

*γ*thus leads to the effective decay rate Γ

_{e}*=*

_{e}*γ*|Ω

_{e}_{1}|

^{2}/|Δ

_{1}|

^{2}∼ 0.01

*γ*. For this proposal, the probability for cavity excitation can be estimated as

_{e}*κ*, this leads to an effective decay rate

_{c}*ô*] = 2

*ôρô*

^{†}−

*ô*

^{†}

*ôρ*−

*ρô*

^{†}

*ô*. To solve the master equation numerically, we have used the Monte Carlo wave function formalism from the quantum trajectory method [38

38. R. Schack and T. A. Brun, “A C++ library using quantum trajectories to solve quantum master equations,” Comput. Phys. Commun. **102**, 210–228 (1997). [CrossRef]

*F*= 〉

*ψ*|

_{f}*ρ*|

_{a}*ψ*〉, where

_{f}*ρ*is the final reduced density matrix of the atoms, under different values for the parameter

_{a}*κ*. The atomic system starts from the joint ground state |000···000〉 in each cavity. Figures 2(a) and (b) show the calculated populations, coherences, and fidelity for the case of two atoms trapped in each cavity. We can see that (Fig. 2(a)) at the time

_{c}*τ*= 2

*π*/

*δ*the state (13) is obtained with a fidelity higher than 99% in the relatively strong coupling regime. However, from Fig. 2(c) and (d), we find that, for the larger number of atoms even the same cavity decay rate leads to more pronounced degradation of the generated state. It seems that for large number of atoms the produced entangled states are much easier to be spoiled by losses, i.e., off-diagonal elements of the atomic density matrix may decay more rapidly. Therefore, for a cloud containing a few hundred of atoms, to generate the target entangled states with a high fidelity may demand more stringent conditions.

20. 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 (London) **450**, 272–276 (2007). [CrossRef]

22. D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. **12**065038 (2010). [CrossRef]

^{87}Rb, with the ground states |0〉 and |1〉 corresponding to the |5

*S*

_{1/2}〉 hyperfine levels, and the excited state |

*e*〉 corresponding to the |5

*P*

_{1/2}〉 sub-states. It is noted that the strong coupling of cold

^{87}Rb clouds with the fiber-based cavity has been realized in recent experiments [20

**450**, 272–276 (2007). [CrossRef]

22. D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. **12**065038 (2010). [CrossRef]

*g*

_{0}|/2

*π*= 10.6MHZ to |

*g*

_{0}|/2

*π*= 215MHz. We choose the cavity QED parameters as those in Ref. [20

**450**, 272–276 (2007). [CrossRef]

*g*

_{0}|/2

*π*= 215MHz,

*κ*/2

*π*= 53MHz,

*γ*/2

*π*= 3MHz. Other experimental parameters can be chosen as Δ

_{0}/2

*π*= 20GHz, Δ

_{1}/2

*π*= −20GHz,Δ

_{3}/2

*π*= 40GHz, |Ω

_{0}|/2

*π*= 200MHz,|Ω

_{1}|/2

*π*= 2GHz, |Ω

_{2}|/2

*π*= 2GHz, |Ω

_{3}|/2

*π*= 3GHz,

*ν*/2

*π*= 20MHz,

*δ*/2

*π*= 2MHz. The fiber length can be chosen as

*L*≲ 1m in most realistic experimental situations. With the chosen parameters, for a few hundred of cold atoms trapped in the cavity, the time to prepare the entangled state

*τ*∼ 0.5

*μ*s.

## 4. Conclusions

^{87}Rb clouds and fiber-based cavity. We have also discussed how to use the generated multiatom states to produce the NOON state for the two cavities. Experimental implementation of this proposal may offer a promising platform for implementing long-distance quantum communications with atomic clouds trapped in separated cavities connected by optical fibers.

