Abstract

We explore the asymmetric Einstein-Podolsky-Rosen (EPR) steering of field modes via atomic coherent effects. A resonant four-level system in double-cascade configuration is under our consideration, where the atoms are excited by the applied fields from one cascade channel and two cavity modes are generated from the other cascade transition. The results show two cavity modes are suitable for achieving the steady-state one-way EPR steering. We analyze the physics in terms of the dressed-atom Bogoliubov-field-mode approach. It is found that one of two Bogoliubov modes is mediated by the resonant coupling of the dressed atoms and the other is decoupled from them. This leads to the so-called one-channel dissipation, by which the dressed atoms absorb the average excitations from one transformed mode and then two original modes are pulled into the asymmetric correlation. Remarkably, the present scheme is focused on the full-resonant interaction not only between the classical fields, the cavity modes and the bare atoms, but also between the Bogoliubov modes and dressed atoms, which will induce the one-way steering simply via adjusting the intensity of an external field. Furthermore, the EPR steering could occur between the field modes with the large frequency difference, such as optical and microwave fields, which is more useful for the practical quantum communication. Based on the one-channel dissipation, the obtainable one-way EPR steering is rather against the dynamic fluctuations and is regardless of the initial state.

© 2017 Optical Society of America

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    [Crossref]
  42. G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: Entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
    [Crossref]
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2015 (6)

M. Piani and J. Watrous, “Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 114, 060404 (2015).
[Crossref] [PubMed]

H. T. Tan, X. C. Zhang, and G. X. Li, “Steady-state one-way Einstein-Podolsky-Rosen steering in optomechanical interfaces,” Phys. Rev. A 91, 032121 (2015).
[Crossref]

Q. Y. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref] [PubMed]

I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
[Crossref] [PubMed]

S. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167 (2015).
[Crossref]

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91, 043820 (2015).
[Crossref]

2014 (3)

Q. Y. He and Z. Ficek, “Einstein-Podolsky-Rosen paradox and quantum steering in a three-mode optomechanical system,” Phys. Rev. A 89, 022332 (2014).
[Crossref]

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarant, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Y. Z. Law, L. P. Thinh, J.-D. Bancal, and V. Scarani, “Quantum randomness extraction for various levels of characterization of the devices,” J. Phys. A 47, 424028 (2014).
[Crossref]

2013 (6)

M. D. Reid, “Signifying quantum benchmarks for qubit teleportation and secure quantum communication using Einstein-Podolsky-Rosen steering inequalities,” Phys. Rev. A 88, 062338 (2013).
[Crossref]

M. K. Olsen, “Asymmetric Gaussian harmonic steering in second-harmonic generation,” Phys. Rev. A 88, 051802 (2013).
[Crossref]

M. K. Olsen and J. F. Corney, “Non-Gaussian continuous-variable entanglement and steering,” Phys. Rev. A 87, 033839 (2013).
[Crossref]

Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88, 052121 (2013).
[Crossref]

Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
[Crossref]

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
[Crossref]

2012 (1)

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering,” Nat. Photonics 6, 596–599 (2012).
[Crossref]

2011 (3)

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified criteria for multipartite quantum nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

Y. B. Yu, J. T. Sheng, and M. Xiao, “Generation of bright quadricolor continuous-variable entanglement by four-wave-mixing process,” Phys. Rev. A 83, 012321 (2011).
[Crossref]

2010 (2)

S. L. W. Midgley, A. J. Ferris, and M. K. Olsen, “Asymmetric Gaussian steering: When Alice and Bob disagree,” Phys. Rev. A 81, 022101 (2010).
[Crossref]

K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

2009 (2)

J. Y. Li and X. M. Hu, “Laser oscillation and light entanglement via dressed-state phase-dependent electromagnetically induced transparency,” Phys. Rev. A 80, 053829 (2009).
[Crossref]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

2008 (3)

M. K. Olsen and A. S. Bradley, “Bright bichromatic entanglement and quantum dynamics of sum frequency generation,” Phys. Rev. A 77, 023813 (2008).
[Crossref]

