Abstract

By analyzing the nonlinear optical response in an asymmetric coupled double quantum well structure based on the intersubband transitions, we show that a giant Kerr nonlinearity with a relatively large cross-phase modulation coefficient can be used to produce efficient photonphoton entanglement and implement an all-optical two-qubit quantum polarization phase gate. We also demonstrate that such photon-photon entanglement is practically controllable and may facilitate more practical applications in all-optical quantum information and computation.

© 2008 Optical Society of America

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References

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  1. H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).
  2. K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
    [CrossRef] [PubMed]
  3. S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).
  4. C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
    [CrossRef]
  5. A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
    [CrossRef]
  6. C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
    [CrossRef]
  7. H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
    [CrossRef] [PubMed]
  8. P. Ginzburg and M. Orenstein, “Slow light and voltage control of group velocity in resonantly coupled quantum wells,” Opt. Express 14, 12467–12472 (2006).
    [CrossRef] [PubMed]
  9. H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
    [CrossRef]
  10. C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
    [CrossRef]
  11. L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
    [CrossRef]
  12. J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
    [CrossRef]
  13. P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
    [CrossRef] [PubMed]
  14. P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
    [CrossRef] [PubMed]
  15. W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
    [CrossRef]
  16. S. Sarkar, Y. Guo, and H. Wang, “Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells,” Opt. Express 14, 2845–2850 (2006).
    [CrossRef] [PubMed]
  17. H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
    [CrossRef] [PubMed]
  18. M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
    [CrossRef]
  19. P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
    [CrossRef]
  20. J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
    [CrossRef]
  21. J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).
  22. J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
    [CrossRef] [PubMed]
  23. G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).
  24. Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
    [CrossRef]
  25. M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
    [CrossRef]
  26. H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
    [CrossRef]
  27. W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
    [CrossRef]
  28. Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
    [CrossRef]
  29. I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
    [CrossRef]
  30. D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
    [CrossRef]
  31. E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
    [CrossRef]

2008 (1)

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[CrossRef]

2007 (1)

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

2006 (5)

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[CrossRef]

S. Sarkar, Y. Guo, and H. Wang, “Tunable optical delay via carrier induced exciton dephasing in semiconductor quantum wells,” Opt. Express 14, 2845–2850 (2006).
[CrossRef] [PubMed]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

P. Ginzburg and M. Orenstein, “Slow light and voltage control of group velocity in resonantly coupled quantum wells,” Opt. Express 14, 12467–12472 (2006).
[CrossRef] [PubMed]

2005 (4)

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[CrossRef]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[CrossRef]

2004 (5)

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[CrossRef]

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[CrossRef]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[CrossRef]

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[CrossRef] [PubMed]

2003 (1)

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

2002 (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

2000 (1)

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

1998 (1)

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

1997 (3)

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

1996 (2)

1993 (2)

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

1992 (1)

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

1991 (1)

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Agrawal, G. P.

G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).

Artoni, M.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

Bassani, F.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

Boller, K. J.

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Brener, I.

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

Butov, L. V.

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

Campman, K. L.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Capasso, F.

J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
[CrossRef] [PubMed]

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

Cataliotti, F.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

Chang, S. W.

Chang-Hasnain, C.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

Chang-Hasnain, C. J.

Chu, S.-N. G.

Chuang, S. L.

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[CrossRef] [PubMed]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Crankshaw, S.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

Czajkowski, G.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

Davoudi, B.

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

Deng, L.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[CrossRef]

Dynes, J. F.

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

Elsaesser, T.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Faist, J.

Fleischhauer, M.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[CrossRef]

Forstner, J.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Fox, A.M.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Gao, J.-Y.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

Ginzburg, P.

Gossard, A. C.

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Guo, Y.

Hang, C.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

Harris, S. E.

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Hernandez, G.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[CrossRef]

Hey, R.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Hou, J. M.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[CrossRef]

Huang, G.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

Imamoglu, A.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Joshi, A.

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[CrossRef]

Kaindl, R. A.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Kang, H.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[CrossRef]

Knorr, A.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Kohler, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Ku, P. C.

La Rocca, G. C.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

Lee, R.-K.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[CrossRef]

Lee, S.-C.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Leo, K.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Li, J.

