Abstract

We investigate entanglement dynamics of three driven atoms off-resonantly coupled with a single-mode cavity under quantum-jump-based feedback control. The results demonstrate that the tripartite entanglement can be effectively enhanced and the steady W state and asymmetric W states can be obtained by setting the Rabi frequencies of classical fields and choosing the local quantum feedback control. Furthermore, the tripartite decoherence-free entangled states are found when the atoms are driven by classical fields with appropriate Rabi frequencies. The asymmetric W states and W state can be converted into each other via feedback control. In theory, the multiqubit W state can be generated and stabilized by our approach.

© 2013 Optical Society of America

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  41. P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
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  42. S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2012

J. Song, Y. Xia, and X. D. Sun, “Noise-induced quantum correlations via quantum feedback control,” J. Opt. Soc. Am. B 29, 268–273 (2012).
[CrossRef]

X. Q. Shao, T. Y. Zheng, and S. Zhang, “Engineering steady three-atom singlet states via quantum-jump-based feedback,” Phys. Rev. A 85, 042308 (2012).
[CrossRef]

J. Song, Y. Xia, X. D. Sun, and H. S. Song, “Dissipative preparation of multibody entanglement via quantum feedback control,” Phys. Rev. A 86, 034303 (2012).
[CrossRef]

X. W. Hou, M. F. Wan, and Z. Q. Ma, “Tripartite entanglement dynamics for mixed states in the Tavis-Cummings model with intrinsic decoherence,” Eur. Phys. J. D 66, 152 (2012).
[CrossRef]

2011

M. R. Hwang, D. Park, and E. Jung, “Tripartite entanglement in a noninertial frame,” Phys. Rev. A 83, 012111 (2011).
[CrossRef]

J. Wang and J. Jing, “Multipartite entanglement of fermionic systems in noninertial frames,” Phys. Rev. A 83, 022314 (2011).
[CrossRef]

R. N. Stevenson, J. J. Hope, and A. R. R. Carvalho, “Engineering steady states using jump-based feedback for multipartite entanglement generation,” Phys. Rev. A 84, 022332 (2011).
[CrossRef]

R. N. Stevenson, A. R. R. Carvalho, and J. J. Hope, “Production of entanglement in Raman three-level systems using feedback,” Eur. Phys. J. D 61, 523–529 (2011).
[CrossRef]

W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, “Generating and stabilizing the Greenberger-Horne-Zeilinger state in circuit QED: joint measurement, Zeno effect, and feedback,” Phys. Rev. A 83, 042313 (2011).
[CrossRef]

Y. Li, B. Luo, and H. Guo, “Entanglement and quantum discord dynamics of two atoms under practical feedback control,” Phys. Rev. A 84, 012316 (2011).
[CrossRef]

C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

N. B. An, J. Kim, and K. Kim, “Entanglement dynamics of three interacting two-level atoms within a common structured environment,” Phys. Rev. A 84, 022329 (2011).
[CrossRef]

2010

N. B. An, J. Kim, and K. Kim, “Nonperturbative analysis of entanglement dynamics and control for three qubits in a common lossy cavity,” Phys. Rev. A 82, 032316 (2010).
[CrossRef]

F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
[CrossRef]

S. C. Hou, X. L. Huang, and X. X. Yi, “Suppressing decoherence and improving entanglement by quantum-jump-based feedback control in two-level systems,” Phys. Rev. A 82, 012336 (2010).
[CrossRef]

2009

K. Härkönen, F. Plastina, and S. Maniscalco, “Dicke model and environment-induced entanglement in ion-cavity QED,” Phys. Rev. A 80, 033841 (2009).
[CrossRef]

2008

J. G. Li, J. Zou, B. Shao, and J. F. Cai, “Steady atomic entanglement with different quantum feedbacks,” Phys. Rev. A 77, 012339 (2008).
[CrossRef]

