Abstract

With the presence of the signal pulse, a quantum dot (QD) four-level structure interacting with four fields forms a double-cascade configuration. The linear optical properties for amplification, absorption, and dispersion of two weak near-infrared (NIR) lights in this scheme are investigated. It shows that the amplification, transparency, normal and anomalous dispersion of the probe and signal fields, i.e., the two NIR waves, can be achieved by adjusting the relative phase of the applied lasers, the probe detuning, and the two pump Rabi energies appropriately, while when the signal pulse is removed, the nonlinear optical phenomenon four-wave mixing (FWM) originating from quantum interference is demonstrated. A highly efficient FWM process with a NIR mixing field generated can be realized in this system. Such investigation in a semiconductor QD system with flexible design and widely adjustable parameters may provide new possibilities for realizing the efficient generation and gain of NIR waves and manipulating light propagation between subluminal and superluminal in the solid-state materials.

© 2012 Optical Society of America

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    [CrossRef]
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  4. E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
    [CrossRef]
  5. V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
    [CrossRef]
  6. L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).
  7. P. K. Nielsen, H. Thyrrestrup, J. Mørk, and B. Tromborg, “Numerical investigation of electromagnetically induced transparency in a quantum dot structure,” Opt. Express 15, 6396–6408 (2007).
    [CrossRef]
  8. C.-H. Yuan, and K.-D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).
  9. X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
    [CrossRef]
  10. J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).
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  16. Y. Wu and X. Yang, “Highly efficient four-wave mixing in double-Λ system in ultraslow propagation regime,” Phys. Rev. A 70, 053818 (2004).
  17. Y. Wu and X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).
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    [CrossRef]
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  22. J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.
  23. J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
    [CrossRef]
  24. K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
    [CrossRef]
  25. X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
    [CrossRef]
  26. W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).
  27. M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
    [CrossRef]
  28. K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).
  29. H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).
  30. C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
    [CrossRef]
  31. W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).
  32. J. F. Dynes and E. Paspalakis, “Phase control of electron population, absorption, and dispersion properties of a semiconductor quantum well,” Phys. Rev. B 73, 233305 (2006).
  33. Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
    [CrossRef]
  34. A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B Lasers Opt. 79, 65–69 (2004).
  35. C. Zhu and G. Huang, “Slow-light solitons in coupled asymmetric quantum wells via interband transitions,” Phys. Rev. B 80, 235408 (2009).
  36. Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71053806 (2005).
  37. D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
    [CrossRef]
  38. H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
    [CrossRef]
  39. H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).
  40. L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).
  41. Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state medium,” Opt. Lett. 29, 2064–2066 (2004).
    [CrossRef]

2011

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

2010

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

2009

C. Zhu and G. Huang, “Slow-light solitons in coupled asymmetric quantum wells via interband transitions,” Phys. Rev. B 80, 235408 (2009).

P. K. Pathak and S. Hughes, “Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity,” Phys. Rev. B 79, 205416 (2009).

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

2008

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33, 381–383 (2008).
[CrossRef]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
[CrossRef]

2007

P. K. Nielsen, H. Thyrrestrup, J. Mørk, and B. Tromborg, “Numerical investigation of electromagnetically induced transparency in a quantum dot structure,” Opt. Express 15, 6396–6408 (2007).
[CrossRef]

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

C.-H. Yuan, K.-D. Zhu, and Y.-W. Jiang, “Slow light control with electric fields in vertically coupled InGaAs/GaAs quantum dots,” J. Appl. Phys. 102, 023109 (2007).

Y. Wu and X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

2006

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Backward four-wave mixing in a four-level medium with electromagnetically induced transparency,” J. Opt. Soc. Am. B 23, 718–722 (2006).
[CrossRef]

C.-H. Yuan, and K.-D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

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

2005

Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71053806 (2005).