H. J. Kim, A. H. Khosa, H. W. Lee, and M. S. Zubairy, “One-atom correlated-emission laser,” Phys. Rev. A 77, 023817 (2008).
[Crossref]

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: Entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[Crossref]

2007 (5)

M. Kiffner, M. S. Zubairy, J. Evers, and C. H. Keitel, “Two-mode single-atom laser as a source of entangled light,” Phys. Rev. A 75, 033816 (2007).
[Crossref]

S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein-Podolsky-Rosen-Entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
[Crossref] [PubMed]

G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
[Crossref]

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

C. H. Raymond Ooi, Q. Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory,” Phys. Rev. A 75, 013820 (2007).
[Crossref]

2006 (1)

N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen correlation,” Phys. Rev. A 74, 060101 (2006).
[Crossref]

2005 (4)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
[Crossref]

H. Xiong, M. O. Scully, and M. S. Zubairy, “Correlated spontaneous emission laser as an entanglement amplifier,” Phys. Rev. Lett. 94, 023601 (2005).
[Crossref] [PubMed]

H. T. Tan, S. Y. Zhu, and M. S. Zubairy, “Continuous-variable entanglement in a correlated spontaneous emission laser,” Phys. Rev. A 72, 022305 (2005).
[Crossref]

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

2004 (1)

P. Barberis-Blostein and N. Zagury, “Field correlations in electromagnetically induced transparency,” Phys. Rev. A 70, 053827 (2004).
[Crossref]

2002 (1)

N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, “Quantum cryptography,” Rev. Mod. Phys. 74, 145–195 (2002).
[Crossref]

1996 (1)

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[Crossref]

1990 (1)

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
[Crossref] [PubMed]

1964 (1)

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

1935 (2)

E. Schrödinger, “Discussion of probability relations between separated systems,” Math. Proc. Cambridge Philos. Soc. 31, 555–562 (1935).
[Crossref]

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete,” Phys. Rev. 47, 777–780 (1935).
[Crossref]

Adesso, G.

Q. Y. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
[Crossref] [PubMed]

I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
[Crossref] [PubMed]

Andersen, U. L.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Arimondo, E.

E. Arimondo, “Coherent population trapping in laser spectroscopy,” Prog. Opt. 35, 257–354 (1996).
[Crossref]

Armstrong, S.

S. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167 (2015).
[Crossref]

Bachor, H. A.

S. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167 (2015).
[Crossref]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Bancal, J.-D.

Y. Z. Law, L. P. Thinh, J.-D. Bancal, and V. Scarani, “Quantum randomness extraction for various levels of characterization of the devices,” J. Phys. A 47, 424028 (2014).
[Crossref]

Barberis-Blostein, P.

P. Barberis-Blostein and N. Zagury, “Field correlations in electromagnetically induced transparency,” Phys. Rev. A 70, 053827 (2004).
[Crossref]

Bauchrowitz, J.

S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
[Crossref]

Bell, J. S.

J. S. Bell, “On the Einstein Podolsky Rosen paradox,” Physics 1, 195–200 (1964).

Bowen, W. P.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Bradley, A. S.

M. K. Olsen and A. S. Bradley, “Bright bichromatic entanglement and quantum dynamics of sum frequency generation,” Phys. Rev. A 77, 023813 (2008).
[Crossref]

Braunstein, S. L.

S. L. Braunstein and P. van Loock, “Quantum information with continuous variables,” Rev. Mod. Phys. 77, 513–577 (2005).
[Crossref]

Brunner, N.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarant, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Cavalcanti, D.

N. Brunner, D. Cavalcanti, S. Pironio, V. Scarant, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
[Crossref]

Cavalcanti, E. G.

E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified criteria for multipartite quantum nonlocality,” Phys. Rev. A 84, 032115 (2011).
[Crossref]

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Chen, P.

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91, 043820 (2015).
[Crossref]

Cheng, G. L.

