Abstract

We study a physical system for creation of quantum correlations by quantum feedback control. The system is composed of two three-level atoms, each of which interacts with one of two coupled cavities. By appropriately choosing the feedback strength, we show that an arbitrary initial state can be deterministically driven to a steady-state that has a nonzero quantum discord or entanglement. It is also found that the effect of atomic spontaneous emission on quantum correlations is suppressed efficiently by increasing the frequency detuning.

© 2012 Optical Society of America

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  1. E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein-Podolsky-Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
    [CrossRef]
  2. D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
    [CrossRef]
  3. A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
    [CrossRef]
  4. J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
    [CrossRef]
  5. W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” J. New Phys. 10, 013026 (2008).
  6. H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2002).
    [CrossRef]
  7. P. Giorda and M. G. A. Paris, “Gaussian quantum discord,” Phys. Rev. Lett. 105, 020503 (2010).
    [CrossRef]
  8. Y. H. Wang and H. S. Song, “Preparation of multi-atom specially entangled W-class state and splitting quantum information,” Chin. Sci. Bull. 54, 2599–2605 (2009).
  9. 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]
  10. Y. Li, J. Zhou, and H. Guo, “Effect of the dipole-dipole interaction for two atoms with different couplings in a non-Markovian environment,” Phys. Rev. A 79, 012309 (2009).
  11. D. F. Mundarain and M. Orszag, “Entanglement distillation with local common reservoirs,” Phys. Rev. A 79, 022306(2009).
  12. F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).
  13. B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
    [CrossRef]
  14. J. Q. Liao, J. F. Huang, L. M. Kuang, and C. P. Sun, “Coherent excitation-energy transfer and quantum entanglement in a dimer,” Phys. Rev. A 82, 052109 (2010).
  15. B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101(2010).
  16. M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 022103 (2010).
  17. A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system-bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
    [CrossRef]
  18. S. Das and G. S. Agarwal, “Protecting bipartite entanglement by quantum interferences,” Phys. Rev. A 81, 052341 (2010).
    [CrossRef]
  19. 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).
  20. Q. L. He, J. B. Xu, D. X. Yao, and Y. Q. Zhang, “Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord,” Phys. Rev. A 84, 022312 (2011).
  21. V. P. Belavkin, “Measurement, filtering and control in quantum open dynamical systems,” Rep. Math. Phys. 43, A405–A425 (1999).
    [CrossRef]
  22. H. M. Wiseman and G. J. Milburn, “Quantum theory of optical feedback via homodyne detection,” Phys. Rev. Lett. 70, 548–551(1993).
    [CrossRef]
  23. A. C. Doherty and K. Jacobs, “Feedback control of quantum systems using continuous state estimation,” Phys. Rev. A 60, 2700–2711 (1999).
    [CrossRef]
  24. 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]
  25. 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).
  26. A. R. Carvalho and J. J. Hope, “Stabilizing entanglement by quantum-jump-based feedback,” Phys. Rev. A 76, 010301(R) (2007).
    [CrossRef]
  27. 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]
  28. 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).
  29. 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 (2011).
    [CrossRef]
  30. D. Xue, J. Zou, J. G. Li, W. Y. Chen, and B. Shao, “Controlling entanglement between two separated atoms by quantum-jump-based feedback,” J. Phys. B 43, 045503 (2010).
  31. X. S. Liu, W. Z. Liu, R. B. Wu, and G. L. Long, “Control of state localization in a two-level quantum system,” J. Opt. B: Quantum Semiclass. Opt 7, 66–69 (2005).
  32. J. Wang, H. M. Wiseman, and G. J. Milburn, “Dynamical creation of entanglement by homodyne-mediated feedback,” Phys. Rev. A 71, 042309 (2005).
  33. J. G. Li, J. Zou, B. Shao, and J. F. Cai, “Steady atomic entanglement with different quantum feedbacks,” Phys. Rev. A 77, 012339 (2008).
  34. Z. Liu, L. L. Kuang, K. Hu, L. T. Xu, S. H. Wei, L. Z. Guo, and X. Q. Li, “Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control,” Phys. Rev. A 82, 032335 (2010).
  35. M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143(2000).
    [CrossRef]
  36. D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Polarization conversion in a silica microsphere,” Nature (London) 421, 925–928 (2003).
    [CrossRef]
  37. A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
    [CrossRef]
  38. C. D. Ogden, E. K. Irish, and M. S. Kim, “Dynamics in a coupled-cavity array,” Phys. Rev. A 78, 063805 (2008).
    [CrossRef]
  39. J. Cho, D. G. Angelakis, and S. Bose, “Simulation of high-spin Heisenberg models in coupled cavities,” Phys. Rev. A 78, 062338 (2008).
  40. J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
    [CrossRef]
  41. D. G. Angelakis and A. Kay, “Weaving light-matter qubits into a one way quantum computer,” arXiv:quant-ph/0702133 .
  42. J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).
  43. M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).
  44. J. Song, Y. Xia, and H. S. Song, “One-step generation of cluster state by adiabatic passage in coupled cavities,” Appl. Phys. Lett. 96, 071102 (2010).
  45. K. Härkönen, F. Plastina, and S. Maniscalco, “Dicke model and environment-induced entanglement in ion-cavity QED,” Phys. Rev. A 80, 033841 (2009).
    [CrossRef]
  46. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
    [CrossRef]
  47. T. Yu and J. H. Eberly, “Finite-time disentanglement via spontaneous emission,” Phys. Rev. Lett. 93, 140404 (2004).
  48. P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306–3309 (1997).
    [CrossRef]
  49. M. J. Kastoryano, F. Reiter, and A. S. Sorensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
    [CrossRef]
  50. D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
    [CrossRef]
  51. S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).
  52. H. M. Wiseman, S. Mancini, and J. Wang, “Bayesian feedback versus Markovian feedback in a two-level atom,” Phys. Rev. A 66, 013807 (2002).
    [CrossRef]