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

Li, T.

Li, Y.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

Liu, H. C.

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

Luo, M. S. C.

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

Ma, L.

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

Marangos, J. P.

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[CrossRef]

Miller, D. A. B.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Moewe, M.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

Nikonov, D. E.

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

Nuss, M. C.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Orenstein, M.

Ottaviani, C.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

Palinginis, P.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[CrossRef] [PubMed]

Paspalakis, E.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[CrossRef]

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

Pfeiffer, L. N.

Phillips, C. C.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

Planken, P. C. M.

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

Ploog, K. H.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Reimann, K.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Roskos, H. G.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Sarkar, S.

Schmidt, H.

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

H. Schmidt and A. Imamoglu, “Giant Kerr nonlinearities obtained by electromagnetically induced transparency,” Opt. Lett. 21, 1936–1938 (1996).
[CrossRef] [PubMed]

Schmitt-Rink, S.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Sedgwick, F.

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

P. C. Ku, F. Sedgwick, C. J. Chang-Hasnain, P. Palinginis, T. Li, H. Wang, S. W. Chang, and S. L. Chuang, “Slow light in semiconductor quantum wells,” Opt. Lett. 29, 2291–2293 (2004).
[CrossRef] [PubMed]

Serapiglia, G. B.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

Shah, J.

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

Silvestri, L.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

Sirtori, C.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

J. Faist, C. Sirtori, F. Capasso, S.-N. G. Chu, L. N. Pfeiffer, and K. W. West, “Tunable Fano interference in intersubband absorption,” Opt. Lett. 21, 985–988 (1996).
[CrossRef] [PubMed]

Terzis, A. F.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[CrossRef]

Tombesi, P.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

Tsaousidou, M.

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[CrossRef]

Vitali, D.

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

Vodopyanov, K. L.

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

Waldmüller, I.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Wang, H.

West, K. W.

Woerner, M.

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

Wootters, W. K.

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

Wu, J.-H.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

Wu, Y.

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[CrossRef]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[CrossRef]

Xiao, M.

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[CrossRef]

Xu, J.-H.

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

Yang, W. X.

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[CrossRef]

Yang, X.

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[CrossRef]

Zhu, Y. F.

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[CrossRef]

Appl. Phys. Lett. (1)

H. Schmidt, K. L. Campman, A. C. Gossard, and A. Imamoglu, “Tunneling induced transparency: Fano interference in intersubband transitions,” Appl. Phys. Lett. 70, 3455–3457 (1997).
[CrossRef]

Eur. Phys. J. B (1)

L. Silvestri, F. Bassani, G. Czajkowski, and B. Davoudi, “Electromagnetically induced transparency in asymmetric double quantum wells,” Eur. Phys. J. B 27, 89–102 (2002).
[CrossRef]

Opt. Commun. (1)

J. Li, “Coherent control of optical bistability in tunnel-coupled double quantum wells,” Opt. Commun. 274, 366–371 (2007).
[CrossRef]

Opt. Express (2)

Opt. Express. (1)

P. Palinginis, F. Sedgwick, S. Crankshaw, M. Moewe, and C. Chang-Hasnain, “Room temperature slow light in a quantum-well waveguide via coherent population oscillation,” Opt. Express. 13, 9909–9915 (2005).
[CrossRef] [PubMed]

Opt. Lett. (3)

Phys. (1)

S. E. Harris, “Electromagnetically Induced Transparency,” Phys. Today  50, 36–42 (1997).

Phys. Rev. A (6)

A. Joshi and M. Xiao, “Phase gate with a four-level inverted-Y system,” Phys. Rev. A 72, 062319(1–5) (2005).
[CrossRef]

C. Hang, Y. Li, L. Ma, and G. Huang, “Three-way entanglement and three-qubit phase gate based on a coherent six-level atomic system,” Phys. Rev. A 74, 012319(1–7) (2006).
[CrossRef]

W. X. Yang, J. M. Hou, and R.-K. Lee, “Ultraslow bright and dark solitons in semiconductor quantum wells,” Phys. Rev. A 77, 033838(1–7) (2008).
[CrossRef]

J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. A 73, 233305(1–4) (2006).

