Abstract

We propose a scheme for dissipative preparation of W-type entangled steady states of three atoms trapped in an optical cavity. The scheme is based on the competition between the decay processes into and out of the target state. By suitable choice of system parameters, we resolve the whole evolution process and employ the effective operator formalism to engineer four independent decay processes so that the target state becomes the stationary state of the quantum system. The scheme requires neither the preparation of definite initial states nor precise control of system parameters and preparation time.

© 2012 Optical Society of America

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    [CrossRef]
  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]
  3. 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]
  4. 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).
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  5. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).
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    [CrossRef]
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  14. A. F. Alharbi, and Z. Ficek, “Deterministic creation of stationary entangled states by dissipation,” Phys. Rev. A 82, 054103 (2010).
    [CrossRef]
  15. L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
    [CrossRef]
  16. J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
    [CrossRef]
  17. H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
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  18. B. S. Shi, and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  24. W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
    [CrossRef]
  25. X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
    [CrossRef]
  26. G. C. Guo, and Y. S. Zhang, “Scheme for preparation of the W state via cavity quantum electrodynamics,” Phys. Rev. A 65, 054302 (2002).
    [CrossRef]
  27. S. B. Zheng, “Scalable generation of multi-atom W states with a single resonant interaction,” J. Opt. B 7, 10–13 (2005).
    [CrossRef]
  28. X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
    [CrossRef]
  29. R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
    [CrossRef]
  30. A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
    [CrossRef]
  31. A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
    [CrossRef]
  32. A. S. Sørensen, and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
    [CrossRef]

2012 (1)

F. Reiter, and A. S. Sørensen, “Effective operator formalism for open quantum systems,” Phys. Rev. A 85, 032111 (2012).
[CrossRef]

2011 (8)

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

E. D. Valle, “Steady-state entanglement of two coupled qubits,” J. Opt. Soc. Am. B 28, 228–235 (2011).
[CrossRef]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[CrossRef]

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
[CrossRef]

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

L. Memarzadeh, and S. Mancini, “Stationary entanglement achievable by environment-induced chain links,” Phys. Rev. A 83, 042329 (2011).
[CrossRef]

K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, “Entanglement distillation by dissipation and continuous quantum repeaters,” Phys. Rev. Lett. 107, 120502 (2011).
[CrossRef]

2010 (2)

A. F. Alharbi, and Z. Ficek, “Deterministic creation of stationary entangled states by dissipation,” Phys. Rev. A 82, 054103 (2010).
[CrossRef]

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

2008 (1)

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

2006 (2)

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
[CrossRef]

2005 (2)

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

S. B. Zheng, “Scalable generation of multi-atom W states with a single resonant interaction,” J. Opt. B 7, 10–13 (2005).
[CrossRef]

2004 (3)

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

2003 (2)

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

A. S. Sørensen, and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef]

2002 (2)

B. S. Shi, and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[CrossRef]

G. C. Guo, and Y. S. Zhang, “Scheme for preparation of the W state via cavity quantum electrodynamics,” Phys. Rev. A 65, 054302 (2002).
[CrossRef]

2000 (2)

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (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]

1998 (1)

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[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]

1992 (1)

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]

1991 (1)

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

Alharbi, A. F.

A. F. Alharbi, and Z. Ficek, “Deterministic creation of stationary entangled states by dissipation,” Phys. Rev. A 82, 054103 (2010).
[CrossRef]

Becher, C.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Beige, A.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Benhelm, J.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Bennett, C. H.

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]

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]

Bialczak, R. C.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Birnbaum, K. M.

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Blatt, R.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Boca, A.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Boozer, A. D.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Bose, S.

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
[CrossRef]

Bourennane, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Brassard, G.

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]

Bruss, D.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Busch, J.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Chen, X.-Y.

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

Cho, J.

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
[CrossRef]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Cirac, J. I.