2011

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).

Q. L. He, J. B. Xu, D. X. Yao, and Y. Q. Zhang, “Sudden transition between classical and quantum decoherence in dissipative cavity QED and stationary quantum discord,” Phys. Rev. A 84, 022312 (2011).

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 (2011).
[CrossRef]

J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).

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

2010

S. B. Zheng, C. P. Yang, and F. Nori, “Arbitrary control of coherent dynamics for distant qubits in a quantum network,” Phys. Rev. A 82, 042327 (2010).

J. Song, Y. Xia, and H. S. Song, “One-step generation of cluster state by adiabatic passage in coupled cavities,” Appl. Phys. Lett. 96, 071102 (2010).

D. Xue, J. Zou, J. G. Li, W. Y. Chen, and B. Shao, “Controlling entanglement between two separated atoms by quantum-jump-based feedback,” J. Phys. B 43, 045503 (2010).

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).

Z. Liu, L. L. Kuang, K. Hu, L. T. Xu, S. H. Wei, L. Z. Guo, and X. Q. Li, “Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control,” Phys. Rev. A 82, 032335 (2010).

P. Giorda and M. G. A. Paris, “Gaussian quantum discord,” Phys. Rev. Lett. 105, 020503 (2010).
[CrossRef]

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).

J. Q. Liao, J. F. Huang, L. M. Kuang, and C. P. Sun, “Coherent excitation-energy transfer and quantum entanglement in a dimer,” Phys. Rev. A 82, 052109 (2010).

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101(2010).

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 022103 (2010).

A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system-bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
[CrossRef]

S. Das and G. S. Agarwal, “Protecting bipartite entanglement by quantum interferences,” Phys. Rev. A 81, 052341 (2010).
[CrossRef]

2009

Y. Li, J. Zhou, and H. Guo, “Effect of the dipole-dipole interaction for two atoms with different couplings in a non-Markovian environment,” Phys. Rev. A 79, 012309 (2009).

D. F. Mundarain and M. Orszag, “Entanglement distillation with local common reservoirs,” Phys. Rev. A 79, 022306(2009).

Y. H. Wang and H. S. Song, “Preparation of multi-atom specially entangled W-class state and splitting quantum information,” Chin. Sci. Bull. 54, 2599–2605 (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).

C. D. Ogden, E. K. Irish, and M. S. Kim, “Dynamics in a coupled-cavity array,” Phys. Rev. A 78, 063805 (2008).
[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Simulation of high-spin Heisenberg models in coupled cavities,” Phys. Rev. A 78, 062338 (2008).

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (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]

W. Y. Huo and G. L. Long, “Entanglement and squeezing in solid-state circuits,” J. New Phys. 10, 013026 (2008).

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]

2007

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

B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
[CrossRef]

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

2006

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).