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

S. Maniscalco, F. Francica, R. L. Zaffino, N. Lo Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
[CrossRef]

I. Sainz and G. Björk, “Quantum error correction may delay, but also cause, entanglement sudden death,” Phys. Rev. A 77, 052307 (2008).
[CrossRef]

2007

J. Laurat, K. S. Choi, H. Deng, C. W. Chou, and H. J. Kimble, “Heralded entanglement between atomic ensembles: preparation, decoherence, and scaling,” Phys. Rev. Lett. 99, 180504 (2007).
[CrossRef]

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

A. R. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301 (2007).
[CrossRef]

S. Mancini and H. M. Wiseman, “Optimal control of entanglement via quantum feedback,” Phys. Rev. A 75, 012330 (2007).
[CrossRef]

Y. C. Ou and H. Fan, “Monogamy inequality in terms of negativity for three-qubit states,” Phys. Rev. A 75, 062308 (2007).
[CrossRef]

2006

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
[CrossRef]

S. Mancini, “Markovian feedback to control continuous-variable entanglement,” Phys. Rev. A 73, 010304(R) (2006).
[CrossRef]

P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
[CrossRef]

T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
[CrossRef]

G. Gordon and G. Kurizki, “Preventing multipartite disentanglement by local modulations,” Phys. Rev. Lett. 97, 110503 (2006).
[CrossRef]

2005

S. Mancini and J. Wang, “Towards feedback control of entanglement,” Eur. Phys. J. D 32, 257–260 (2005).
[CrossRef]

J. Wang, H. M. Wiseman, and G. J. Milburn, “Dynamical creation of entanglement by homodyne-mediated feedback,” Phys. Rev. A 71, 042309 (2005).
[CrossRef]

2004

J. M. Geremia, J. K. Stockton, and H. Mabuchi, “Real-time quantum feedback control of atomic spin-squeezing,” Science 304, 270–273 (2004).
[CrossRef]

J. E. Reiner, W. P. Smith, L. A. Orozco, H. M. Wiseman, and J. Gambetta, “Quantum feedback in a weakly driven cavity QED system,” Phys. Rev. A 70, 023819 (2004).
[CrossRef]

W. Dür and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
[CrossRef]

A. R. R. Carvalho, F. Mintert, and A. Buchleitner, “Decoherence and multipartite entanglement,” Phys. Rev. Lett. 93, 230501 (2004).
[CrossRef]

T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
[CrossRef]

2003

J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
[CrossRef]

2002

C. Simon and J. Kempe, “Robustness of multiparty entanglement,” Phys. Rev. A 65, 052327 (2002).
[CrossRef]

N. V. Morrow, S. K. Dutta, and G. Raithel, “Feedback control of atomic motion in an optical lattice,” Phys. Rev. Lett. 88, 093003 (2002).
[CrossRef]

2000

V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61, 052306 (2000).
[CrossRef]

1999

A. C. Doherty and K. Jacobs, “Feedback control of quantum systems using continuous state estimation,” Phys. Rev. A 60, 2700–2711 (1999).
[CrossRef]

V. P. Belavkin, “Measurement, filtering and control in quantum open dynamical systems,” Rep. Math. Phys. 43, A405–A425 (1999).
[CrossRef]

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

1998

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

L. M. Duan and G. C. Guo, “Optimal quantum codes for preventing collective amplitude damping,” Phys. Rev. A 58, 3491–3495 (1998).
[CrossRef]

1994

H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
[CrossRef]

1993

H. M. Wiseman and G. J. Milburn, “Quantum theory of optical feedback via homodyne detection,” Phys. Rev. Lett. 70, 548–551 (1993).
[CrossRef]

Agrawal, P.

P. Agrawal and A. Pati, “Perfect teleportation and superdense coding with W states,” Phys. Rev. A 74, 062320 (2006).
[CrossRef]

Almeida, M. P.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

Amini, H.

C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

An, N. B.