K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, “Entanglement distillation by dissipation and continuous quantum repeaters,” Phys. Rev. Lett. 107, 120502 (2011).
[CrossRef]

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Cleland, A. N.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Crépeau, C.

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]

De, S.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

DiVincenzo, D. P.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Dür, W.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Eibl, M.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Ekert, A.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Ekert, A. K.

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

Feng, M.

X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
[CrossRef]

Ficek, Z.

A. F. Alharbi, and Z. Ficek, “Deterministic creation of stationary entangled states by dissipation,” Phys. Rev. A 82, 054103 (2010).
[CrossRef]

Fuchs, C. A.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Gao, K. L.

X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
[CrossRef]

Gorbachev, V. N.

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

Guo, G. C.

G. C. Guo, and Y. S. Zhang, “Scheme for preparation of the W state via cavity quantum electrodynamics,” Phys. Rev. A 65, 054302 (2002).
[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]

Häffner, H.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Hänsel, W.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Ivanov, S. S.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Jensen, K.

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[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]

Kastoryano, M. J.

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[CrossRef]

Kiesel, N.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Kim, M. S.

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
[CrossRef]

Kimble, H. J.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Koch, M.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Krauter, H.

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

Kubanek, A.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Kurtsiefer, C.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Lancaster, G. P. T.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Lenander, M.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Lucero, E.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Machiavello, C.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Mancini, S.

L. Memarzadeh, and S. Mancini, “Stationary entanglement achievable by environment-induced chain links,” Phys. Rev. A 83, 042329 (2011).
[CrossRef]

Mariantoni, M.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Martinis, J. M.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Mathis, W.

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

Memarzadeh, L.

L. Memarzadeh, and S. Mancini, “Stationary entanglement achievable by environment-induced chain links,” Phys. Rev. A 83, 042329 (2011).
[CrossRef]

Miller, R.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Mølmer, K.

A. S. Sørensen, and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef]

Murr, K.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Muschik, C. A.

K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, “Entanglement distillation by dissipation and continuous quantum repeaters,” Phys. Rev. Lett. 107, 120502 (2011).
[CrossRef]

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

Neeley, M.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Nielsen, M. A.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Northup, T. E.

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

O’Connell, A. D.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Ourjoumtsev, A.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Pahlke, K.

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

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]

Petersen, J. M.

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

Pinkse, P. W. H.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Polzik, E. S.

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

Reiter, F.

F. Reiter, and A. S. Sørensen, “Effective operator formalism for open quantum systems,” Phys. Rev. A 85, 032111 (2012).
[CrossRef]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[CrossRef]

Rempe, G.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Riebe, M.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Rodichkina, A. A.

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

Roos, C. F.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Sank, D.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Schirmer, S. G.

X. T. Wang, and S. G. Schirmer, “Generating maximal entanglement between non-interacting atoms by collective decay and symmetry breaking,” http://arxiv.org/abs/1005.2114 .

Schmidt-Kaler, F.

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Schuster, I.

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

Shen, L. T.

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

Shi, B. S.

B. S. Shi, and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[CrossRef]

Smolin, J. A.

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

Sørensen, A. S.

F. Reiter, and A. S. Sørensen, “Effective operator formalism for open quantum systems,” Phys. Rev. A 85, 032111 (2012).
[CrossRef]

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[CrossRef]

A. S. Sørensen, and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef]

Spiller, T. P.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Tomita, A.

B. S. Shi, and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[CrossRef]

Torosov, B. T.

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Trubilko, A. I.

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

Valle, E. D.

Vidal, G.

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

Vollbrecht, K. G. H.

K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, “Entanglement distillation by dissipation and continuous quantum repeaters,” Phys. Rev. Lett. 107, 120502 (2011).
[CrossRef]

Wang, H.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Wang, X. T.

X. T. Wang, and S. G. Schirmer, “Generating maximal entanglement between non-interacting atoms by collective decay and symmetry breaking,” http://arxiv.org/abs/1005.2114 .