H. Kang, G. Hernandez, and Y. F. Zhu, “Superluminal and slow light propagation in cold atoms,” Phys. Rev. A 70, 011801(R)(1–4) (2004).
[CrossRef]

Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70 053818(1–5) (2004).
[CrossRef]

Phys. Rev. B (4)

I. Waldmüller, J. Forstner, S.-C. Lee, A. Knorr, M. Woerner, K. Reimann, R. A. Kaindl, T. Elsaesser, R. Hey, and K. H. Ploog, “Optical dephasing of coherent intersubband transitions in a quasi-two-dimensional electron gas,” Phys. Rev. B 69, 205307(1–9) (2004).
[CrossRef]

E. Paspalakis, M. Tsaousidou, and A. F. Terzis, “Coherent manipulation of a strongly driven semiconductor quantum well,” Phys. Rev. B 73, 125344(1–5) (2006).
[CrossRef]

M. S. C. Luo, S. L. Chuang, P. C. M. Planken, I. Brener, and M. C. Nuss, “Coherent double-pulse control of quantum beats in a coupled quantum well,” Phys. Rev. B 48, 11043–11050 (1993).
[CrossRef]

P. C. M. Planken, I. Brener, M. C. Nuss, M. S. C. Luo, and S. L. Chuang, “Coherent control of terahertz charge oscillations in a coupled quantum well using phase-locked optical pulses,” Phys. Rev. B 48, 4903–4906 (1993).
[CrossRef]

Phys. Rev. Lett. (7)

Y. Wu and L. Deng, “Ultraslow optical solitons in a cold four-state medium,” Phys. Rev. Lett. 93, 143904(1–4) (2004).
[CrossRef]

D. E. Nikonov, A. Imamoglu, L. V. Butov, and H. Schmidt, “Collective intersubband excitations in quantum wells: Coulomb interaction versus subband dispersion,” Phys. Rev. Lett. 79, 4633–4636 (1997).
[CrossRef]

W. K. Wootters, “Entanglement of formation of an arbitrary state of two qubits,” Phys. Rev. Lett. 80, 2245–2248 (1998).
[CrossRef]

H. G. Roskos, M. C. Nuss, J. Shah, K. Leo, D. A. B. Miller, A.M. Fox, S. Schmitt-Rink, and K. Kohler, “Coherent submillimeter-wave emission from charge oscillations in a double-well potential,” Phys. Rev. Lett. 68, 2216–2219 (1992).
[CrossRef] [PubMed]

J.-H. Wu, J.-Y. Gao, J.-H. Xu, L. Silvestri, M. Artoni, G. C. La Rocca, and F. Bassani “Ultrafast All Optical Switching via Tunable Fano Interference,” Phys. Rev. Lett. 95, 057401(1–4) (2005).
[CrossRef]

C. Ottaviani, D. Vitali, M. Artoni, F. Cataliotti, and P. Tombesi, “Polarization Qubit Phase Gate in Driven Atomic Media,” Phys. Rev. Lett. 90, 197902(1–4) (2003).
[CrossRef]

K. J. Boller, A. Imamoglu, and S. E. Harris “Observation of electromagnetically induced transparency,” Phys. Rev. Lett. 66, 2593–2596 (1991).
[CrossRef] [PubMed]

Physica E (1)

C. C. Phillips, E. Paspalakis, G. B. Serapiglia, C. Sirtori, and K. L. Vodopyanov, “Observation of electromagnetically induced transparency and measurements of subband dynamics in a semiconductor quantum well,” Physica E 7, 166–173 (2000).
[CrossRef]

Rev. Mod. Phys. (1)

M. Fleischhauer, A. Imamoglu, and J. P. Marangos, “Electromagnetically induced transparency: Optics in coherent media,” Rev. Mod. Phys. 77, 633–674 (2005).
[CrossRef]

Other (2)

G. P. Agrawal, “Nonlinear fiber optics,” (3rd ed.Academic Press, New York, 2001).

H. C. Liu and F. Capasso, “Intersubband Transitions in Quantum Wells: Physics and Device Applications,” (Academic Press, 2000).

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Figures (5)

Fig. 1.
Fig. 1.