2005

X. S. Liu, W. Z. Liu, R. B. Wu, and G. L. Long, “Control of state localization in a two-level quantum system,” J. Opt. B: Quantum Semiclass. Opt 7, 66–69 (2005).

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

2004

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
[CrossRef]

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

2003

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Polarization conversion in a silica microsphere,” Nature (London) 421, 925–928 (2003).
[CrossRef]

2002

H. M. Wiseman, S. Mancini, and J. Wang, “Bayesian feedback versus Markovian feedback in a two-level atom,” Phys. Rev. A 66, 013807 (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]

H. Ollivier and W. H. Zurek, “Quantum discord: a measure of the quantumness of correlations,” Phys. Rev. Lett. 88, 017901 (2002).
[CrossRef]

2001

J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
[CrossRef]

2000

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143(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. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

1998

D. W. Vernooy, A. Furusawa, N. P. Georgiades, V. S. Ilchenko, and H. J. Kimble, “Cavity QED with high-Q whispering gallery modes,” Phys. Rev. A 57, R2293–R2296 (1998).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245 (1998).
[CrossRef]

1997

P. Zanardi and M. Rasetti, “Noiseless quantum codes,” Phys. Rev. Lett. 79, 3306–3309 (1997).
[CrossRef]

E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein-Podolsky-Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
[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]

Agarwal, G. S.

S. Das and G. S. Agarwal, “Protecting bipartite entanglement by quantum interferences,” Phys. Rev. A 81, 052341 (2010).
[CrossRef]

Ali, M. M.

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 022103 (2010).

Angelakis, D. G.

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Simulation of high-spin Heisenberg models in coupled cavities,” Phys. Rev. A 78, 062338 (2008).

D. G. Angelakis and A. Kay, “Weaving light-matter qubits into a one way quantum computer,” arXiv:quant-ph/0702133 .

Armani, D. K.

D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Polarization conversion in a silica microsphere,” Nature (London) 421, 925–928 (2003).
[CrossRef]

Arruda, L. G. E.

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).

Bayindir, M.

M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143(2000).
[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).

Belavkin, V. P.

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

Bellomo, B.

B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
[CrossRef]

Bertet, P.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

Blais, A.

A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
[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).

Bose, S.

J. Cho, D. G. Angelakis, and S. Bose, “Fractional quantum hall state in coupled cavities,” Phys. Rev. Lett. 101, 246809 (2008).
[CrossRef]

J. Cho, D. G. Angelakis, and S. Bose, “Simulation of high-spin Heisenberg models in coupled cavities,” Phys. Rev. A 78, 062338 (2008).

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
[CrossRef]

Brandão, F. G. S. L.

M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (2007).

Brasil, C. A.

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).

Brune, M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
[CrossRef]

E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein-Podolsky-Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
[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).

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).

Caldeira, A. O.

F. F. Fanchini, T. Werlang, C. A. Brasil, L. G. E. Arruda, and A. O. Caldeira, “Non-Markovian dynamics of quantum discord,” Phys. Rev. A 81, 052107 (2010).

Carvalho, A. R.

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

Carvalho, A. R. R.

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 (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]

Chen, P. W.

M. M. Ali, P. W. Chen, and H. S. Goan, “Decoherence-free subspace and disentanglement dynamics for two qubits in a common non-Markovian squeezed reservoir,” Phys. Rev. A 82, 022103 (2010).

Chen, W. Y.

D. Xue, J. Zou, J. G. Li, W. Y. Chen, and B. Shao, “Controlling entanglement between two separated atoms by quantum-jump-based feedback,” J. Phys. B 43, 045503 (2010).

Chen, Z. Q.

B. Wang, Z. Y. Xu, Z. Q. Chen, and M. Feng, “Non-Markovian effect on the quantum discord,” Phys. Rev. A 81, 014101(2010).

Cho, J.

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Z. Liu, L. L. Kuang, K. Hu, L. T. Xu, S. H. Wei, L. Z. Guo, and X. Q. Li, “Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control,” Phys. Rev. A 82, 032335 (2010).

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J. Q. Liao, J. F. Huang, L. M. Kuang, and C. P. Sun, “Coherent excitation-energy transfer and quantum entanglement in a dimer,” Phys. Rev. A 82, 052109 (2010).

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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
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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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Z. Liu, L. L. Kuang, K. Hu, L. T. Xu, S. H. Wei, L. Z. Guo, and X. Q. Li, “Deterministic creation and stabilization of entanglement in circuit QED by homodyne-mediated feedback control,” Phys. Rev. A 82, 032335 (2010).