Wasilewski, W.

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

Weides, M.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Weinfurter, H.

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Wenner, J.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Wiesner, S. J.

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]

Wootters, W. K.

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]

Wu, H.-Z.

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

Yamamoto, T.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Yang, Z.-B.

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

Yin, Y.

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Zhang, X. L.

X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
[CrossRef]

Zhang, Y. S.

G. C. Guo, and Y. S. Zhang, “Scheme for preparation of the W state via cavity quantum electrodynamics,” Phys. Rev. A 65, 054302 (2002).
[CrossRef]

Zheng, S. B.

S. B. Zheng, “Scalable generation of multi-atom W states with a single resonant interaction,” J. Opt. B 7, 10–13 (2005).
[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]

Zheng, S.-B.

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

Zhiliba, A. I.

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

Zou, X. B.

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

J. Opt. B (1)

S. B. Zheng, “Scalable generation of multi-atom W states with a single resonant interaction,” J. Opt. B 7, 10–13 (2005).
[CrossRef]

J. Opt. Soc. Am. B (1)

J. Phys. B (1)

R. Miller, T. E. Northup, K. M. Birnbaum, A. Boca, A. D. Boozer, and H. J. Kimble, “Trapped atoms in cavity QED: coupling quantized light and matter,” J. Phys. B 38, S551–S565 (2005).
[CrossRef]

Nature (1)

M. Neeley, R. C. Bialczak, M. Lenander, E. Lucero, M. Mariantoni, A. D. O’Connell, D. Sank, H. Wang, M. Weides, J. Wenner, Y. Yin, T. Yamamoto, A. N. Cleland, and J. M. Martinis, “Generation of three-qubit entangled states using superconducting phase qubits,” Nature 467, 570–573 (2010).
[CrossRef]

Phys. Lett. A (2)

B. S. Shi, and A. Tomita, “Teleportation of an unknown state by W state,” Phys. Lett. A 296, 161–164 (2002).
[CrossRef]

V. N. Gorbachev, A. I. Trubilko, A. A. Rodichkina, and A. I. Zhiliba, “Can the states of the W-class be suitable for teleportation?” Phys. Lett. A 314, 267–271 (2003).
[CrossRef]

Phys. Rev. A (10)

D. Bruss, D. P. DiVincenzo, A. Ekert, C. A. Fuchs, C. Machiavello, and J. A. Smolin, “Optimal universal and state-dependent quantum cloning,” Phys. Rev. A 57, 2368–2378 (1998).
[CrossRef]

W. Dür, G. Vidal, and J. I. Cirac, “Three qubits can be entangled in two inequivalent ways,” Phys. Rev. A 62, 062314 (2000).
[CrossRef]

X. B. Zou, K. Pahlke, and W. Mathis, “Quantum entanglement of four distant atoms trapped in different optical cavities,” Phys. Rev. A 69, 052314 (2004).
[CrossRef]

G. C. Guo, and Y. S. Zhang, “Scheme for preparation of the W state via cavity quantum electrodynamics,” Phys. Rev. A 65, 054302 (2002).
[CrossRef]

X. L. Zhang, K. L. Gao, and M. Feng, “Preparation of cluster states and W states with superconducting quantum-interference-device qubits in cavity QED,” Phys. Rev. A 74, 024303 (2006).
[CrossRef]

L. Memarzadeh, and S. Mancini, “Stationary entanglement achievable by environment-induced chain links,” Phys. Rev. A 83, 042329 (2011).
[CrossRef]

A. F. Alharbi, and Z. Ficek, “Deterministic creation of stationary entangled states by dissipation,” Phys. Rev. A 82, 054103 (2010).
[CrossRef]

L. T. Shen, X.-Y. Chen, Z.-B. Yang, H.-Z. Wu, and S.-B. Zheng, “Steady-state entanglement for distant atoms by dissipation in coupled cavities,” Phys. Rev. A 84, 064302 (2011).
[CrossRef]