N. B. An, J. Kim, and K. Kim, “Entanglement dynamics of three interacting two-level atoms within a common structured environment,” Phys. Rev. A 84, 022329 (2011).
[CrossRef]

N. B. An, J. Kim, and K. Kim, “Nonperturbative analysis of entanglement dynamics and control for three qubits in a common lossy cavity,” Phys. Rev. A 82, 032316 (2010).
[CrossRef]

Bacon, D.

D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

Becher, C.

P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
[CrossRef]

Belavkin, V. P.

V. P. Belavkin, “Measurement, filtering and control in quantum open dynamical systems,” Rep. Math. Phys. 43, A405–A425 (1999).
[CrossRef]

Björk, G.

I. Sainz and G. Björk, “Quantum error correction may delay, but also cause, entanglement sudden death,” Phys. Rev. A 77, 052307 (2008).
[CrossRef]

Blatt, R.

P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
[CrossRef]

Briegel, H. J.

W. Dür and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
[CrossRef]

Brune, M.

C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Buchleitner, A.

A. R. R. Carvalho, F. Mintert, and A. Buchleitner, “Decoherence and multipartite entanglement,” Phys. Rev. Lett. 93, 230501 (2004).
[CrossRef]

Bushev, P.

P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
[CrossRef]

Cai, J. F.

J. G. Li, J. Zou, B. Shao, and J. F. Cai, “Steady atomic entanglement with different quantum feedbacks,” Phys. Rev. A 77, 012339 (2008).
[CrossRef]

Carvalho, A. R. R.

R. N. Stevenson, J. J. Hope, and A. R. R. Carvalho, “Engineering steady states using jump-based feedback for multipartite entanglement generation,” Phys. Rev. A 84, 022332 (2011).
[CrossRef]

R. N. Stevenson, A. R. R. Carvalho, and J. J. Hope, “Production of entanglement in Raman three-level systems using feedback,” Eur. Phys. J. D 61, 523–529 (2011).
[CrossRef]

A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
[CrossRef]

A. R. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301 (2007).
[CrossRef]

A. R. R. Carvalho, F. Mintert, and A. Buchleitner, “Decoherence and multipartite entanglement,” Phys. Rev. Lett. 93, 230501 (2004).
[CrossRef]

Choi, K. S.

J. Laurat, K. S. Choi, H. Deng, C. W. Chou, and H. J. Kimble, “Heralded entanglement between atomic ensembles: preparation, decoherence, and scaling,” Phys. Rev. Lett. 99, 180504 (2007).
[CrossRef]

Chou, C. W.

J. Laurat, K. S. Choi, H. Deng, C. W. Chou, and H. J. Kimble, “Heralded entanglement between atomic ensembles: preparation, decoherence, and scaling,” Phys. Rev. Lett. 99, 180504 (2007).
[CrossRef]

Chuang, I. L.

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

Coffman, V.

V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61, 052306 (2000).
[CrossRef]

Davidovich, L.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

de Melo, F.

M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
[CrossRef]

Deng, H.

J. Laurat, K. S. Choi, H. Deng, C. W. Chou, and H. J. Kimble, “Heralded entanglement between atomic ensembles: preparation, decoherence, and scaling,” Phys. Rev. Lett. 99, 180504 (2007).
[CrossRef]

Ding, X.

W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, “Generating and stabilizing the Greenberger-Horne-Zeilinger state in circuit QED: joint measurement, Zeno effect, and feedback,” Phys. Rev. A 83, 042313 (2011).
[CrossRef]

Doherty, A. C.

A. C. Doherty and K. Jacobs, “Feedback control of quantum systems using continuous state estimation,” Phys. Rev. A 60, 2700–2711 (1999).
[CrossRef]

Dotsenko, I.

C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
[CrossRef]

Duan, L. M.

L. M. Duan and G. C. Guo, “Optimal quantum codes for preventing collective amplitude damping,” Phys. Rev. A 58, 3491–3495 (1998).
[CrossRef]

Dubin, F.

P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
[CrossRef]

Dür, W.