T. Hatano, M. Stopa, and S. Tarucha, “Single-electron delocalization in hybrid vertical-lateral double quantum dots,” Science 309, 268–271 (2005).
[CrossRef]

2004

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B Lasers Opt. 79, 65–69 (2004).

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

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

Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state medium,” Opt. Lett. 29, 2064–2066 (2004).
[CrossRef]

2003

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electro magnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

2002

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

2000

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

1994

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

1990

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

Abstreiter, G.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

Bayer, M.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

Becerra, F. E.

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

Berman, P. R.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Beveratos, A.

M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
[CrossRef]

Böhn, G.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

Borri, P.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Bracker, A. S.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Brunner, K.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

Chang, W. H.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Chao, C. C.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Chen, A.-X.

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Chen, W.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

Chen, Y. T.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Cheng, S. J.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

De Franceschi, S.

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Deng, L.

Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state medium,” Opt. Lett. 29, 2064–2066 (2004).
[CrossRef]

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

Ding, C.

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

Doty, M. F.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[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. B 73, 233305 (2006).

Elzerman, J. M.

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Eto, M.

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Field, J. E.

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

Forchel, A.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Gammon, D.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Gong, M.

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

Gong, S.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

Gord, J. R.

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

Goshima, K.

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

Govorov, A. O.

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).

Guo, G.-C.

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

Guo, H.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

Hagley, E. W.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

Han, D.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

Hao, X.

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

Harris, S. E.

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

Hatano, T.

T. Hatano, M. Stopa, and S. Tarucha, “Single-electron delocalization in hybrid vertical-lateral double quantum dots,” Science 309, 268–271 (2005).
[CrossRef]

He, L.

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

Hernandez, G.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Backward four-wave mixing in a four-level medium with electromagnetically induced transparency,” J. Opt. Soc. Am. B 23, 718–722 (2006).
[CrossRef]

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

Höfling, S.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Hsu, P. S.

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33, 381–383 (2008).
[CrossRef]

Hsu, Y.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Huang, C.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

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C. Zhu and G. Huang, “Slow-light solitons in coupled asymmetric quantum wells via interband transitions,” Phys. Rev. B 80, 235408 (2009).

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H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Hughes, S.

P. K. Pathak and S. Hughes, “Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity,” Phys. Rev. B 79, 205416 (2009).

Imamoglu, A.

S. E. Harris, J. E. Field, and A. Imamoglu, “Nonlinear optical processes using electromagnetically induced transparency,” Phys. Rev. Lett. 64, 1107–1110 (1990).
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Jiang, Y.-W.

C.-H. Yuan, K.-D. Zhu, and Y.-W. Jiang, “Slow light control with electric fields in vertically coupled InGaAs/GaAs quantum dots,” J. Appl. Phys. 102, 023109 (2007).

Jin, S.

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

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A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B Lasers Opt. 79, 65–69 (2004).

Kang, H.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Backward four-wave mixing in a four-level medium with electromagnetically induced transparency,” J. Opt. Soc. Am. B 23, 718–722 (2006).
[CrossRef]

Kasprzak, J.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Katzer, D. S.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Kistner, C.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Komori, K.

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

Korenev, V. L.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Kouwenhoven, L. P.

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Kozuma, M.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

Langbein, W.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Larque, M.

M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
[CrossRef]

Lee, R.-K.

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Li, C.-F.

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

Li, J.

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

Li, X.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Lin, C. H.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Lin, S. D.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Lu, H.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

Lü, X.-Y.

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

Mørk, J.

Muljarov, E. A.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

Nielsen, P. K.

Niu, Y.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

Orozco, L. A.

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

Oulton, R.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

Park, D.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Paspalakis, E.

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

Pathak, P. K.

P. K. Pathak and S. Hughes, “Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity,” Phys. Rev. B 79, 205416 (2009).

Patnaik, A. K.

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33, 381–383 (2008).
[CrossRef]

Payne, M. G.

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

Philip, I. R.