F. Reiter, and A. S. Sørensen, “Effective operator formalism for open quantum systems,” Phys. Rev. A 85, 032111 (2012).
[CrossRef]

J. Busch, S. De, S. S. Ivanov, B. T. Torosov, T. P. Spiller, and A. Beige, “Cooling atom-cavity systems into entangled states,” Phys. Rev. A 84, 022316 (2011).
[CrossRef]

Phys. Rev. Lett. (12)

M. J. Kastoryano, F. Reiter, and A. S. Sørensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
[CrossRef]

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

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]

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]

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]

J. Cho, S. Bose, and M. S. Kim, “Optical pumping into many-body entanglement,” Phys. Rev. Lett. 106, 020504 (2011).
[CrossRef]

H. Krauter, C. A. Muschik, K. Jensen, W. Wasilewski, J. M. Petersen, J. I. Cirac, and E. S. Polzik, “Entanglement generated by dissipation and steady state entanglement of two macroscopic objects,” Phys. Rev. Lett. 107, 080503 (2011).
[CrossRef]

K. G. H. Vollbrecht, C. A. Muschik, and J. I. Cirac, “Entanglement distillation by dissipation and continuous quantum repeaters,” Phys. Rev. Lett. 107, 120502 (2011).
[CrossRef]

A. D. Boozer, A. Boca, R. Miller, T. E. Northup, and H. J. Kimble, “Cooling to the ground state of axial motion for one atom strongly coupled to an optical cavity,” Phys. Rev. Lett. 97, 083602 (2006).
[CrossRef]

A. Kubanek, A. Ourjoumtsev, I. Schuster, M. Koch, P. W. H. Pinkse, K. Murr, and G. Rempe, “Two-photon gateway in one-atom cavity quantum electrodynamics,” Phys. Rev. Lett. 101, 203602 (2008).
[CrossRef]

A. S. Sørensen, and K. Mølmer, “Measurement induced entanglement and quantum computation with atoms in optical cavities,” Phys. Rev. Lett. 91, 097905 (2003).
[CrossRef]

M. Eibl, N. Kiesel, M. Bourennane, C. Kurtsiefer, and H. Weinfurter, “Experimental realization of a three-qubit entangled W state,” Phys. Rev. Lett. 92, 077901 (2004).
[CrossRef]

Science (1)

C. F. Roos, M. Riebe, H. Häffner, W. Hänsel, J. Benhelm, G. P. T. Lancaster, C. Becher, F. Schmidt-Kaler, and R. Blatt, “Control and measurement of three-qubit entangled states,” Science 304, 1478–1480 (2004).
[CrossRef]

Other (3)

X. T. Wang, and S. G. Schirmer, “Generating maximal entanglement between non-interacting atoms by collective decay and symmetry breaking,” http://arxiv.org/abs/1005.2114 .

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

F. Reiter, M. J. Kastoryano, and A. S. Sørensen, “Entangled steady-states of two atoms in an optical cavity by engineered decay” (2011), http://arxiv.org/abs/1110.1024 .

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Figures (4)

Fig. 1.
Fig. 1.

(a) Experimental setup for engineering W-type entangled steady state for three atoms via dissipation in an optical cavity. (b) Level diagram of a single atom. The |1|2 transition couples resonantly with coupling constant g to the cavity field. Four off-resonance optical lasers with detuning Δk and Rabi frequency Ωk drive the transition |0|2 (k=1,2) and |1|2 (k=3,4), respectively.

Fig. 2.
Fig. 2.

Populations of the target state |S1,3 (left axis) and the purity of the system (green solid line, right axis) as a function of time for a random initial state. The curves are plotted for a set of optimal parameters C=80, γ=1.5κ, Ω1=Ω3=Ω, Ω4=2Ω2=1.2Ω. (a) Ω=0.04g. (b) Ω=0.08g. Numerical results in Eq. (10) (red dashed) correspond with numerical curves obtained from the full master equation (blue solid line) well.