W. Dür and H. J. Briegel, “Stability of macroscopic entanglement under decoherence,” Phys. Rev. Lett. 92, 180403 (2004).
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J. Wang, H. M. Wiseman, and G. J. Milburn, “Dynamical creation of entanglement by homodyne-mediated feedback,” Phys. Rev. A 71, 042309 (2005).
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J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
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J. E. Reiner, W. P. Smith, L. A. Orozco, H. M. Wiseman, and J. Gambetta, “Quantum feedback in a weakly driven cavity QED system,” Phys. Rev. A 70, 023819 (2004).
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J. Joo, Y. J. Park, S. Oh, and J. Kim, “Quantum teleportation via a W state,” New J. Phys. 5, 136 (2003).
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F. Francica, F. Plastina, and S. Maniscalco, “Quantum Zeno and anti-Zeno effects on quantum and classical correlations,” Phys. Rev. A 82, 052118 (2010).
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K. Härkönen, F. Plastina, and S. Maniscalco, “Dicke model and environment-induced entanglement in ion-cavity QED,” Phys. Rev. A 80, 033841 (2009).
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S. Maniscalco, F. Francica, R. L. Zaffino, N. Lo Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
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P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
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C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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N. V. Morrow, S. K. Dutta, and G. Raithel, “Feedback control of atomic motion in an optical lattice,” Phys. Rev. Lett. 88, 093003 (2002).
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J. E. Reiner, W. P. Smith, L. A. Orozco, H. M. Wiseman, and J. Gambetta, “Quantum feedback in a weakly driven cavity QED system,” Phys. Rev. A 70, 023819 (2004).
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C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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J. G. Li, J. Zou, B. Shao, and J. F. Cai, “Steady atomic entanglement with different quantum feedbacks,” Phys. Rev. A 77, 012339 (2008).
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X. Q. Shao, T. Y. Zheng, and S. Zhang, “Engineering steady three-atom singlet states via quantum-jump-based feedback,” Phys. Rev. A 85, 042308 (2012).
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J. E. Reiner, W. P. Smith, L. A. Orozco, H. M. Wiseman, and J. Gambetta, “Quantum feedback in a weakly driven cavity QED system,” Phys. Rev. A 70, 023819 (2004).
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J. Song, Y. Xia, X. D. Sun, and H. S. Song, “Dissipative preparation of multibody entanglement via quantum feedback control,” Phys. Rev. A 86, 034303 (2012).
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J. Song, Y. Xia, X. D. Sun, and H. S. Song, “Dissipative preparation of multibody entanglement via quantum feedback control,” Phys. Rev. A 86, 034303 (2012).
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J. Song, Y. Xia, and X. D. Sun, “Noise-induced quantum correlations via quantum feedback control,” J. Opt. Soc. Am. B 29, 268–273 (2012).
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M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
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P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, “Feedback cooling of a single trapped ion,” Phys. Rev. Lett. 96, 043003 (2006).
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R. N. Stevenson, A. R. R. Carvalho, and J. J. Hope, “Production of entanglement in Raman three-level systems using feedback,” Eur. Phys. J. D 61, 523–529 (2011).
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R. N. Stevenson, J. J. Hope, and A. R. R. Carvalho, “Engineering steady states using jump-based feedback for multipartite entanglement generation,” Phys. Rev. A 84, 022332 (2011).
[CrossRef]

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J. M. Geremia, J. K. Stockton, and H. Mabuchi, “Real-time quantum feedback control of atomic spin-squeezing,” Science 304, 270–273 (2004).
[CrossRef]