G. L. Cheng, X. M. Hu, W. X. Zhong, and Q. Li, “Two-channel interaction of squeeze-transformed modes with dressed atoms: Entanglement enhancement in four-wave mixing in three-level systems,” Phys. Rev. A 78, 033811 (2008).
[Crossref]

Cohen-Tannoudji, C.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, 1992).

Corney, J. F.

M. K. Olsen and J. F. Corney, “Non-Gaussian continuous-variable entanglement and steering,” Phys. Rev. A 87, 033839 (2013).
[Crossref]

Davidovich, L.

S. Pielawa, G. Morigi, D. Vitali, and L. Davidovich, “Generation of Einstein-Podolsky-Rosen-Entangled radiation through an atomic reservoir,” Phys. Rev. Lett. 98, 240401 (2007).
[Crossref] [PubMed]

Doherty, A. C.

S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
[Crossref]

Drummond, P. D.

M. D. Reid, P. D. Drummond, W. P. Bowen, E. G. Cavalcanti, P. K. Lam, H. A. Bachor, U. L. Andersen, and G. Leuchs, “The Einstein-Podolsky-Rosen paradox: From concepts to applications,” Rev. Mod. Phys. 81, 1727–1751 (2009).
[Crossref]

Du, S. W.

C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91, 043820 (2015).
[Crossref]

Duhme, J.

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
[Crossref]

Dupont-Roc, J.

C. Cohen-Tannoudji, J. Dupont-Roc, and G. Grynberg, Atom-Photon Interactions (Wiley, 1992).

Eberle, T.

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J. Y. Li and X. M. Hu, “Laser oscillation and light entanglement via dressed-state phase-dependent electromagnetically induced transparency,” Phys. Rev. A 80, 053829 (2009).
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C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91, 043820 (2015).
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G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
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M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–673 (2005).
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N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen correlation,” Phys. Rev. A 74, 060101 (2006).
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I. Kogias, A. R. Lee, S. Ragy, and G. Adesso, “Quantification of Gaussian quantum steering,” Phys. Rev. Lett. 114, 060403 (2015).
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C. H. Raymond Ooi, Q. Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory,” Phys. Rev. A 75, 013820 (2007).
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S. Armstrong, M. Wang, R. Y. Teh, Q. H. Gong, Q. Y. He, J. Janousek, H. A. Bachor, M. D. Reid, and P. K. Lam, “Multipartite Einstein-Podolsky-Rosen steering and genuine tripartite entanglement with optical networks,” Nat. Phys. 11, 167 (2015).
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Q. Y. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
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Q. Y. He and M. D. Reid, “Einstein-Podolsky-Rosen paradox and quantum steering in pulsed optomechanics,” Phys. Rev. A 88, 052121 (2013).
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Q. Y. He and M. D. Reid, “Genuine Multipartite Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 111, 250403 (2013).
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Q. Y. He, L. Rosales-Zárate, G. Adesso, and M. D. Reid, “Secure continuous variable teleportation and Einstein-Podolsky-Rosen steering,” Phys. Rev. Lett. 115, 180502 (2015).
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V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering,” Nat. Photonics 6, 596–599 (2012).
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Y. Z. Law, L. P. Thinh, J.-D. Bancal, and V. Scarani, “Quantum randomness extraction for various levels of characterization of the devices,” J. Phys. A 47, 424028 (2014).
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N. Brunner, D. Cavalcanti, S. Pironio, V. Scarant, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
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S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
[Crossref]

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering,” Nat. Photonics 6, 596–599 (2012).
[Crossref]

T. Eberle, V. Händchen, J. Duhme, T. Franz, R. F. Werner, and R. Schnabel, “Strong Einstein-Podolsky-Rosen entanglement from a single squeezed light source,” Phys. Rev. A 83, 052329 (2011).
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C. Shu, X. X. Guo, P. Chen, M. M. T. Loy, and S. W. Du, “Narrowband biphotons with polarization-frequency-coupled entanglement,” Phys. Rev. A 91, 043820 (2015).
[Crossref]

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K. Hammerer, A. S. Sørensen, and E. S. Polzik, “Quantum interface between light and atomic ensembles,” Rev. Mod. Phys. 82, 1041–1093 (2010).
[Crossref]