M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
[CrossRef]

Piermarocchi, C.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Ponomarev, I. V.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Qamar, S.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

Qi, Y.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

Ramirez, H. Y.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Reinecke, T. L.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Reitzenstein, S.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Reuter, D.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Rolston, S. L.

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

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Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electro magnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

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S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Scheibner, M.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Schneider, C.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Schwab, M.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

Sham, L. J.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Si, L.-G.

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

Stavarache, V.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Steel, D.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Steel, D. G.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Stievater, T. H.

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Stinaff, E. A.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Stopa, M.

T. Hatano, M. Stopa, and S. Tarucha, “Single-electron delocalization in hybrid vertical-lateral double quantum dots,” Science 309, 268–271 (2005).
[CrossRef]

Strauss, M.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

Sugaya, T.

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

Sun, B.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Sun, H.

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

Takagahara, T.

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

Tarucha, S.

T. Hatano, M. Stopa, and S. Tarucha, “Single-electron delocalization in hybrid vertical-lateral double quantum dots,” Science 309, 268–271 (2005).
[CrossRef]

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Thyrrestrup, H.

Tränkle, G.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

Tromborg, B.

Tseng, H. C.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Ulloa, S. E.

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).

van der Wiel, W. G.

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Villas-Bôas, J. M.

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).

Wang, H.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

Wang, L.-G.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

Ware, M. E.

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

Weimann, G.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

Welch, G. R.

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

P. S. Hsu, A. K. Patnaik, and G. R. Welch, “Controlled parametric generation in a double-ladder system via all-resonant four-wave mixing,” Opt. Lett. 33, 381–383 (2008).
[CrossRef]

Wieck, A. D.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Willis, R. T.

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

Woggon, U.

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Wu, Y.

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Y. Wu and X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).

Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71053806 (2005).

Y. Wu and L. Deng, “Ultraslow bright and dark optical solitons in a cold three-state medium,” Opt. Lett. 29, 2064–2066 (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 (2004).

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electro magnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Xiang, Y.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

Xiao, M.

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B Lasers Opt. 79, 65–69 (2004).

Xu, X.

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

Yakovlev, D. R.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

Yang, W.-X.

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Yang, X.

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

Y. Wu and X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).

Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71053806 (2005).

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

You, W. T.

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

Yu, R.

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

Yuan, C.-H.

C.-H. Yuan, K.-D. Zhu, and Y.-W. Jiang, “Slow light control with electric fields in vertically coupled InGaAs/GaAs quantum dots,” J. Appl. Phys. 102, 023109 (2007).

C.-H. Yuan, and K.-D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).

Zeng, Y.

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

Zhang, J.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Backward four-wave mixing in a four-level medium with electromagnetically induced transparency,” J. Opt. Soc. Am. B 23, 718–722 (2006).
[CrossRef]

Zhu, C.

C. Zhu and G. Huang, “Slow-light solitons in coupled asymmetric quantum wells via interband transitions,” Phys. Rev. B 80, 235408 (2009).

Zhu, K.-D.

C.-H. Yuan, K.-D. Zhu, and Y.-W. Jiang, “Slow light control with electric fields in vertically coupled InGaAs/GaAs quantum dots,” J. Appl. Phys. 102, 023109 (2007).

C.-H. Yuan, and K.-D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).

Zhu, S.-Y.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

Zhu, Y.

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Backward four-wave mixing in a four-level medium with electromagnetically induced transparency,” J. Opt. Soc. Am. B 23, 718–722 (2006).
[CrossRef]

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electro magnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

Zubairy, M. S.

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

Zunger, A.

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

Appl. Phys. B Lasers Opt.

A. Joshi and M. Xiao, “Optical bistability in a three-level semiconductor quantum-well system,” Appl. Phys. B Lasers Opt. 79, 65–69 (2004).

Appl. Phys. Lett.