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J. Song, Y. Xia, and X. D. Sun, “Noise-induced quantum correlations via quantum feedback control,” J. Opt. Soc. Am. B 29, 268–273 (2012).
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J. Song, Y. Xia, X. D. Sun, and H. S. Song, “Dissipative preparation of multibody entanglement via quantum feedback control,” Phys. Rev. A 86, 034303 (2012).
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M. P. Almeida, F. de Melo, M. Hor-Meyll, A. Salles, S. P. Walborn, P. H. Souto Ribeiro, and L. Davidovich, “Environment-induced sudden death of entanglement,” Science 316, 579–582 (2007).
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J. Wang and J. Jing, “Multipartite entanglement of fermionic systems in noninertial frames,” Phys. Rev. A 83, 022314 (2011).
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J. Wang, H. M. Wiseman, and G. J. Milburn, “Dynamical creation of entanglement by homodyne-mediated feedback,” Phys. Rev. A 71, 042309 (2005).
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[CrossRef]

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W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, “Generating and stabilizing the Greenberger-Horne-Zeilinger state in circuit QED: joint measurement, Zeno effect, and feedback,” Phys. Rev. A 83, 042313 (2011).
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D. A. Lidar, D. Bacon, and K. B. Whaley, “Concatenating decoherence-free subspaces with quantum error correcting codes,” Phys. Rev. Lett. 82, 4556–4559 (1999).
[CrossRef]

D. A. Lidar, I. L. Chuang, and K. B. Whaley, “Decoherence-free subspaces for quantum computation,” Phys. Rev. Lett. 81, 2594–2597 (1998).
[CrossRef]

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S. Mancini and H. M. Wiseman, “Optimal control of entanglement via quantum feedback,” Phys. Rev. A 75, 012330 (2007).
[CrossRef]

J. Wang, H. M. Wiseman, and G. J. Milburn, “Dynamical creation of entanglement by homodyne-mediated feedback,” Phys. Rev. A 71, 042309 (2005).
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H. M. Wiseman, “Quantum theory of continuous feedback,” Phys. Rev. A 49, 2133–2150 (1994).
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H. M. Wiseman and G. J. Milburn, “Quantum theory of optical feedback via homodyne detection,” Phys. Rev. Lett. 70, 548–551 (1993).
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V. Coffman, J. Kundu, and W. K. Wootters, “Distributed entanglement,” Phys. Rev. A 61, 052306 (2000).
[CrossRef]

Xia, Y.

J. Song, Y. Xia, and X. D. Sun, “Noise-induced quantum correlations via quantum feedback control,” J. Opt. Soc. Am. B 29, 268–273 (2012).
[CrossRef]

J. Song, Y. Xia, X. D. Sun, and H. S. Song, “Dissipative preparation of multibody entanglement via quantum feedback control,” Phys. Rev. A 86, 034303 (2012).
[CrossRef]

Xu, L.

W. Feng, P. Wang, X. Ding, L. Xu, and X. Q. Li, “Generating and stabilizing the Greenberger-Horne-Zeilinger state in circuit QED: joint measurement, Zeno effect, and feedback,” Phys. Rev. A 83, 042313 (2011).
[CrossRef]

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S. C. Hou, X. L. Huang, and X. X. Yi, “Suppressing decoherence and improving entanglement by quantum-jump-based feedback control in two-level systems,” Phys. Rev. A 82, 012336 (2010).
[CrossRef]

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T. Yu and J. H. Eberly, “Quantum open system theory: bipartite aspects,” Phys. Rev. Lett. 97, 140403 (2006).
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T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
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S. Maniscalco, F. Francica, R. L. Zaffino, N. Lo Gullo, and F. Plastina, “Protecting entanglement via the quantum Zeno effect,” Phys. Rev. Lett. 100, 090503 (2008).
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S. B. Zheng, “Splitting quantum information via W states,” Phys. Rev. A 74, 054303 (2006).
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C. Sayrin, I. Dotsenko, X. X. Zhou, B. Peaudecerf, T. Rybarczyk, S. Gleyzes, P. Rouchon, M. Mirrahimi, H. Amini, M. Brune, J. M. Raimond, and S. Haroche, “Real-time quantum feedback prepares and stabilizes photon number states,” Nature 477, 73–77 (2011).
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Figures (7)

Fig. 1.
Fig. 1.

(a) Schematic view of the model. When the light from the leaky cavity is detected in a photodetector, a feedback pulse is triggered. (b) Level configuration of a single atom in the cavity.