(a) Schematic band diagram of the asymmetric CQW structure consisting of a wide well (WW) and a narrow well (NW). (b) Schematic of the four-level electronic system synthesized in CQW structure. Ω p (σ +polarization), Ω s (σ-polarization), and Ω c are the Rabi frequencies of the probe, signal, and cw control fields, respectively. The Δ i j denotes the corresponding detunings. (c) Possible arrangement of experimental apparatus. Ec represents the control field and Ep (Es ) represents the σ+ (σ-) polarized probe (signal) field, respectively.

Fig. 2.
Fig. 2.

The real and imaginary parts of (a) the linear susceptibility χ(1)p=N|µ13|2/h̄ε0χ′(1)p, and (b) third-order self-Kerr susceptibility χ(3,S)p=N|µ13| 4/h̄3ε0χ′(3,S)p versus the detuning of the probe field Δ13 (in the unit of meV). Other parameters used here are given by γ2 =0, γ3l =γ4l =3.5meV, γdph3=γ dph4=1.5meV, Δ24=8meV, Ω c =25meV, and Ω s =2.5meV.

Fig. 3.
Fig. 3.

The real and imaginary parts of the third-order cross-Kerr susceptibilities for (a) the probe field χ(3,C) p =N13|224|2/h̄3ε0χ′(3,C)p, and (b) the signal field χ(3,C)s=N13|224|2/h̄3ε0χ′(3,C)s versus the detunings Δ24 (in the unit of meV) at the center of EIT window. Other parameters used are the same as those in Fig. 2.

Fig. 4.
Fig. 4.

Dimensionless group velocities (νg ) p,s /ν of the probe and signal fields versus the detunings of the signal field Δ24 (in the unit of meV) for ν=106m/s, in which the solid and dashed lines denote the probe and signal fields, respectively.

Fig. 5.
Fig. 5.

The concurrence versus the detuning of the signal field (in the unit of meV) for two different Rabi frequencies of control field.

Equations (16)

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

i A 1 t = Ω p * A 3 ,
i A 2 t = ( Δ 23 i γ 2 2 ) A 2 + Ω c * A 3 + Ω s * A 4 ,
i A 3 t = ( Δ 13 i γ 3 2 ) A 3 + Ω p A 1 + Ω c A 2 + i κ A 4 ,
i A 4 t = ( Δ 24 i γ 4 2 ) A 4 + Ω s A 2 + i κ A 3 ,
A j = 2 , 3 , 4 = ( c Ω c * i Ω s * κ ) δ j 2 + ( b c + Ω s 2 ) δ j 3 + ( i b κ Ω c * Ω s ) δ j 4 a b c + b κ 2 a Ω s 2 c Ω c 2 + i κ ( Ω c * Ω s + Ω c Ω s * ) Ω p ,
χ p = N μ 13 2 h ̄ ε 0 A 3 A 1 * Ω p χ p ( 1 ) + χ p ( 3 , S ) E p 2 + χ p ( 3 , C ) E s 2 ,
χ s = N μ 24 2 h ̄ ε 0 A 4 A 2 * Ω s χ s ( 3 , C ) E p 2 ,
( n g ) i = Re [ χ ] + ( ω i 2 ) ( Re [ χ ] ω ) ω i
ϕ 3 , C p = k p L π 3 2 h ̄ 2 Ω s peak 2 4 μ 24 2 e r f [ ζ p ] ζ p R e [ χ p ( 3 , C ) ] ,
ϕ 3 , C s = k s L π 3 2 h ̄ 2 Ω p peak 2 4 μ 13 2 e r f [ ζ s ] ζ s R e [ χ s ( 3 , C ) ] ,
0 p 0 s exp [ i ( ϕ 0 p + ϕ 0 s ) ] 0 p 0 s ,
0 p 1 s exp [ i ( ϕ 0 p + ϕ 0 s ) ] 0 p 1 s ,
1 p 1 s exp [ i ( ϕ Λ p + ϕ 0 s ) ] 1 p 1 s ,
1 p 0 s exp [ i ( ϕ total p + ϕ 0 s ) ] 1 p 0 s .
E F ( C ) = h ( 1 + 1 C 2 2 ) ,
C ( ρ ̂ ) = max { 0 , λ 1 λ 2 λ 3 λ 4 } ,

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