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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).

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J. Q. Liao, J. F. Huang, L. M. Kuang, and C. P. Sun, “Coherent excitation-energy transfer and quantum entanglement in a dimer,” Phys. Rev. A 82, 052109 (2010).

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B. Bellomo, R. Lo Franco, and G. Compagno, “Non-Markovian effects on the dynamics of entanglement,” Phys. Rev. Lett. 99, 160502 (2007).
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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).

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E. Hagley, X. Maître, G. Nogues, C. Wunderlich, M. Brune, J. M. Raimond, and S. Haroche, “Generation of Einstein-Podolsky-Rosen pairs of atoms,” Phys. Rev. Lett. 79, 1–5 (1997).
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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
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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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A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
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A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143(2000).
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J. W. Pan, M. Daniell, S. Gasparoni, G. Weihs, and A. Zeilinger, “Experimental demonstration of four-photon entanglement and high-fidelity teleportation,” Phys. Rev. Lett. 86, 4435–4438 (2001).
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D. Bouwmeester, J. W. Pan, M. Daniell, H. Weinfurter, and A. Zeilinger, “Observation of three-photon Greenberger-Horne-Zeilinger entanglement,” Phys. Rev. Lett. 82, 1345–1349 (1999).
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P. Giorda and M. G. A. Paris, “Gaussian quantum discord,” Phys. Rev. Lett. 105, 020503 (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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M. J. Hartmann, F. G. S. L. Brandão, and M. B. Plenio, “Effective spin systems in coupled microcavities,” Phys. Rev. Lett. 99, 160501 (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).

Raimond, J. M.

A. Rauschenbeutel, G. Nogues, S. Osnaghi, P. Bertet, M. Brune, J. M. Raimond, and S. Haroche, “Step-by-step engineered multiparticle entanglement,” Science 288, 2024–2028 (2000).
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A. R. R. Carvalho, A. J. S. Reid, and J. J. Hope, “Controlling entanglement by direct quantum feedback,” Phys. Rev. A 78, 012334 (2008).
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M. J. Kastoryano, F. Reiter, and A. S. Sorensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
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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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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
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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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J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).

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J. Song, Y. Xia, and H. S. Song, “One-step generation of cluster state by adiabatic passage in coupled cavities,” Appl. Phys. Lett. 96, 071102 (2010).

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M. J. Kastoryano, F. Reiter, and A. S. Sorensen, “Dissipative preparation of entanglement in optical cavities,” Phys. Rev. Lett. 106, 090502 (2011).
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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 (2011).
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J. Q. Liao, J. F. Huang, L. M. Kuang, and C. P. Sun, “Coherent excitation-energy transfer and quantum entanglement in a dimer,” Phys. Rev. A 82, 052109 (2010).

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J. Song, X. D. Sun, Y. Xia, and H. S. Song, “Efficient creation of continuous-variable entanglement for two atomic ensembles in coupled cavities,” Phys. Rev. A 83, 052309 (2011).

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A. G. Dijkstra and Y. Tanimura, “Non-Markovian entanglement dynamics in the presence of system-bath coherence,” Phys. Rev. Lett. 104, 250401 (2010).
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M. Bayindir, B. Temelkuran, and E. Ozbay, “Tight-binding description of the coupled defect modes in three-dimensional photonic crystals,” Phys. Rev. Lett. 84, 2140–2143(2000).
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D. K. Armani, T. J. Kippenberg, S. M. Spillane, and K. J. Vahala, “Polarization conversion in a silica microsphere,” Nature (London) 421, 925–928 (2003).
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A. Wallraff, D. I. Schuster, A. Blais, L. Frunzio, R. S. Huang, J. Majer, S. Kumar, S. M. Girvin, and R. J. Schoelkopf, “Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics,” Nature (London) 431, 162–167 (2004).
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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic view of the model. Conditioned on the measurement of the output of the leaky cavity, a feedback operation is applied to the atom. (b) The level configuration of the atoms.

Fig. 2.
Fig. 2.

Discord and concurrence versus time t when the initial state of system is (a)  ψ 1 and (b)  ψ 2 , respectively. Other common parameters: λ k = λ , Ω k = λ , Ω k = 0.1 λ , ϵ = 1 , Δ 2 = 10 λ , ν = 10 λ , Γ = 0 , and κ k = λ / 3 .