## Acknowledgments

## References and links

1. | J. S. Bell, “On the einstein-podolsky-rosen paradox,” Phys. |

2. | D. M. Greenberger, M.A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. |

3. | M. A. Nielsen and I. L. Chuang, |

4. | W. Dur, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A |

5. | H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. |

6. | For a review see, K. Hammerer, A. S. Sorensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. |

7. | For a review see, L.-M. Duan and C. Monroe, “Colloquium: Quantum networks with trapped ions,” Rev. Mod. Phys. |

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

9. | For a review see, D. Jaksch and P. Zoller, “The cold atom Hubbard toolbox,” Ann. Phys. |

10. | H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. |

11. | H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in Context,” Science |

12. | J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. |

13. | A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. |

14. | E. Solano, G. S. Agarwal, and H. Walther, “Strong-driving-assisted multipartite entanglement in cavity QED,” Phys. Rev. Lett. |

15. | P.-B. Li, Y. Gu, Q.-H. Gong, and G.-C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A |

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

17. | P.-B. Li, Y. Gu, Q.-H. Gong, and G.-C. Guo, “Generation of two-mode entanglement between separated cavities,” J. Opt. Soc. Am. B |

18. | S. Kang, Y. Choi, S. Lim, W. Kim, J.-R. Kim, J.-H. Lee, and K. An, “Continuous control of the coupling constant in an atom-cavity system by using elliptic polarization and magnetic sublevels,” Opt. Express. |

19. | H. J. Kimble, “The quantum internet,” Nature (London) |

20. | 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 (London) |

21. | M. Trupke, E. A. Hinds, S. Eriksson, E. A. Curtis, Z. Moktadir, E. Kukharenka, and M. Kraft, “Microfabricated high-finesse optical cavity with open access and small volume,” Appl. Phys. Lett. |

22. | D. Hunger, T. Steinmetz, Y. Colombe, C. Deutsch, T. W. Hansch, and J. Reichel, “A fiber Fabry-Perot cavity with high finesse,” New J. Phys. |

23. | T. Pellizzari, “Quantum networking with optical fibres,” Phys. Rev. Lett. |

24. | A. Serafini, S. Mancini, and S. Bose, “Distributed quantum computation via optical fibers,” Phys. Rev. Lett. |

25. | Z. Q. Yin and F. L. Li, “Multiatom and resonant interaction scheme for quantum state transfer and logical gates between two remote cavities via an optical fiber,” Phys. Rev. A |

26. | P. Peng and F. L. Li, “Entangling two atoms in spatially separated cavities through both photon emission and absorption processes,” Phys. Rev. A |

27. | Y. L. Zhou, Y. M. Wang, L. M. Liang, and C. Z. Li, “Quantum state transfer between distant nodes of a quantum network via adiabatic passage,” Phys. Rev. A |

28. | J. Busch and A. Beige, “Generating single-mode behavior in fiber-coupled optical cavities,” arXiv:1009.1011v2 (2010). |

29. | X.-Y. Lu, P.-J. Song, J.-B. Liu, and X. Yang, “N-qubit W state of spatially separated single molecule magnets,” Opt. Express |

30. | K. T. Kapale and J. P. Dowling, “Bootstrapping approach for generating maximally path-entangled photon states,” Phys. Rev. Lett. |

31. | T. Brandes, “Coherent and collective quantum optical effects in mesoscopic systems,” Phys. Rep. |

32. | D. F. V. James, “Quantum computation with hot and cold ions: an assessment of proposed schemes,” Fortschr. Phys. |

33. | A. Sørensen and K. Mølmer, “Entanglement and quantum computation with ions in thermal motion,” Phys. Rev. A |

34. | S. L. Zhu, Z. D. Wang, and P. Zanardi, “Geometric quantum computation and multiqubit entanglement with superconducting qubits inside a cavity,” Phys. Rev. Lett. |

35. | K. Mølmer and A. Sørensen, “Multiparticle entanglement of hot trapped ions,” Phys. Rev. Lett. |