V. Stavarache, D. Reuter, A. D. Wieck, M. Schwab, D. R. Yakovlev, R. Oulton, and M. Bayer, “Control of quantum dot excitons by lateral electric fields,” Appl. Phys. Lett. 89, 123105 (2006).
[CrossRef]

C.-H. Yuan, and K.-D. Zhu, “Voltage-controlled slow light in asymmetry double quantum dots,” Appl. Phys. Lett. 89, 052115 (2006).

Eur. Phys. J. D

D. Han, Y. Zeng, H. Guo, W. Chen, H. Lu, and C. Huang, “Effects of the upper level coupling field on lasing without inversion in a V-type system,” Eur. Phys. J. D 42, 489–493 (2007).
[CrossRef]

J. Appl. Phys.

C.-H. Yuan, K.-D. Zhu, and Y.-W. Jiang, “Slow light control with electric fields in vertically coupled InGaAs/GaAs quantum dots,” J. Appl. Phys. 102, 023109 (2007).

J. Opt. Soc. Am. B

J. Phys. B

J. Li, R. Yu, L.-G. Si, X.-Y. Lü, and X. Yang, “Propagation of a voltage-controlled infrared laser pulse and electro-optic switch in a coupled quantum-dot nanostructure,” J. Phys. B 42, 055509 (2009).

H. Sun, Y. Niu, S. Jin, and S. Gong, “Phase control of cross-phase modulation with electromagnetically induced transparency,” J. Phys. B 40, 3037–3043 (2007).

Nature

S. Sasaki, S. De Franceschi, J. M. Elzerman, W. G. van der Wiel, M. Eto, S. Tarucha, and L. P. Kouwenhoven, “Kondo effect in an integer-spin quantum dot,” Nature 405, 764–767 (2000).
[CrossRef]

Nature Mater.

J. Kasprzak, S. Reitzenstein, E. A. Muljarov, C. Kistner, C. Schneider, M. Strauss, S. Höfling, A. Forchel, and W. Langbein, “Up on the Jaynes-Cummings ladder of a quantum-dot/microcavity system,” Nature Mater. 9, 304–308 (2010).
[CrossRef]

Opt. Commun.

Y. Qi, Y. Niu, Y. Xiang, H. Wang, and S. Gong, “Phase dependence of cross-phase modulation in asymmetric quantum wells,” Opt. Commun. 284, 276–281 (2011).
[CrossRef]

Opt. Express

Opt. Lett.

Phys. Lett. A

C. Ding, X. Hao, J. Li, and X. Yang, “Efficient generation of maximally entangled states via four-wave mixing in a semiconductor quantum-dot nanostructure,” Phys. Lett. A 374, 680–686 (2010).
[CrossRef]

Phys. Rev. A

W.-X. Yang, A.-X. Chen, R.-K. Lee, and Y. Wu, “Matched slow optical soliton pairs via biexciton coherence in quantum dots,” Phys. Rev. A 84, 013835 (2011).

Y. Wu and X. Yang, “Electromagnetically induced transparency in V-, Λ-, and cascade-type schemes beyond steady-state analysis,” Phys. Rev. A 71053806 (2005).

H. Kang, G. Hernandez, J. Zhang, and Y. Zhu, “Phase-controlled light switching at low light levels,” Phys. Rev. A 73, 011802(R) (2006).
[CrossRef]

Y. Wu, J. Saldana, and Y. Zhu, “Large enhancement of four-wave mixing by suppression of photon absorption from electro magnetically induced transparency,” Phys. Rev. A 67, 013811 (2003).

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

M. Larque, I. R. Philip, and A. Beveratos, “Bell inequalities and density matrix for polarization-entangled photons out of a two-photon cascade in a single quantum dot,” Phys. Rev. A 77, 042118 (2008).
[CrossRef]

F. E. Becerra, R. T. Willis, S. L. Rolston, and L. A. Orozco, “Nondegenerate four-wave mixing in rubidium vapor: The diamond configuration,” Phys. Rev. A 78, 013834 (2008).
[CrossRef]

P. S. Hsu, G. R. Welch, J. R. Gord, and A. K. Patnaik, “Propagation dynamics of controlled cross-talk via interplay between χ(1) and χ(3) processes,” Phys. Rev. A 83, 053819 (2011).