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S. Steinlechner, J. Bauchrowitz, T. Eberle, and R. Schnabel, “Strong Einstein-Podolsky-Rosen steering with unconditional entangled states,” Phys. Rev. A 87, 022104 (2013).
[Crossref]

V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering,” Nat. Photonics 6, 596–599 (2012).
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C. H. Raymond Ooi, Q. Q. Sun, M. S. Zubairy, and M. O. Scully, “Correlation of photon pairs from the double Raman amplifier: Generalized analytical quantum Langevin theory,” Phys. Rev. A 75, 013820 (2007).
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N. Takei, N. Lee, D. Moriyama, J. S. Neergaard-Nielsen, and A. Furusawa, “Time-gated Einstein-Podolsky-Rosen correlation,” Phys. Rev. A 74, 060101 (2006).
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H. T. Tan, X. C. Zhang, and G. X. Li, “Steady-state one-way Einstein-Podolsky-Rosen steering in optomechanical interfaces,” Phys. Rev. A 91, 032121 (2015).
[Crossref]

G. X. Li, H. T. Tan, and M. Macovei, “Enhancement of entanglement for two-mode fields generated from four-wave mixing with the help of the auxiliary atomic transition,” Phys. Rev. A 76, 053827 (2007).
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Y. Z. Law, L. P. Thinh, J.-D. Bancal, and V. Scarani, “Quantum randomness extraction for various levels of characterization of the devices,” J. Phys. A 47, 424028 (2014).
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M. Piani and J. Watrous, “Necessary and Sufficient Quantum Information Characterization of Einstein-Podolsky-Rosen Steering,” Phys. Rev. Lett. 114, 060404 (2015).
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N. Brunner, D. Cavalcanti, S. Pironio, V. Scarant, and S. Wehner, “Bell nonlocality,” Rev. Mod. Phys. 86, 419–478 (2014).
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V. Händchen, T. Eberle, S. Steinlechner, A. Samblowski, T. Franz, R. F. Werner, and R. Schnabel, “Observation of one-way Einstein-Podolsky-Rosen steering,” Nat. Photonics 6, 596–599 (2012).
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E. G. Cavalcanti, Q. Y. He, M. D. Reid, and H. M. Wiseman, “Unified criteria for multipartite quantum nonlocality,” Phys. Rev. A 84, 032115 (2011).
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S. J. Jones, H. M. Wiseman, and A. C. Doherty, “Entanglement, Einstein-Podolsky-Rosen correlations, bell nonlocality, and steering,” Phys. Rev. A 76, 052116 (2007).
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H. Xiong, M. O. Scully, and M. S. Zubairy, “Correlated spontaneous emission laser as an entanglement amplifier,” Phys. Rev. Lett. 94, 023601 (2005).
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Figures (6)

Fig. 1
Fig. 1 (a) The resonantly-coupled four-level ladder atomic system. Two laser fields are resonantly applied to the atomic transitions |1〉 – |2〉 and |2〉 – |4〉, respectively, and two cavity modes are generated from the corresponding transitions |1〉 – |3〉 and |3〉 – |4〉. (b) The one-channel interaction between the dressed atoms and the Bogoliubov mode b1. (c) The one-channel coupling of the dressed atoms with the Bogoliubov mode b2. (d) The steady-state populations ρ 00 s s and ρ 33 s s for a single atom.
Fig. 2
Fig. 2 The variable T12(21) versus the ratio Ω21 of Rabi frequencies for two pump fields for Ω21 > g2/g1. The corresponding parameters are chosen as κ = 0.1γ, C1 = 0.48γ2, C2 = 0.48γ2 (a), C2 = 0.72γ2 (b), C2 = 0.96γ2 (c), C2 = 1.2γ2 (d).
Fig. 3
Fig. 3 The variables S12(21) and T12(21) with respect to Ω21, where the parameters are given by κ = 0.1γ, C2 = 18.75γ2, C1 = 48γ2 (a) and C1 = 75γ2 (b) for the case of Ω21 < g2/g1.
Fig. 4
Fig. 4 The average photon number difference b 1 b 1 b 2 b 2 versus Ω21, where the parameters are κ = 0.1γ, C1 = 0.48γ2, C2 = 0.96γ2 (a), κ = 0.1γ, C1 = 75γ2, C2 = 18.75γ2 (b), C1 = C2 = 5γ2, κ1 = 0.05γ, κ2 = 0.1γ (c), and C1 = C2 = 50γ2, κ1 = 0.08γ, κ2 = 0.04γ (d). The inset maps in (a,b) are the number difference for the same coupling strengths and cavity losses with κ = 0.1γ, C1 = C2 = 0.48γ2.
Fig. 5
Fig. 5 The variables T12(21) depending on Ω21 for κ1 < κ2, where the parameters are C1 = C2 = 5γ2, κ1 = 0.05γ, κ2 = 0.1γ (a) and κ2 = 0.15γ (b).
Fig. 6
Fig. 6 The variables T12(21) as a the function of Ω21 for κ1 > κ2, in which the parameters are C1 = C2 = 50γ2, κ2 = 0.04γ, κ1 = 0.08γ (a) and κ1 = 0.1γ (b).