Fig. 3.
Fig. 3.

Stationary state fidelity F as a function of γ/κ for different values of C and Ω.

Fig. 4.
Fig. 4.

Stationary state fidelity F as a function of cooperativity parameter C for γ=1.5κ, Ω=0.04g. The inset gives the coefficient of the linear scaling in F as a function of C.

Tables (2)

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Table 1. Decay Rates μeff,|y,|S1,3 and μeff,|S1,3,|y Correspond to the Effective Decay Channels from |y to |S1,3 and from |S1,3 to |y, Respectively, by Combining Four Independent Decay Processes in Eq. (9)

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Table 2. Decay Rates μeff,|y,|111 and μeff,|111,|y Correspond to the Effective Decay Channels from |y to |111 and from |111 to |y, Respectively, by Combining Four Independent Decay Processes in Eq. (9)

Equations (23)

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H0(k)=Δkaa+m=13Δk|2m2|+m=13(ga|2m1|+ga|1m2|),
V+(k)=Ωk3m=13|2m0|,(k=1,2),
V+(k)=Ωk3m=13|2m1|,(k=3,4),
ρ.=i[ρ,H(k)]+x{Lxρ(Lx)12[(Lx)Lxρ+ρ(Lx)Lx]},
ρ.=i[ρ,Heff,k]+x{Leff,kxρ(Leff,kx)12[(Leff,kx)Leff,kxρ+ρ(Leff,kx)Leff,kx]}.
Heff,k=12V(HNH,k1+(HNH,k1))V+,
Leff,kx=LxHNH,k1V+,
|S1,j=13(ei2jπ3|100+ei4jπ3|010+|001),|S2,j=13(ei2jπ3|110+ei4jπ3|101+|011),
μeff,|y,|z=k=14μeff,|y,|z(k)
P.y=zy(μeff,|y,|zPzμeff,|z,|yPy),
1F7.2C1.
H0(1)=Δ1aa+m=13Δ1|2m2|+m=13(ga|2m1|+ga|1m2|.),
V+(1)=Ω13m=13|2m0|.
Heff,1=Re[δ˜1Ω123R˜1,1]|000000|+Re[δ˜1Ω129R˜3,1]|S2,3S2,3|+Re[δ˜1Ω1218R˜2,1](|S1,1S1,1|+|S1,2S1,2|+4|S1,3S1,3|)+Re[Ω126Δ˜1](|S1,1S1,1|+|S1,2S1,2|)+Re[Ω129Δ˜1](|S2,1S2,1|+|S2,2S2,2|),
Leff,1κ=κgΩ13R˜1,1|S1,3000|κgΩ13R˜3,1|111S2,3|κgΩ13R˜2,1(ei2π3|S2,1S1,2|ei2π3|S2,2S1,1|+2|S2,3S1,3|),