L.-G. Wang, S. Qamar, S.-Y. Zhu, and M. S. Zubairy, “Manipulation of the Raman process via incoherent pump, tunable intensity, and phase control,” Phys. Rev. A 77, 033833(2008).

Phys. Rev. B

P. K. Pathak and S. Hughes, “Generation of entangled photon pairs from a single quantum dot embedded in a planar photonic-crystal cavity,” Phys. Rev. B 79, 205416 (2009).

K. Goshima, K. Komori, T. Sugaya, and T. Takagahara, “Formation and control of acorrelated exciton two-qubit system in a coupled quantum dot,” Phys. Rev. B 79, 205313 (2009).

H. Y. Ramirez, C. H. Lin, C. C. Chao, Y. Hsu, W. T. You, S. Y. Huang, Y. T. Chen, H. C. Tseng, W. H. Chang, S. D. Lin, and S. J. Cheng, “Optical fine structures of highly quantized InGaAs/GaAs self-assembled quantum dots,” Phys. Rev. B 81, 245324 (2010).

J. M. Villas-Bôas, A. O. Govorov, and S. E. Ulloa, “Coherent control of tunneling in a quantum dot molecule,” Phys. Rev. B 69, 125342 (2004).

W. Langbein, P. Borri, U. Woggon, V. Stavarache, D. Reuter, and A. D. Wieck, “Control of fine-structure splitting and biexciton binding in InxGa1−xAs quantum dots by annealing,” Phys. Rev. B 69, 161301 (2004).

Y. Wu and X. Yang, “Four-wave mixing in molecular magnets via electromagnetically induced transparency,” Phys. Rev. B 76, 054425 (2007).

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

C. Zhu and G. Huang, “Slow-light solitons in coupled asymmetric quantum wells via interband transitions,” Phys. Rev. B 80, 235408 (2009).

Phys. Rev. Lett.

K. Brunner, G. Abstreiter, G. Böhn, G. Tränkle, and G. Weimann, “Sharp-line photoluminescence and two-photon absorption of zero-dimensional biexcitons in a GaAs/AlGaAs structure,” Phys. Rev. Lett. 73, 1138–1141 (1994).
[CrossRef]

L. He, M. Gong, C.-F. Li, G.-C. Guo, and A. Zunger, “Highly reduced fine-structure splitting in InAs/InP quantum dots offering an Efficient on-demand entangled 1.55 μm photon emitter,” Phys. Rev. Lett. 101, 157405 (2008).

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

L. Deng, M. Kozuma, E. W. Hagley, and M. G. Payne, “Opening optical four-wave mixing channels with giant enhancement using ultraslow pump waves,” Phys. Rev. Lett. 88, 143902 (2002).

Science

T. Hatano, M. Stopa, and S. Tarucha, “Single-electron delocalization in hybrid vertical-lateral double quantum dots,” Science 309, 268–271 (2005).
[CrossRef]

E. A. Stinaff, M. Scheibner, A. S. Bracker, I. V. Ponomarev, V. L. Korenev, M. E. Ware, M. F. Doty, T. L. Reinecke, and D. Gammon, “Optical signatures of coupled quantum dots,” Science 311, 636–639 (2006).
[CrossRef]

X. Xu, B. Sun, P. R. Berman, D. G. Steel, A. S. Bracker, D. Gammon, and L. J. Sham, “Coherent optical spectroscopy of a strongly driven quantum dot,” Science 317, 929–932 (2007).
[CrossRef]