Tables (2)

Tables Icon

Table 1 Possibility and Impossibility of one-way EPR steering for Ω21 > 1.

Tables Icon

Table 2 Possibility and Impossibility of one-way EPR steering for Ω21 < 1.

Equations (33)

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ρ ˙ = i [ H 0 + H I , ρ ] + ρ ,
H 0 = 2 μ = 1 N a [ ( Ω 1 σ 21 μ + Ω 1 * σ 12 μ ) + ( Ω 2 σ 42 μ + Ω 2 * σ 24 μ ) ] ,
H I = μ = 1 N a [ g 1 ( a 1 σ 31 μ + a 1 σ 13 μ ) + g 2 ( a 2 σ 43 μ + a 2 σ 34 μ ) ] ,
ρ = c ρ + j = 1 , k = 2 , 3 ( j , k ρ + k , j + 3 ρ ) .
| + μ = 1 2 ( sin θ | 4 μ + | 2 μ + cos θ | 1 μ ) , | 0 μ = cos θ | 4 μ + sin θ | 1 μ , | μ = 1 2 ( sin θ | 4 μ | 2 μ + cos θ | 1 μ ) ,
H I = μ = 1 N a [ ( g 1 sin θ a 1 g 2 cos θ a 2 ) σ 30 μ + ( g 1 sin θ a 1 g 2 cos θ a 2 ) σ 03 μ ] .
ρ 33 s s = 3 sin 2 θ cos 2 θ 2 + 2 cos 2 θ , ρ 00 s s = sin 2 θ + sin 4 θ 2 + 2 cos 2 θ ,
b 1 = a 1 cosh r a 2 sinh r , b 2 = a 2 cosh r a 1 sinh r ,
H ˜ I = G μ = 1 N a ( b 1 σ 30 μ + b 1 σ 03 μ ) , ( Ω 2 Ω 1 > g 2 g 1 )
H ˜ I = G μ = 1 N a ( b 2 σ 03 μ + b 2 σ 30 μ ) , ( Ω 2 Ω 1 < g 2 g 1 )
d d t ρ ˜ = i [ H ˜ I , ρ ˜ ] + a ρ ˜ + c ρ ˜ ,
c ρ ˜ = l m l , m = 1 , 2 [ κ m 2 ( b l ρ ˜ b l b l b l ρ ˜ ) + κ l 2 ( N + 1 ) ( b l ρ ˜ b l b l b l ρ ˜ ) + κ l 2 M ( b l ρ ˜ b m + b m ρ ˜ b l b l b m ρ ˜ b m b l ρ ˜ ) ] + H . c . ,
d d t ρ ˜ c = l = 1 , 2 [ A l 2 ( b l ρ ˜ c b l b l b l ρ c ) + B l 2 ( b l ρ ˜ c b l b l b l ρ ˜ c ) ] + c ρ ˜ c ,
A 1 = 2 G 2 N a ρ 33 s s / Γ , B 1 = 2 G 2 N a ρ 00 s s / Γ ; A 2 = B 2 = 0 , ( Ω 2 Ω 1 > g 2 g 1 )
A 1 = B 1 = 0 ; A 2 = 2 G 2 N a ρ 00 s s / Γ , B 2 = 2 G 2 N a ρ 33 s s / Γ , ( Ω 2 Ω 1 < g 2 g 1 )