Fig. 3.
Fig. 3.

(a) Variation of discord and concurrence from the initial state | g 1 , g 2 | 0 1 , 0 2 . Discord and concurrence versus time t under the feedback action for (b)  ψ 1 and (c)  ψ 2 . (d) Time evolution of discord and concurrence for different decay rates. The other parameters are the same as in Fig. 2.

Fig. 4.
Fig. 4.

(a) Discord and (b) concurrence versus time t , with the initial state being | g 1 , g 2 , for the case ϵ = { 0 , 0.2 , 0.4 , 0.6 , 0.8 } . The other parameters are the same as in Fig. 2.

Fig. 5.
Fig. 5.

Time evolution of discord and concurrence for different initial states (a)  Ψ and (b)  | f 1 , g 2 | 0 1 , 0 2 for the case of Γ = 0 . (c) Discord and concurrence of steady-state versus detuning Δ 2 with Γ = 0.1 κ 1 . The other parameters are the same as in Fig. 2.

Equations (8)

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

H 0 = k = 1 , 2 ω f | f k f k | + ω e | e k e k | + ω 0 a k a k , H i = k = 1 , 2 ( λ k | g k e k | a k + Ω k | e k f k | e i ω t + Ω k | f k g k | e i ω t + H.c. ) + ν ( a 1 a 2 + a 1 a 2 ) ,
a 1 = A + B 2 , a 2 = A B 2 ,
H i = k = 1 , 2 [ Ω k | f k e k | e i Δ 2 t + Ω k | f k g k | + λ k 2 | g k e k | ( A e i ( Δ 1 ν ) t + ( 1 ) k + 1 B e i ( Δ 1 + ν ) t ) + H.c. ] ,
H 1 = k = 1 , 2 [ Δ 2 | e k e k | + ( Ω k | f k e k | + Ω k | g k f k | + H.c. ) ] + ( λ 1 2 | g 1 e 1 | ( A + B ) + λ 2 2 | g 2 e 2 | ( A B ) + H.c. ) 2 ν B B ,
ρ . = i [ H 1 , ρ ] k = 1 , 2 [ κ k 2 ( a k a k ρ 2 a k ρ a k + ρ a k a k ) Γ 2 ( σ k e g σ k g e ρ 2 σ k g e ρ σ k e g + ρ σ k e g σ k g e ) Γ 2 ( σ k e f σ k f e ρ 2 σ k f e ρ σ k e f + ρ σ k e f σ k f e ) ] .
ρ . = i [ H 2 , ρ ] k = 1 , 2 ( 1 ϵ ) κ k 2 ( a k a k ρ 2 a k ρ a k + ρ a k a k ) k = 1 , 2 ϵ κ k 2 ( a k a k ρ 2 U k a k ρ a k U k + ρ a k a k ) l = 1 4 Γ 2 Δ 2 2 ( X l X l ρ 2 X l ρ X l + ρ X l X l ) ,
X 1 = Ω 1 | f 1 f 1 | λ 1 2 | f 1 g 1 | a 1 , X 2 = Ω 2 | f 2 f 2 | λ 2 2 | f 2 g 2 | a 2 , X 3 = Ω 1 | g 1 f 1 | λ 1 2 | g 1 g 1 | a 1 , X 4 = Ω 2 | g 2 f 2 | λ 2 2 | g 2 g 2 | a 2 , H 2 = k = 1 2 [ Ω k 2 | f k f k | Δ 2 + λ k 2 | g k g k | 2 Δ 2 A A + λ k 2 | g k g k | 2 ( Δ 2 + 2 ν ) B B + ( λ k Ω k | f k g k | Δ 2 A + Ω k | f k g k | + H.c. ) ] ,
Ψ = 1 3 ( 1 3 | g 1 , g 2 g 1 , g 2 | + 1 6 | f 1 , g 2 f 1 , g 2 | + 1 6 | f 1 , g 2 g 1 , f 2 | + 1 6 | g 1 , f 2 f 1 , g 2 | + 1 6 | g 1 , f 2 g 1 , f 2 | + 1 3 | f 1 , f 2 f 1 , f 2 | ) ( | 0 1 , 0 2 0 1 , 0 2 | + | 1 1 , 1 2 1 1 , 1 2 | + | 2 1 , 2 2 2 1 , 2 2 | ) .

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