Fig. 2.
Fig. 2.

π123 as a function of time and driving strength Ω3/g (a) without feedback control and (b) with the feedback control F=πσ3x/2. The system is initially in the state |001. Ω1=Ω2=g. Other common parameters: Δ=50g, κ=g·t is in units of (103g)1.

Fig. 3.
Fig. 3.

Time evolution of π123 for the initial state |001 under different feedback controls. (a) and (c) symmetric feedback control F=i=13λσix. (b) and (d) local feedback control F=λσ3x. (a) and (b) Ω1=Ω2=Ω3=g. (c) and (d) Ω1=Ω2=g, Ω3=2g. The other parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

Time evolution of π123 for different initial entangled states (a) |W, (b) |W+, and (c) |W·Ω1=Ω2=g. The feedback control is F=πσ3x/2 except in the case of Ω3=g (F=πσ2x/2) for the initial state |W (bottom) and without feedback control (top). (d) |φ. Ω1=Ω3=g. The feedback Hamiltonian is F=πσ2x/2 (bottom) and without feedback control (top). The other parameters are the same as in Fig. 2. Ω3=g (dot–dashed curve), Ω3=2g (dashed curve), Ω3=2g (dotted curve), and Ω3=2g (solid curve) in (a), (b), and (c). The legend corresponding to (d) is given by replacing Ω3 by Ω2 in the legend for (a), (b), and (c).

Fig. 5.
Fig. 5.

Stationary entanglement π123 as a function of driving strength Ω3/g for different initial states (a) without feedback control and (b) with the feedback control F=πσ3x/2. The other parameters are the same as in Fig. 2.

Fig. 6.
Fig. 6.

Effect of different detection efficiencies on π123 for the initial state |001. Δ=50g, κ=Ω1=Ω2=g, Ω3=2g, F=πσ3x/2.

Fig. 7.
Fig. 7.

Time evolution of π123 in the cases of different atomic spontaneous emissions. γj=γ, κ=g/3. The other parameters are the same as in Fig. 6.

Equations (20)

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

HI=i=13g(a|2ii0|eiΔt+a|0ii2|eiΔt)+Ωi2(|2ii1|ei(Δ+δi)t+|1ii2|ei(Δ+δi)t),
HI=i=13g(a|2ii0|+|0ii2|a)+Ωi2(|2ii1|+|1ii2|)+Δ|2ii2|δi|1ii1|.
ρ˙=i[HI,ρ]κ2(aaρ2UfbaρaUfb+ρaa),
ΔΩi,g,κ,
Heff=i=13Ωig2Δ(aσi++σia)g2Δaa|0ii0|+(Ωi24Δδi)|1ii1|,
ρ˙=g2Δ2κD[Ufb(Ω1σ1+Ω2σ2+Ω3σ3)]ρ,
D[c]ρcρc12(ccρ+ρcc).
π123=13(π1+π2+π3),
π1=N1(23)2N122N132,π2=N2(13)2N212N232,π3=N3(12)2N312N322.
|ϕ=α|100+β|010+γ|001,
|W=13(|100+|010+|001).
|W±=12(|100+|010±2|001).
|φ=16(|1002|010+|001).
ρ˙=i=1ng2Δ2κD[UfbΩiσi]ρ,
|ϕn=α1|1000+α2|0100++αn|0001,
|Wn=1n(|1000+|0100++|0001).
ρ˙=i=13ηg2Δ2κD[UfbΩiσi]ρ+(1η)g2Δ2κD[Ωiσi]ρ,
ρ˙=i[HI,ρ]+κD[Ufba]ρ+i=13j=0,1γjD[|jii2|]ρ,
ρ˙=i[Heff,ρ]+κD[Ufba]ρ+i=13j=0,1γjΔ2D[Cji]ρ,
C1i=Ωi|1ii1|+g|1ii0|a,C0i=Ωi|0ii1|+g|0ii0|a.

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