Leff,1γ,0,m=γδ˜1Ω132R˜1,1|000000|+(γδ˜1Ω1182R˜2,1+iγΩ162Δ˜1)(|S1,1S1,1|+|S1,2S1,2|)+(γδ˜1Ω1182R˜2,1iγΩ162Δ˜1)(ei2mπ3|S1,3S1,1|+ei2mπ3|S1,3S1,2|)γδ˜1Ω1182R˜2,1(2ei2mπ3|S1,1S1,2|+2ei2mπ3|S1,2S1,1|)+γδ˜1Ω192R˜2,1(ei2mπ3|S1,1S1,3|ei2mπ3|S1,2S1,3|+2|S1,3S1,3|)+γδ˜1Ω192R˜3,1(ei2(m1)π3|S2,1S2,3|+ei2(m1)π3|S2,2S2,3|+|S2,3S2,3|)+γΩ192Δ˜1(ei2(m1)π3|S2,1S2,1|+|S2,2S2,1|+ei2(m1)π3|S2,3S2,1|)+γΩ192Δ˜1(|S2,1S2,2|+ei2(m1)π3|S2,2S2,2|+ei2(m1)π3|S2,3S2,2|),
Leff,1γ,1,m=γδ˜1Ω136R˜1,1(ei2mπ3|S1,1000|+ei2mπ3|S1,2000|+|S1,3000|)+(γδ˜1Ω1182R˜2,1+iγΩ162Δ˜1)(ei2(m2)π3|S2,1S1,1|+ei2(m2)π3|S2,2S1,2|)+(γδ˜1Ω1182R˜2,1iγΩ162Δ˜1)(ei2mπ3|S2,3S1,1|+ei2mπ3|S2,3S1,2|)γδ˜1Ω192R˜2,1(ei2π3|S2,2S1,1|+ei2π3|S2,1S1,2|)+γδ˜1Ω192R˜2,1(ei2(m1)π3|S2,1S1,3|ei2(m1)π3|S2,2S1,3|+2|S2,3S1,3|)+γΩ136Δ˜1(ei2mπ3|111S2,1|+ei2mπ3|111S2,2|)+γδ˜12Ω1236R˜3,1|111S2,3|,
Δ˜k=Δkiγ2,δ˜k=Δkiκ2,R˜n,k=Δ˜kδ˜kng2,
V+(3)=Ω33m=13|2m1|.
Heff,3=Re[δ˜3Ω329R˜1,3](|S1,1S1,1|+|S1,2S1,2|+|S1,3S1,3|)+Re[2δ˜3Ω329R˜2,3](|S2,1S2,1|+|S2,2S2,2|+|S2,3S2,3|)+Re[δ˜3Ω323R˜3,3]|111111|,
Leff,3κ=κgΩ33R˜1,3(|S1,1S1,1|+|S1,2S1,2|+|S1,3S1,3|)+2κgΩ33R˜2,3(|S2,1S2,1|+|S2,2S2,2|+|S2,3S2,3|)+κgΩ3R˜3,3|111111|,
Leff,3γ,0,m=γδ˜3Ω336R˜1,3(ei2mπ3|000S1,1|+ei2mπ3|000S1,2|+|000S1,3|)+γδ˜3Ω392R˜2,3(2ei2(m2)π3|S1,1S2,1|ei2π3|S1,2S2,1|ei2(m1)π3|S1,3S2,1|)+γδ˜3Ω392R˜2,3(ei2π3|S1,1S2,2|+2ei2(m2)π3|S1,2S2,2|ei2(m1)π3|S1,3S2,2|)+γδ˜3Ω392R˜2,3(ei2mπ3|S1,1S2,3|ei2mπ3|S1,2S2,3|+2|S1,3S2,3|)+γδ˜3Ω336R˜3,3(ei2(m1)π3|S2,1111|+ei2(m1)π3|S2,2111|+|S2,3111|),
Leff,3γ,1,m=γδ˜3Ω392R˜1,3(|S1,1S1,1|+ei2mπ3|S1,2S1,1|+ei2mπ3|S1,3S1,1|)+γδ˜3Ω392R˜1,3(ei2mπ3|S1,1S1,2|+|S1,2S1,2|+ei2mπ3|S1,3S1,2|)+γδ˜3Ω392R˜1,3(ei2mπ3|S1,1S1,3|+ei2mπ3|S1,2S1,3|+|S1,3S1,3|)+γδ˜3Ω392R˜2,3(2|S2,1S2,1|ei2(m1)π3|S2,2S2,1|ei2(m1)π3|S2,3S2,1|)+γδ˜3Ω392R˜2,3(ei2(m1)π3|S2,1S2,2|+2|S2,2S2,2|ei2(m1)π3|S2,3S2,2|)+γδ˜3Ω392R˜2,3(ei2(m1)π3|S2,1S2,3|ei2(m1)π3|S2,2S2,3|+2|S2,3S2,3|)+γδ˜3Ω332R˜3,3|111111|.

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