36. | K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. |

37. | I. E. Linington and N. V. Vitanov, “Decoherence-free preparation of Dicke states of trapped ions by collective stimulated Raman adiabatic passage,” Phys. Rev. A |

38. | R. Schack and T. A. Brun, “A C++ library using quantum trajectories to solve quantum master equations,” Comput. Phys. Commun. |

**OCIS Codes**

(270.5580) Quantum optics : Quantum electrodynamics

(270.5585) Quantum optics : Quantum information and processing

**ToC Category:**

Quantum Optics

**History**

Original Manuscript: October 26, 2010

Revised Manuscript: November 15, 2010

Manuscript Accepted: November 26, 2010

Published: January 11, 2011

**Citation**

Peng-Bo Li and Fu-Li Li, "Deterministic generation of multiparticle entanglement in a coupled cavity-fiber system," Opt. Express **19**, 1207-1216 (2011)

http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-2-1207

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### References

- J. S. Bell, “On the einstein-podolsky-rosen paradox,” Phys. 1, 195–200 (1964).
- D. M. Greenberger, M. A. Horne, A. Shimony, and A. Zeilinger, “Bell’s theorem without inequalities,” Am. J. Phys. 58, 1131–1143 (1990). [CrossRef]
- M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University Press, Cambridge 2000).
- W. Dur, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000). [CrossRef]
- H. J. Briegel and R. Raussendorf, “Persistent entanglement in arrays of interacting particles,” Phys. Rev. Lett. 86, 910–913 (2001). [CrossRef] [PubMed]
- For a review see,K. Hammerer, A. S. Sorensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010) (and references therein). [CrossRef]
- For a review see, L.-M. Duan, and C. Monroe, “Colloquium: Quantum networks with trapped ions,” Rev. Mod. Phys. 82, 1209–1224 (2010) (and references therein). [CrossRef]
- R. Blatt and D. Wineland, “Entangled states of trapped atomic ions,” Nature 453, 1008–1015 (2008). [CrossRef]
- For a review see, D. Jaksch, and P. Zoller, “The cold atom Hubbard toolbox,” Ann. Phys. 315, 52–79 (2005) (and references therein). [CrossRef]
- H. J. Kimble, “Strong interactions of single atoms and photons in cavity QED,” Phys. Scr. T 76, 127–137 (1998). [CrossRef]
- H. Mabuchi and A. C. Doherty, “Cavity quantum electrodynamics: coherence in Context,” Science 298, 1372–1377 (2002). [CrossRef] [PubMed]
- J. I. Cirac, P. Zoller, H. J. Kimble, and H. Mabuchi, “Quantum state transfer and entanglement distribution among distant nodes in a quantum network,” Phys. Rev. Lett. 78, 3221–3224 (1997). [CrossRef]
- A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Reversible state transfer between light and a single trapped atom,” Phys. Rev. Lett. 98, 193601 (2007).
- E. Solano, G. S. Agarwal, and H. Walther, “Strong-driving-assisted multipartite entanglement in cavity QED,” Phys. Rev. Lett. 90, 027903 (2003). [CrossRef] [PubMed]
- P.-B. Li, Y. Gu, Q.-H. Gong, and G.-C. Guo, “Quantum-information transfer in a coupled resonator waveguide,” Phys. Rev. A 79, 042339 (2009). [CrossRef]
- 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]
- P.-B. Li, Y. Gu, Q.-H. Gong, and G.-C. Guo, “Generation of two-mode entanglement between separated cavities,” J. Opt. Soc. Am. B 26, 189–193 (2009). [CrossRef]
- S. Kang, Y. Choi, S. Lim, W. Kim, J.-R. Kim, J.-H. Lee, and K. An, “Continuous control of the coupling constant in an atom-cavity system by using elliptic polarization and magnetic sublevels,” Opt. Express 18, 9286–9302 (2010). [CrossRef] [PubMed]
- H. J. Kimble, “The quantum internet,” Nature 453, 1023–1030 (2008). [CrossRef]
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