X. Li, Y. Wu, D. Steel, D. Gammon, T. H. Stievater, D. S. Katzer, D. Park, C. Piermarocchi, and L. J. Sham, “An all-optical quantum gate in a semiconductor quantum dot,” Science 301, 809–811 (2003).
[CrossRef]

Other

J. Kasprzak, W. Langbein, S. Reitzenstein, C. Kistner, C. Schneider, M. Strauss, S. Höfling, and A. Forchel, “Coherent dynamics of one- and two-photon states in a strongly coupled single quantum dot-cavity system,” in Conference on Lasers and Electro-Optics/International Quantum Electronics Conference, OSA Technical Digest (CD) (Optical Society of America, 2009), paper CMBB7.

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Figures (7)

Fig. 1.
Fig. 1.

(a) The energy-level arrangement of GaAs/AlGaAs QD under study. (b) Schematic of the corresponding energy levels and transitions in the QD structure. The sample with four levels interacts with two cw laser pump fields coupling respectively the transitions | 1 | 3 and | 2 | 3 (carrier frequencies ω c , ω d and electric field amplitudes E c , E d ) and two weak pulsed fields driving the transitions | 0 | 1 and | 0 | 2 (carrier frequency ω p , ω s and electric field amplitudes E p , E s ).

Fig. 2.
Fig. 2.

The absorption (amplification) spectra of two weak NIR fields: (a)  Im ( χ p ) and (b)  Im ( χ s ) versus the relative phase ϕ with different ratios of the pump-c Rabi energy Ω c to the pump-d Rabi energy Ω d . Other parameters are Ω p = Ω s , Δ p = Δ c = Δ s = 0 , γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Fig. 3.
Fig. 3.

The absorption (amplification) and dispersion responses versus the relative phase ϕ : (a)  ( Ω c , Ω d ) = ( 2 , 1 ) meV for the probe and (b)  ( Ω c , Ω d ) = ( 1 , 2 ) meV for the signal. Other parameters are Ω p = Ω s , Δ p = Δ c = Δ s = 0 , γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Fig. 4.
Fig. 4.

The absorpton (amplification) and dispersion responses of two weak NIR fields: (a)  Im ( χ p ) , (b)  Im ( χ s ) , (c)  Re ( χ p ) , (d)  Re ( χ s ) as a function of the single-photon detuning Δ p with different ratios of the pump-c Rabi energy Ω c to the pump-d Rabi energy Ω d . Other parameters are Ω p = Ω s , ϕ = 0 , Δ c = 0 , Δ s = Δ p (so Δ d = 0 ), γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Fig. 5.
Fig. 5.

The absorption (amplification) and dispersion responses of two weak NIR fields: (a)  Im ( χ p ) , (b)  Im ( χ s ) , (c)  Re ( χ p ) , (d)  Re ( χ s ) as a function of the single-photon detuning Δ p with different values of the relative phase ϕ . Other parameters are Ω p = Ω s , Ω c = Ω d = 2 meV , Δ c = 0 , Δ s = Δ p (so Δ d = 0 ), γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Fig. 6.
Fig. 6.

The generated FWM NIR-signal amplitude and the input probe amplitude versus the depth of penetration κ z . Other parameters are κ z = 0.5 meV , Δ p = Δ c = Δ s = 0 , γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Fig. 7.
Fig. 7.

(a) The FWM NIR-signal efficiency η versus the depth of penetration κ z . (b) The FWM NIR-signal efficiency η as a function of the pump-c Rabi energy Ω c with four fixed values of the pump-d Rabi energy Ω d under κ z = 0.5 meV . Other parameters are ω s = 1.25 ω p , Δ p = Δ c = Δ s = 0 , γ 1 = 0.054 meV , γ 2 = 0.054 meV , and γ 3 = 0.108 meV .