d d t b 1 b 1 = 2 μ 1 b 1 b 1 + ( A 1 + κ N ) , d d t b 2 b 2 = 2 μ 2 b 2 b 2 + ( A 2 + κ N ) , d d t b 1 b 2 = ( μ 1 + μ 2 ) b 1 b 2 κ M ,
b 1 b 1 = ( A 1 + κ N ) / 2 μ 1 , b 2 b 2 = ( A 2 + κ N ) / 2 μ 2 , b 1 b 2 = κ M / ( μ 1 + μ 2 ) .
S 12 = V inf ( X 1 ) V inf ( Y 1 ) < 1 , ( 2 1 )
S 21 = V inf ( X 2 ) V inf ( Y 2 ) < 1 , ( 1 2 )
( b 1 b 2 + M / 2 ) 2 > ( b 1 b 1 N / 2 ) ( b 2 b 2 + 1 / 2 N / 2 ) , ( 2 1 )
( b 1 b 2 + M / 2 ) 2 > ( b 2 b 2 N / 2 ) ( b 1 b 1 + 1 / 2 N / 2 ) . ( 1 2 )
T 12 = ( b 1 b 2 + M / 2 ) 2 ( b 1 b 1 N / 2 ) ( b 2 b 2 N / 2 + 1 / 2 ) > 0 , ( 2 1 )
T 21 = ( b 1 b 2 + M / 2 ) 2 ( b 2 b 2 N / 2 ) ( b 1 b 1 N / 2 + 1 / 2 ) > 0 , ( 1 2 )
d d t b 1 = μ 1 b 1 + η b 2 ,
d d t b 2 = μ 2 b 2 η b 1 ,
d d t b 1 b 1 = 2 μ 1 b 1 b 1 + η ( b 1 b 2 + b 1 b 2 ) + ( A 1 + κ 2 N ) ,
d d t b 2 b 2 = 2 μ 2 b 2 b 2 η ( b 1 b 2 + b 1 b 2 ) + ( A 2 + κ 1 N ) ,
d d t b 1 b 2 = ( μ 1 + μ 2 ) b 1 b 2 η ( b 1 b 1 b 2 b 2 ) M ( κ 1 + κ 2 ) / 2 ,
b 1 b 1 = 1 P [ μ 2 ( μ 1 + μ 2 ) ( A 1 + κ 2 N ) 2 μ 2 η D + η 2 ( A 1 + A 2 + ( κ 1 + κ 2 ) N ) ] ,
b 2 b 2 = 1 P [ μ 1 ( μ 1 + μ 2 ) ( A 2 + κ 1 N ) 2 μ 1 η D + η 2 ( A 1 + A 2 + ( κ 1 + κ 2 ) N ) ] ,
b 1 b 2 = 1 P [ 2 D μ 1 μ 2 η μ 2 ( A 1 + κ 2 N ) + η μ 1 ( A 2 + κ 1 N ) ] ,
a 1 a 2 = ( 2 N + 1 ) n 12 + M ( n 1 + n 2 + 1 ) , a 1 a 1 = N ( n 1 + n 2 + 1 ) + 2 M n 12 + n 1 , a 2 a 2 = N ( n 1 + n 2 + 1 ) + 2 M n 12 + n 2 ,
( n 12 + M / 2 ) 2 > ( n 1 N / 2 ) ( ( n 2 + 1 / 2 ) N / 2 ) , ( 2 1 ) ( n 12 + M / 2 ) 2 > ( n 2 N / 2 ) ( ( n 1 + 1 / 2 ) N / 2 ) . ( 1 2 )

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