Equations (24)

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H int I = Δ p S 11 + ( Δ p + Δ c ) S 33 + ( Δ p + Δ c Δ d ) S 22 ( Ω p e i ϕ p S 10 + Ω c e i ϕ c S 31 + Ω d e i ϕ d S 32 + Ω s e i ϕ s S 20 + h . c . ) .
A 0 t = i Ω p A 1 + i Ω s A 2 , A 1 t = ( i Δ p + γ 1 ) A 1 + i Ω p A 0 + i Ω c A 3 , A 2 t = ( i Δ s + γ 2 ) A 2 + i Ω s A 0 + i Ω d A 3 e i ϕ , A 3 t = [ i ( Δ p + Δ c ) + γ 3 ] A 3 + i Ω c A 1 + i Ω d A 2 e i ϕ ,
P p ( s ) = ϵ 0 χ p ( s ) E p ( s ) = N μ 01 ( 2 ) A 1 ( 2 ) A 0 * ,
χ p = N | μ 01 | 2 ϵ 0 χ p ,
χ s = N | μ 02 | 2 ϵ 0 χ s ,
χ p = A 1 Ω p = Ω d 2 ( i γ 2 Δ s ) [ i γ 3 ( Δ p + Δ c ) ] Ω c Ω d Ω s e i ϕ / Ω p ( i γ 1 Δ p ) ( i γ 2 Δ s ) [ i γ 3 ( Δ p + Δ c ) ] Ω c 2 ( i γ 2 Δ s ) Ω d 2 ( i γ 1 Δ p ) ,
χ s = A 2 Ω s = Ω c 2 ( i γ 1 Δ p ) [ i γ 3 ( Δ p + Δ c ) ] Ω c Ω d Ω p e i ϕ / Ω s ( i γ 1 Δ p ) ( i γ 2 Δ s ) [ i γ 3 ( Δ p + Δ c ) ] Ω c 2 ( i γ 2 Δ s ) Ω d 2 ( i γ 1 Δ p ) .
χ p = 1 M [ Ω d 2 ( i γ Δ ) ( i γ 3 Δ ) Ω c Ω d e i ϕ ] ,
χ s = 1 M [ Ω c 2 ( i γ Δ ) ( i γ 3 Δ ) Ω c Ω d e i ϕ ] ,
Ω p z = i 2 π ω p μ 10 c P p = i κ 01 ( T p T Ω p Ω c Ω d T Ω s ) ,
Ω s z = i 2 π ω s μ 20 c P s = i κ 02 ( T s T Ω s Ω c Ω d T Ω p ) ,
Ω p / Ω p 0 = R + e i λ + z R e i λ z ,
Ω s / Ω p 0 = R ( e i λ z e i λ + z ) ,
η = | E s ( out ) E p ( in ) | 2 = | μ 01 | 2 | μ 02 | 2 | R ( e i λ z e i λ + z ) | 2 ,
ω s Ω c 2 Ω d 2 exp ( 2 B z ) ω p [ ( T p T s ) 2 + 4 Ω c 2 Ω d 2 ] ,
T p = Ω d 2 ( i γ 2 Δ s ) [ i γ 3 ( Δ p + Δ c ) ] ,
T s = Ω c 2 ( i γ 1 Δ p ) [ i γ 3 ( Δ p + Δ c ) ] ,
T = ( i γ 1 Δ p ) ( i γ 2 Δ s ) [ i γ 3 ( Δ p + Δ c ) ] Ω c 2 ( i γ 2 Δ s ) Ω d 2 ( i γ 1 Δ p ) ,
R + = κ 01 T p κ 02 T s + G 2 G ,
R = κ 01 T p κ 02 T s G 2 G ,
λ + = κ 01 T p + κ 02 T s + G 2 T ,
λ = κ 12 T p + κ 14 T s G 2 T ,
R = κ 02 Ω c Ω d G ,
G = ( κ 01 T p κ 02 T s ) 2 + 4 κ 01 κ 02 Ω c 2 Ω d 2 .

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